Optimization method for supersaturation degree in fog

Abstract

The invention relates to an in-fog supersaturation degree optimization method, which comprises the following steps of: smoothing and refining logarithmic concentration before reverse integration by utilizing a cubic spline interpolation preprocessing mode, so that data can be effectively smoothed, and errors of numerical integration can be reduced; according to the method, the supersaturation degree is estimated through reverse integration and temperature dynamic compensation, the actual activation rate and the theoretical activation rate are introduced for error analysis, the optimal integral threshold value is determined, errors caused by improper setting of the integral threshold value in a traditional method are reduced, and finally optimization of the supersaturation degree estimation method is achieved. According to the method, the problems of data isolation, error accumulation and insufficient environmental adaptability in the prior art are solved, the difference between mode simulation and measurement results can be reduced, the uncertainty of aerosol-cloud interaction simulation is reduced, and meanwhile, the parameterization process of the micro-physical process is improved.

Description

Technical Field

[0001] The invention relates to the field of information technology, and in particular to a method for optimizing supersaturation in fog based on κ-Köhler theory. Background Art

[0002] Accurate estimation of supersaturation in fog is a key problem in studying the formation mechanism of fog and improving fog forecast models. The existing technology has significant deficiencies in estimation accuracy and is difficult to accurately reflect the microscopic physical changes in the growth process of droplets. The technical problem is how to effectively integrate and analyze complex observation data, including droplet spectra, aerosol spectra, and cloud condensation nucleus spectra. The technical difficulties faced in the data processing process include: how to match and interpolate observation data of different time scales to ensure the continuity and consistency of the data; how to select a suitable integration threshold in the reverse integration process to balance the computational efficiency and estimation accuracy; how to accurately evaluate the activation process of cloud condensation nuclei and effectively associate it with the supersaturation estimation results. In addition, since the formation and evolution of fog are affected by many factors, how to consider the dynamic changes of environmental conditions in the estimation process and how to evaluate and reduce the uncertainty of the estimation results are technical problems that need to be solved urgently. The solution to these problems is not only related to the accuracy of supersaturation estimation, but also directly affects our understanding of the microscopic process of fog formation and the improvement of our prediction ability. Summary of the invention

[0003] The present invention provides a method for optimizing supersaturation in fog, which mainly comprises the following steps: S101: Obtain observation data of fog droplet spectrum, aerosol spectrum and cloud condensation nucleus spectrum during fog process in the studied area, as well as raindrop spectrum observation data during the same study period; S102: determining the fog process according to the fog droplet spectrum and raindrop spectrum data; S103: performing cubic spline interpolation on the droplet spectrum data, the interpolated particle sizes are 2.5 μm, 3 μm and 3.5 μm respectively, and negative values ​​are processed in different cases; S104: unifying the time of the aerosol spectrum and the droplet spectrum, extracting the common time interval, and accumulating the droplet spectrum data according to the time window; S105: converting the original counts into number concentration distribution according to the sampling volume and the particle size interval width, and directly reading the spectrum data of the aerosol spectrum as aerosol spectrum data; S106: setting key parameters of the supersaturation calculation model, calculating supersaturation using the reverse integration method and the dynamic threshold correction method, and performing abnormal processing and result optimization; S107: Obtain the time series of cloud condensation nuclei number concentration under the estimated supersaturation, calculate the actual activation rate of cloud condensation nuclei under the actual supersaturation, and perform a significance test; S108: Find the wet critical diameter corresponding to each supersaturation, calculate the activation critical diameter corresponding to each wet critical diameter, regard the particles with a particle size larger than the activation critical diameter as activated particles, integrate the activated particles, and calculate the theoretical activation rates corresponding to different supersaturations; S109: Calculate the cumulative relative error, comprehensively consider the two actual situations of the smaller cumulative relative error and the increase of interpolation stability with the interpolation particle size, determine the optimal integral threshold, and obtain the supersaturation corresponding to the threshold.

[0004] Furthermore, the criterion for determining a fog process is that the average number concentration of fog droplets is greater than or equal to 10 cm -3 And the average liquid water content is greater than or equal to 0.001 gm -3 ; At the same time, the raindrop spectra with a number of less than 10 and a rainfall intensity less than 0.002 mm h were removed. -1 If the precipitation rate after elimination is not 0, it is considered as a precipitation process, and the fog process containing precipitation period is eliminated.

[0005] Furthermore, negative values ​​are handled in different situations, including: For the number concentration after treatment, if there is a negative value and it is located at -5cm -3 -0 cm -3 If the interval is 0, the difference between the two numerical concentrations is considered small and can be approximately corrected to zero. If the negative value exceeds -5cm -3 -0 cm -3 interval, it is considered that the interpolation function makes opposite judgments on the changing trends of the two-level number concentrations, and the opposite of the negative value is taken as the correction value.

[0006] Furthermore, basic observation data is obtained, including: Obtain the dry aerosol particle size distribution data and corresponding timestamp of the aerosol spectrum, with the particle size range of 10nm-10000nm; The droplet spectrum data and timestamp of the droplet spectrum are read, and the particle size range is 2 μm-50 μm. The droplet spectrum data is multiplied by 1000 to convert into nanometer units, and the aerosol spectrum and droplet spectrum data are matched by time alignment.

[0007] Preferably, in step S104, the timestamps of the aerosol spectrum and the droplet spectrum are unified to the hourly precision (time intersection range: 2024-01-03 22:19:01 to 2024-01-04 10:19:01, a total of 11 time points), and the common time interval is extracted. The droplet spectrum data is accumulated according to the time window (the previous hour or the adjacent time interval) and the time step is unified.

[0008] Preferably, the droplet number concentration calculation in step S105 converts the original count into a number concentration distribution according to the sampling volume and the particle size interval width. The calculation steps are as follows: First, the sampling volume Volume is calculated according to the droplet spectrum sampling area and airflow velocity PAS: (1) Where Volume is the sampling volume, PAS is the air velocity (unit: m / s), t is the unit time (usually 1s), S a is the sampling area (S a = 0.41 mm 2 ).

[0009] Secondly, the unit volume (cm -3 ) within the droplet number concentration: (2) In the formula, bin nc is the droplet number concentration per unit volume, bin n is the total droplet number concentration of the droplet spectrum in the sampling volume, and Volume is the sampling volume.

[0010] Preferably, the key parameters of the model are set as follows: the hygroscopicity parameter κ is calculated from the observed data, the temperature T is obtained in real time through the droplet spectrum data, and the droplet surface tension parameter A is calculated. The reverse integration method mainly reversely integrates the aerosol spectrum to find an interval that makes the total concentration of the activated aerosol integral closest to the actual measured concentration (droplet spectrum), and interpolates to obtain the critical activation diameter D when the two are equal. a , and inversely deduce the critical diameter D of the droplet dc The supersaturation SS calculation formula after reverse integration is: (3a) Where A is the droplet surface tension parameter, and its calculation formula is: (3b) In the formula, is the droplet surface tension coefficient (assumed to be the surface tension of pure water at ambient temperature), is the molar mass of water, R is the gas constant (R is approximately equal to 8.314 J / (mol·K)), T is the atmospheric temperature, is the density of liquid water.

[0011] The dynamic threshold correction method introduces an integral threshold to distinguish between activated and unactivated particles, and adjusts the supersaturation SS value by iteratively matching the droplet number concentration. Combined with piecewise linear interpolation, the SS calculation accuracy under low supersaturation conditions is optimized. The exception handling and result optimization parts include: eliminating invalid values ​​(such as infinite values ​​in the estimated results), limiting the SS range (0.02%~0.1%), and ensuring that the results meet the actual atmospheric conditions.

[0012] Preferably, the formula for calculating the actual activation rate of cloud condensation nuclei under actual supersaturation in step S107 is as follows: (4) Where, AR r is the actual activation rate, the cloud condensation nucleus number concentration N CCN N can be set in four ways under SS CCN Fitting is performed based on the time series to obtain the total concentration under a specific SS. d To calculate the total aerosol concentration, we can first calculate the hourly average value within the corresponding time range and then integrate it over time.

[0013] Cloud condensation nucleus number concentration N CCN The fitting formula is as follows: , (5) C and k in the formula are fitting coefficients.

[0014] The significance test of the exponential regression equation of the total number of cloud condensation nuclei concentration can be tested using the F test. For the indicator F, we have: (6) It is subject to the degree of freedom of Distribution. Compare the F value with the For comparison. , think in At the significance level of , the regression equation of the total cloud condensation nucleus concentration is significant, and the exponential fitting method can be used to fit the cloud condensation nucleus concentration. If the F test fails, it is considered that there are few data available for fitting, resulting in a large fitting error, and more cloud condensation nucleus measurement data under different supersaturation settings SS should be considered.

[0015] Preferably, in step S108, the supersaturation SS and D dc The relationship is: (7); A in the formula is shown in formula (3b).

[0016] D dc With D a The relationship is: (8) Particle size larger than D a The particles are regarded as activated particles, and these activated particles are integrated to obtain the total number of activated particles N act . Calculate the activation rates corresponding to different supersaturation SS, and thus find the relationship between activation rate AR and supersaturation SS. The formula is: (9).

[0017] Preferably, the calculation of the relative error in step S109 is performed on the premise that the theoretical activation rate is a true value.

[0018] Compared with the prior art, the present invention has the following beneficial effects: 1) Based on objective observation data and strict reliability analysis, this paper uses the reverse integration method to directly correlate the aerosol spectrum with the droplet number concentration, avoiding the accumulation of errors in traditional forward integration. By dynamically adjusting the integration threshold and distinguishing between activated and unactivated particles, the calculation accuracy under low supersaturation conditions is significantly improved. A method based on the κ-Köhler theory is proposed for estimating supersaturation in fog, which has a solid theoretical basis. 2) The present invention introduces the cubic spline interpolation method to refine and smooth the data of droplet number concentration, further improve the accuracy of reverse integration, reduce the error caused by the irregularity of the original number concentration data, and improve the accuracy of supersaturation estimation; 3) The present invention uses the activation rate to perform error analysis and ultimately determines the optimal integral threshold, which is closely linked to the actual physical process and improves the accuracy and reliability of the research. At the same time, a significance test is performed on the cloud condensation nucleus concentration index fitting, making the results more credible; 4) The estimation method according to the present invention is easy to operate, can improve the accuracy and play a positive role in the study of estimating the supersaturation in fog; 5) The present invention realizes the accurate calculation of aerosol supersaturation through multi-source data fusion, reverse integration algorithm and temperature dynamic compensation, solves the problems of data isolation, error accumulation and insufficient environmental adaptability in the prior art, and provides an efficient and reliable tool for atmospheric cloud research. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is the overall technical route of this method; Figure 2 This is a comparison chart of the dynamic threshold correction effect; Figure 3 The normalized time series of droplet number concentration when the particle size is 2.5 μm, 3 μm, and 3.5 μm are obtained by spline interpolation method; Figure 4 The theoretical activation rate and actual activation rate of the 1st to 7th fog processes under the supersaturation corresponding to five integral thresholds (2μm, 2.5μm, 3μm, 3.5μm and 4μm); Figure 5 The variation of supersaturation with time during the seven fog processes for estimating supersaturation. DETAILED DESCRIPTION

[0020] The present invention will be further described below in conjunction with specific embodiments and corresponding drawings.

[0021] The observation instruments used in this embodiment mainly include the fog monitor model 120 (FM-120) produced by DMT, the scanning mobility particle size spectrometer (SMPS) and the continuous-flow streamwise thermal-gradient cloud condensation nucleus counter (CCNc). The raindrop spectrum used to determine the precipitation process is measured by the OTT Particle Size Velocity (Parsivel) disdrometer produced by OTT Hydromet, Germany.

[0022] FM-120 mainly counts the particle size and number by capturing the scattered light emitted by particles when they pass through the laser beam, and then obtains the droplet spectrum. The instrument has a particle size range of 2μm~50 μm, divided into 30 levels, and a sampling frequency of 1 Hz. SMPS is mainly used to obtain dry aerosol spectrum (PNSD). The instrument consists of an electrostatic aerosol classifier (Electrostatic Classifier, EC, model 3082) and a condensation particle counter (Condensation Particle Counter, CPC, model 3776). The differential mobility analyzer (Differential Mobility Analyzer, DMA, TSI, model 3081) used by EC has a measurement range of 11.3~532 nm. The time resolution of SMPS is 5 min, that is, the aerosol spectrum is scanned once every 5 minutes. The data of cloud condensation nucleus number CCN is measured by particle size, and the supersaturation SS values ​​are set to 0.07%, 0.1%, 0.2%, 0.4% and 0.8%, respectively. The measurement time of the first setting of supersaturation SS was 20 min (a longer stabilization time was required when the supersaturation SS switched from 0.8% to 0.07%), and the measurement time of the other four settings of supersaturation SS was 10 min, with a cycle of 1 h.

[0023] According to the measurement time range of droplet spectrum data and aerosol spectrum data, data observed at the Shanghai Fudan site from November 27, 2023 to February 29, 2024 are selected for statistics of relevant physical quantities, totaling 8 fog processes. According to the temperature record of the droplet spectrum, the optimal integration threshold is determined to be 3.5 μm using this method, and the supersaturation of 7 fog processes is obtained (the supersaturation of one fog process cannot be estimated due to the lack of aerosol spectrum data).

[0024] In the low supersaturation area, the supersaturation before and after dynamic threshold correction is different at the initial moment, while the rest of the area is consistent ( Figure 2 , showing the difference between the supersaturation SS1 without dynamic threshold correction and the corrected supersaturation SS12 in the low supersaturation area during the fifth fog process). Taking the fifth fog process as an example, we used the cubic spline interpolation method to standardize the droplet number concentration in different particle size segments ( Figure 3 , Figure 3 (a) is the normalized time series of droplet number concentration when the particle size is 2.5 μm obtained by spline interpolation method. Figure 3 (b) is the normalized time series of droplet number concentration when the particle size is 3 μm obtained by spline interpolation method. Figure 3(c) is the standardized time series of droplet number concentration when the particle size is 3.5 μm obtained by spline interpolation method. The thick orange solid line represents the change of droplet standardized number concentration corresponding to the interpolated particle size at different times, and the blue solid line and green dotted line represent the change of droplet standardized number concentration when the particle size is 2 and 4 μm, respectively). It can be seen that as the interpolated particle size (orange line) increases, the consistency between the interpolated number concentration change trend and the original data change trend will gradually increase, that is, the interpolation effect will gradually improve. When the interpolation particle size is 3.5 μm, the interpolation effect is relatively optimal. When calculating the actual activation rate, the exponential fitting equation for the CCN number concentration passed the significance test, and the determination coefficient R 2 is 0.98. By comparing the activation rate error, Figure 4 ( Figure 4 (a) to (g) are the theoretical activation rates and actual activation rates of the 1st to 7th fog processes under the supersaturation corresponding to five integral thresholds (2μm, 2.5μm, 3μm, 3.5μm and 4μm). The horizontal axis represents the supersaturation when the integral threshold is 2μm, 4μm, 2.5μm, 3μm, and 3.5μm from left to right. t Represents the theoretical activation rate under a specific supersaturation, and different colors represent different lower limits of aerosol spectrum integration. The error bar represents the difference between the theoretical activation rate and the actual activation rate. It can be seen that smaller errors mainly appear in the intervals corresponding to the last three new thresholds (2.5 μm, 3 μm and 3.5 μm). The cumulative relative error (CRE) was further calculated. When the integration threshold was 2.5 μm, the CRE was the smallest at 10.61, and 3.5 μm was the second at 15.09, but the difference between the two was small. The CRE under other integration thresholds was greater than 30, and the CRE under the traditional 2 μm threshold even reached 210.37. Taking into account the interpolation stability and error analysis results, 3.5 μm was identified as the optimal integration threshold. The SS time series in all cases estimated by this threshold are as follows Figure 5 As shown, the supersaturation values ​​of all processes are consistent with the low supersaturation range of the natural environment.

[0025] The supersaturation estimation method includes the following specific steps: (1) Obtain observational data on droplet spectra, aerosol spectra, and cloud condensation nuclei spectra.

[0026] (2) Perform cubic spline interpolation on the droplet spectrum data, and the interpolated particle sizes are 2.5 μm, 3 μm, and 3.5 μm respectively. Subtract the total number concentration value smaller than the particle size from the interpolated concentration value of a certain particle size. For the processed number concentration, if there is a negative value and it is within -5 cm -3 ~ 0 cm -3If the negative value exceeds this interval, it is considered that the difference between the two number concentrations is small and can be approximately corrected to 0. If the negative value exceeds this interval, it is considered that the interpolation function makes opposite judgments on the change trends of the two number concentrations, and the opposite of the negative value is taken as the correction value.

[0027] (3) The time of the aerosol spectrum (SMPS) and the droplet spectrum (FM) is unified, the common time interval is extracted, and the FM data is accumulated according to the time window.

[0028] (4) Convert the raw counts into number concentration distribution bins based on the sampling volume and particle size interval width. nc , directly read the SMPS spectrum data as aerosol spectrum data. According to the FM sampling area S and airflow velocity PAS, calculate the sampling volume: (1) Where Volume is the sampling volume, PAS is the air velocity (unit: m / s), t is the unit time (usually 1s), S a is the sampling area (S a = 0.41 mm 2 ).

[0029] Secondly, the unit volume (cm -3 ) within the droplet number concentration: (2) In the formula, bin nc is the droplet number concentration per unit volume, bin n is the total droplet number concentration of the droplet spectrum in the sampling volume, and Volume is the sampling volume.

[0030] (5) Set the key parameters of the supersaturation calculation model, use the reverse integration method and the dynamic threshold correction method to calculate the supersaturation respectively, and perform abnormal processing and result optimization to ensure that the results meet the actual atmospheric conditions. The setting of the key parameters of the model includes: the hygroscopicity parameter κ is obtained by observation and calculation (κ is set to 0.34 in the embodiment), the temperature T is obtained in real time through FM data, and the droplet surface tension parameter A is calculated. The reverse integration method mainly reversely integrates the aerosol spectrum to find an interval that makes the total concentration of the activated aerosol integral closest to the actual measured concentration (droplet spectrum), and interpolates to obtain the activation critical diameter D when the two are equal. a , and inversely deduce the critical diameter D of the droplet dc The supersaturation SS calculation formula after reverse integration is: (3a) Where A is the droplet surface tension parameter, and its calculation formula is: (3b) In the formula, is the droplet surface tension coefficient (assumed to be the surface tension of pure water at ambient temperature), is the molar mass of water, R is the gas constant (R is approximately equal to 8.314 J / (mol·K)), T is the atmospheric temperature, is the density of liquid water.

[0031] (6) Calculate the CCN activation rate under actual supersaturation: (4).

[0032] Where, AR r is the actual activation rate, the cloud condensation nucleus number concentration N CCN N can be set in four ways under SS CCN Fitting is performed based on the time series to obtain the total concentration under a specific SS. d To calculate the total aerosol concentration, we can first calculate the hourly average value within the corresponding time range and then integrate it over time.

[0033] The CCN number concentration time series under the estimated SS is obtained by the exponential fitting method. The fitting formula is as follows: (5) , Where SS represents supersaturation, and C and k are fitting coefficients.

[0034] The significance test of the exponential regression equation of the total CCN concentration can be tested using the F test. For the indicator F, we have: (6) , It is subject to the degree of freedom of Distribution. Compare the F value with the For comparison. , think in At the significance level of , the regression equation of the total CCN concentration is significant, and the exponential fitting method can be used to fit the CCN concentration. If the F test fails, it is considered that there are few data available for fitting, resulting in a large fitting error, and more CCN measurement data under different supersaturation settings SS should be considered.

[0035] (7) Based on the supersaturation SS estimated in step (5), according to the wet critical diameter D dc Inversely proportional to supersaturation SS, find the wet critical diameter D at each supersaturation SS dc (Unit: μm). The formula is: (7).

[0036] A in the formula is shown in formula (3b).

[0037] (8) Calculate each wet critical diameter D dc The corresponding activation critical diameter D a (Unit: nm), D dc With D a The relationship is: (8).

[0038] Particle size larger than D a The particles are regarded as activated particles, and these activated particles are integrated to obtain the total number of activated particles N act . Calculate the activation rate corresponding to the supersaturation SS in step (5), and thus find the relationship between AR and supersaturation SS. The formula is: (9).

[0039] Among them, the total aerosol particle number may deviate from the normal value due to changes in the measurement environment, so the aerosol integration interval should be appropriately changed to adapt to the actual activation rate value.

[0040] (9) Calculate the cumulative relative error (CRE), which is the sum of the absolute values ​​of the relative errors under the same integration threshold. Determine the optimal integration threshold by combining the two practical situations that the CRE is smaller and the interpolation stability increases with the increase of the interpolation particle size. The SS corresponding to this threshold is the final result.

[0041] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for optimizing supersaturation in fog, characterized in that: include: Obtain observational data of fog droplet spectrum, aerosol spectrum and cloud condensation nucleus spectrum during fog process in the studied area, as well as observational data of raindrop spectrum in the same study period; Determining the fog process according to the fog drop spectrum and rain drop spectrum data; The droplet spectrum data is interpolated by cubic spline, and the interpolated particle sizes are 2.5 μm, 3 μm and 3.5 μm respectively, and negative values ​​are processed in different cases; Unifying the time of the aerosol spectrum and the droplet spectrum, extracting the common time interval, and accumulating the droplet spectrum data according to the time window; According to the sampling volume and the particle size interval width, the raw counts are converted into number concentration distribution, and the spectrum data of the aerosol spectrum is directly read as aerosol spectrum data; Set the key parameters of the supersaturation calculation model, calculate the supersaturation using the reverse integration method and the dynamic threshold correction method, and perform abnormal processing and result optimization; Obtain the time series of cloud condensation nuclei under estimated supersaturation, calculate the actual activation rate of cloud condensation nuclei under actual supersaturation, and conduct significance test; Find the wet critical diameter corresponding to each supersaturation, calculate the activation critical diameter corresponding to each wet critical diameter, regard the particles with a diameter larger than the activation critical diameter as activated particles, integrate the activated particles, and calculate the theoretical activation rates corresponding to different supersaturations; The cumulative relative error was calculated, and the optimal integral threshold was determined by combining the two practical situations: the cumulative relative error was smaller and the interpolation stability increased with the interpolation particle size, and the supersaturation corresponding to the threshold was obtained.

2. The optimization method according to claim 1, characterized in that: The criterion for judging a fog process is that the average number concentration of fog droplets is greater than or equal to 10 cm -3 And the average liquid water content is greater than or equal to 0.001 gm -3 ; At the same time, the raindrop spectra with a number of less than 10 and a rainfall intensity less than 0.002 mm h were removed. -1 If the precipitation rate after elimination is not 0, it is considered as a precipitation process, and the fog process containing precipitation period is eliminated.

3. The optimization method according to claim 1, characterized in that: The processing of negative values ​​according to different situations includes: For the number concentration after treatment, if there is a negative value and it is located at -5cm -3 -0 cm -3 If the interval is 0, the difference between the two numerical concentrations is considered small and can be approximately corrected to zero. If the negative value exceeds -5cm -3 -0 cm -3 interval, it is considered that the interpolation function makes opposite judgments on the changing trends of the two-level number concentrations, and the opposite of the negative value is taken as the correction value.

4. The optimization method according to claim 1, characterized in that: Get basic observation data, including: Obtain the dry aerosol particle size distribution data and corresponding timestamp of the aerosol spectrum, with the particle size range of 10nm-10000nm; The droplet spectrum data and timestamp of the droplet spectrum are read, and the particle size range is 2 μm-50 μm. The droplet spectrum data is multiplied by 1000 to convert into nanometer units, and the aerosol spectrum and droplet spectrum data are matched by time alignment.

5. The optimization method according to claim 1, characterized in that: Unify the time of aerosol and droplet spectra, including: Unifying the timestamps of the aerosol spectrum and the droplet spectrum to hourly precision, and extracting a common time interval; The droplet spectrum data are accumulated according to the time window, and the time step is unified.

6. The optimization method according to claim 1, characterized in that: The droplet number concentration calculation converts the original count into a number concentration distribution based on the sampling volume and particle size interval width. The calculation process is as follows: According to the droplet spectrum sampling area and air flow velocity, the sampling volume is calculated: (1) Where Volume is the sampling volume, PAS is the airflow velocity, unit: m / s, t is the unit time, S a is the sampling area; Calculate the droplet concentration bin per cubic centimeter based on the original statistical number of droplet spectra nc : (2) In the formula, bin nc is the droplet number concentration per unit volume, bin n is the total droplet number concentration of the droplet spectrum in the sampling volume, and Volume is the sampling volume.

7. The optimization method according to claim 1, characterized in that: The setting of model parameters includes: The hygroscopicity parameter κ is obtained by observation and calculation, the temperature T is obtained in real time through the droplet spectrum data, and the droplet surface tension parameter A is calculated; The reverse integration method mainly reverses the aerosol spectrum to find an interval that makes the total concentration of activated aerosol integration closest to the actual measured concentration. By interpolation, the activation critical diameter Da is obtained when the two are equal, and the droplet wet critical diameter D is inferred. dc , the supersaturation SS calculation formula after reverse integration is: (3a) Where A is the droplet surface tension parameter, and its calculation formula is: (3b) In the formula, is the droplet surface tension coefficient, is the molar mass of water, R is the gas constant, T is the atmospheric temperature, is the density of liquid water.

8. The optimization method according to claim 1, characterized in that: Calculation of the actual activation rate AR of cloud condensation nuclei under actual supersaturation r The formula is as follows: (4) In the formula, AR r is the actual activation rate, the cloud condensation nucleus number concentration N CCN N can be set in four SS CCN The total concentration at a specific SS is obtained by fitting based on the time series, N d is the total aerosol concentration; Cloud condensation nucleus number concentration N CCN The exponential fitting formula is as follows: (5) C and k in the formula are fitting coefficients.

9. The optimization method according to claim 1, characterized in that: Supersaturation SS and critical diameter D dc The relationship is: (6) Where A is the droplet surface tension parameter, and SS is the supersaturation.

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