A method for identifying quasi-biweekly life cycle of atmospheric pollution based on fourier filtering

Abstract

This invention discloses a quasi-bi-weekly lifecycle identification method for air pollution based on Fourier filtering, comprising the following steps: S1, acquiring daily observation data of air pollutant concentrations in the target area, and screening and confirming periods where pollutant concentrations continuously exceed a threshold as independent pollution events; S2, performing Fourier transform on the daily observation data and calculating the power spectrum to verify the existence of a significant quasi-bi-weekly periodic signal; S3, based on the confirmation of a significant quasi-bi-weekly periodic signal, performing Fourier filtering on the original concentration sequence to extract the quasi-bi-weekly scale component sequence; S4, for each pollution event, performing phase localization to achieve quasi-bi-weekly lifecycle identification of pollutant events. This invention can objectively extract oscillation signals at the quasi-bi-weekly scale and accurately determine the phase of a single pollution event within its quasi-bi-weekly cycle, thereby achieving quantitative identification of its lifecycle.

Description

Technical Field

[0001] This invention belongs to the field of atmospheric environment monitoring and data analysis technology, specifically relating to a technology for identifying the inherent periodic life cycle of atmospheric pollution events using signal processing methods. Background Technology

[0002] Accurately identifying and predicting the occurrence, development, and dissipation of pollution incidents is crucial for developing effective pollution prevention and control strategies and issuing health warnings.

[0003] Currently, the analysis of air pollution processes mainly focuses on the static description of the spatiotemporal distribution of pollutant concentrations, transport paths, and chemical components, or on forecasting using numerical models. However, these methods have the following limitations: (1) Insufficient static analysis: Traditional methods are difficult to reveal the inherent periodic oscillation signals within pollution events that are driven by large-scale climate systems (such as monsoons, teleconnections, etc.); (2) Model uncertainty: The forecast results of numerical models are affected by the initial field, physical parameterization scheme, etc., resulting in significant uncertainty and high computational costs; (3) Lack of quantitative identification of the life cycle: Existing technologies rarely quantify the complete life cycle of a pollution event from "initiation-development-peak-dissipation" directly and objectively from observational data, especially for pollution processes with quasi-periodic characteristics.

[0004] Studies have shown that many atmospheric phenomena, including changes in pollutant concentrations, exhibit significant quasi-bicyclic oscillations (with a period of approximately 8-30 days). This signal is closely related to low-frequency atmospheric oscillations. Effectively extracting this signal and correlating it with specific pollution events would allow for a completely new dynamic perspective on the intrinsic rhythms of pollution processes. Currently, a method is lacking that can directly and accurately identify and characterize the quasi-bicyclic lifecycle of air pollution events from observational data. Summary of the Invention

[0005] Purpose of the invention: In view of the problems and deficiencies in the existing technology, the purpose of this invention is to provide a quasi-bi-weekly life cycle identification method for atmospheric pollution based on Fourier filtering. This invention can objectively extract oscillation signals at the quasi-bi-weekly scale from daily pollutant concentration observation data, and accurately determine the phase of a single pollution event in its quasi-bi-weekly cycle, thereby realizing the quantitative identification of its life cycle and providing technical support for the mechanism research and prediction of pollution processes.

[0006] Technical Solution: To achieve the above-mentioned objectives, this invention adopts the following technical solution: a quasi-bi-weekly lifecycle identification method for air pollution based on Fourier filtering, comprising the following steps:

[0007] S1, Air Pollution Time Screening: Obtain daily observation data of air pollutant concentrations in the target area, and screen and confirm periods when pollutant concentrations continuously exceed the threshold as independent pollution events;

[0008] S2, Quasi-bicyclic significance test: Perform Fourier transform on the daily observation data to calculate the power spectrum to test whether there is a significant quasi-bicyclic signal; if there is a significant quasi-bicyclic signal, proceed to step S3, otherwise terminate the method.

[0009] S3, Atmospheric pollutant concentration filtering analysis: Based on the confirmation of the existence of a significant quasi-bi-weekly periodic signal, Fourier filtering is performed on the daily observation data to extract the quasi-bi-weekly scale component sequence;

[0010] S4, Quasi-bi-weekly lifecycle identification: For each pollution event, phase localization is performed to achieve quasi-bi-weekly lifecycle identification of pollutant events.

[0011] Furthermore, in step S1, a threshold of concern for the concentration of air pollutants used to identify pollution events is determined based on ambient air quality standards or historical statistical data. By traversing the daily observation data, time periods in which the concentration of pollutants continuously exceeds the threshold of concern are selected, and these time periods are regarded as independent pollution events.

[0012] Furthermore, the atmospheric pollutant concentrations are calculated using the average daily concentration data from all observation stations in the target area.

[0013] Furthermore, the specific process of the quasi-bi-weekly periodicity significance test described in step S2 is as follows:

[0014] S2.1, the power spectrum is calculated by performing a Fourier transform on the daily observation data of the entire time series using the following formula. ,

[0015] ,

[0016] In the formula, Represents the k-th frequency component The power spectrum below, Represents the k-th frequency component The discrete Fourier transform result at the point, t represents the daily observation data, where t = 1, 2, ..., N, and N represents the total number of days for the daily observation data.

[0017] S2.2, power spectrum If the red noise test calculation within the 8-30 day frequency band reaches a confidence level of 95% or higher, it is considered to exceed the preset significance level;

[0018] S2.3 When there is a spectral peak exceeding the preset significance level, it is determined that the time series has significant quasi-bicyclic oscillations, and proceed to step S3; otherwise, the method is terminated.

[0019] Furthermore, step S3 specifically includes the following steps:

[0020] S3.1, Construct the frequency filtering function As shown in the following formula,

[0021] ,

[0022] In the formula, Represents the frequency filtering function. This represents the k-th frequency component. The minimum value representing the precise frequency band of the quasi-bicycle oscillation. The maximum value of the precise frequency band representing the quasi-bicycle oscillation;

[0023] S3.2, the filtering function Applied to Fourier transform results In the process, the filtered frequency signal is obtained. ,

[0024] ;

[0025] S3.3, based on the filtered frequency signal Perform an inverse Fourier transform to reconstruct the quasi-bicyclic scaling component sequence in the time domain. ,

[0026] ,

[0027] In the formula, This represents a quasi-bicyclic scale component sequence.

[0028] Furthermore, step S4 determines the quasi-bi-weekly phase of the air pollutant event based on the quasi-bi-weekly scale component sequence of pollutant concentration, thereby realizing the quasi-bi-weekly lifecycle identification of the pollution event. The specific process is as follows:

[0029] S4.1, compare and analyze the original concentration sequence and its corresponding quasi-biweekly scale component sequence for each day during the duration of the pollution event: take the evolution process of the quasi-biweekly scale component sequence as a reference period, define the date when the quasi-biweekly component value is 0 in the reference period as the first phase of the period, define the date corresponding to the maximum value of the quasi-biweekly component in the reference period as the third phase, define the date when the original concentration reaches its peak and the quasi-biweekly component value is 0 in the reference period as the fifth phase, define the date corresponding to the minimum value of the quasi-biweekly component in the reference period as the seventh phase, define the date when the quasi-biweekly component value is half of the maximum value between the first and third phases as the second phase, define the date when the quasi-biweekly component value is half of the maximum value between the third and fifth phases as the fourth phase, define the date when the quasi-biweekly component value is half of the minimum value between the fifth and seventh phases as the sixth phase, and define the date when the quasi-biweekly component value is half of the minimum value after the seventh phase as the eighth phase;

[0030] S4.2, Based on the phase determined in step S4.1, the entire duration of the target pollution event is mapped to the baseline cycle, specifically as follows: Phases 1-8 are divided into the cleanup period, cleanup period, accumulation period, transition period, development period, peak period, decay period, and dissipation period, respectively, according to the pollution event and the cleanup phase before its occurrence, thereby realizing the identification of the quasi-bi-weekly life cycle of the pollution event.

[0031] Furthermore, the air pollutants include PM2.5. 2.5 PM 10 Ozone, nitrogen oxides, and carbon monoxide.

[0032] Beneficial Effects: Compared with existing technologies, this invention extracts quasi-bicyclic oscillation signals of pollution events by systematically applying Fourier filtering, revealing for the first time the intrinsic periodic life rhythm hidden behind complex pollution changes and driven by large-scale climate dynamics, thus deepening the understanding of the causes of pollution processes. By introducing a pre-emptive power spectrum significance test, it ensures that the method is only applied to data with quasi-bicyclic characteristics, improving the reliability and persuasiveness of the results, and can adaptively determine the most significant oscillation period, achieving precise fine-tuning of the filtering frequency band and enhancing the method's adaptability. Simultaneously, this invention transforms the identification of pollution lifecycles from subjective experience-based judgment to objective quantitative analysis based on Fourier transform and phase calculation, significantly improving the accuracy and comparability of the results. Furthermore, this method does not rely on complex numerical models, but only on conventional observation data, featuring a clear calculation process and strong technical universality, and can be widely applied to different regions and different pollutants (such as PM2.5, PM2.5, PM2.5). 10 Periodic analysis of (O3, etc.). Attached Figure Description

[0033] Figure 1This is a flowchart of the quasi-bi-weekly lifecycle identification method for air pollution based on Fourier filtering as described in this invention.

[0034] Figure 2 This is a schematic diagram of the eight phases described in this invention.

[0035] Figure 3 The PM described in the embodiments of the present invention 2.5 Power spectrum analysis results of the concentration sequence.

[0036] Figure 4 The PM described in the embodiments of the present invention 2.5 Comparison of concentration sequences before and after filtering. (a) PM 2.5 (a) Concentration sequence; (b) Normalized original sequence and quasi-bicyclic filtered component sequence. The dashed box indicates a pollution event of interest. Detailed Implementation

[0037] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0038] like Figure 1 As shown, the quasi-bi-weekly lifecycle identification method for air pollution based on Fourier filtering of the present invention includes the following steps:

[0039] S1. Air pollution event screening:

[0040] Acquire daily observation data of air pollutant concentrations in the target area within the target time period; determine the air pollutant concentration concern threshold for identifying pollution events based on ambient air quality standards or historical statistical data; iterate through the daily observation data, filter out all time periods in which pollutant concentrations continuously exceed the concern threshold, and define each such time period as an independent pollution event.

[0041] S2, Significance test of quasi-bi-weekly period:

[0042] The daily observation data of the entire time series obtained in step S1 ( t =1,2,..., N ; N The power spectrum of the time series (representing the total number of days of daily observation data) is calculated using a Fast Fourier Transform to examine whether a significant quasi-bicyclic periodic signal exists in the time series. The coefficients are obtained through Fourier transform:

[0043] ,

[0044] in, It is the k-th frequency component. Analyze the power spectrum. Does a spectral peak exist within a quasi-bicyclic frequency band (e.g., the band corresponding to a period of 8-30 days) that exceeds a preset significance level (e.g., 95% confidence level calculated by red noise test)? If so, the time series is determined to have significant quasi-bicyclic oscillations, and the next step is performed; otherwise, the method is terminated or another frequency band is selected for analysis.

[0045] S3. Filtering and analysis of atmospheric pollutant concentration:

[0046] Based on the confirmation of a significant quasi-bicyclic periodic signal in S2, the original concentration sequence was analyzed. Fourier filtering is performed to extract the quasi-bicycle scale component. The precise frequency band range of the quasi-bicycle oscillation is then defined. (For example, it can be fine-tuned according to the specific position of the spectral peak in S2, usually with a period of 8-30 days). Construct a frequency domain filter function. :

[0047] ,

[0048] filter Applied to Fourier transform results The filtered frequency domain signal is obtained. Subsequently, an inverse Fourier transform was performed to reconstruct the quasi-bicyclic scale component sequence in the time domain. :

[0049] ,

[0050] In practical applications, Take the real part of the result of the inverse transformation above.

[0051] S4. Quasi-bi-weekly lifecycle identification: For each contamination event selected in step S1, perform the following sub-steps:

[0052] The original concentration sequence and its corresponding quasi-biweekly scale component sequence for each day during the duration of the pollution event are compared and analyzed. Preferably, the evolution process of the quasi-biweekly scale component sequence is used as a baseline period. The date when the quasi-biweekly component value is 0 within the baseline period is defined as the first phase of the period. The date corresponding to the maximum value of the quasi-biweekly component within the baseline period is defined as the third phase. The date when the original concentration reaches its peak and the quasi-biweekly component value is 0 within the baseline period is defined as the fifth phase. The date corresponding to the minimum value of the quasi-biweekly component within the baseline period is defined as the seventh phase. The date when the quasi-biweekly component value is half of the maximum value between the first and third phases is defined as the second phase. The date when the quasi-biweekly component value is half of the maximum value between the third and fifth phases is defined as the fourth phase. The date when the quasi-biweekly component value is half of the minimum value between the fifth and seventh phases is defined as the sixth phase. The date when the quasi-biweekly component value is half of the minimum value after the seventh phase is defined as the eighth phase.

[0053] Based on the phases, the entire duration of the target pollution event is mapped onto the baseline cycle. Specifically, the pollution event and the cleanup phase preceding it are divided into the clearing phase (phase 1), the cleanup phase (phase 2), the accumulation phase (phase 3), the transition phase (phase 4), the development phase (phase 5), the peak phase (phase 6), the decay phase (phase 7), and the dissipation phase (phase 8), thereby achieving objective and quantitative identification of the quasi-bi-weekly life cycle of the pollution event.

[0054] Example: Taking the winter PM2.5 concentration in a certain city as an example. 2.5 Taking the pollution process as an example

[0055] S1. Air pollution event screening:

[0056] Obtain PM2.5 levels for a city during the winter of 2014 (e.g., December to February of the following year). 2.5 Daily concentration observation data. PM2.5 concentration data. 2.5 Daily average concentrations exceeding 150 μg / m³ are defined as pollution days exceeding the threshold of concern. The data is then traversed to identify all consecutive periods exceeding this threshold. For example, a pollution event lasting from December 20th to December 26th, 2014, can be found.

[0057] S2, Significance test of quasi-bi-weekly period:

[0058] PM2.5 levels were collected throughout the entire winter (approximately 90 days). 2.5 The daily concentration series were subjected to Fast Fourier Transform, and their power spectra were calculated. The results are as follows: Figure 3 As shown, the dashed line represents the 95% confidence level calculated by the red noise test. The results indicate that the sequence exhibits a significant oscillation period on a quasi-bicyclic scale, allowing for further investigation.

[0059] S3. Filtering and analysis of atmospheric pollutant concentration:

[0060] PM2.5 levels were collected throughout the entire winter (approximately 90 days). 2.5 The daily concentration sequence was subjected to Fast Fourier Transform (FFT). The frequency band of the quasi-bicyclic oscillation was set to a period of 8-30 days. Using the inverse Fourier transform, an 8-30 day bandpass filter was designed to filter the original sequence, resulting in a smooth PM concentration sequence containing only the quasi-bicyclic oscillation signal. 2.5 Component sequences (see) Figure 4 ).

[0061] S4, Quasi-bi-weekly lifecycle identification:

[0062] Phase analysis was conducted on the pollution event from December 20th to 26th. In the quasi-biweekly component sequence, within the baseline period of the pollution event, the component value on December 12th was close to 0, defined as phase 1. The component value on December 15th was the lowest point of the period, defined as phase 3. Around December 19th, the quasi-biweekly component sequence approached 0, defined as phase 5. By December 22nd, the quasi-biweekly component sequence reached the highest point of the period, defined as phase 7. On December 13th and 18th, the quasi-biweekly component values ​​reached halfway through the lowest point, defined as phases 2 and 4 respectively. On December 20th and 24th, the quasi-biweekly component values ​​reached halfway through the highest point, defined as phases 6 and 8 respectively.

[0063] Based on this, the lifecycle of this pollution event can be identified as follows: On December 12th, the atmosphere was clean. On December 15th, air quality began to deteriorate from its best state within this cycle. On December 18th, pollutants accumulated, but did not reach pollution levels. December 19th marked the turning point from clean to polluted. On December 20th, pollution worsened, possibly accompanied by an increase in pollution levels and an expansion of the polluted area. On December 22nd, pollution reached its peak, the climax of this pollution event. On December 24th, the pollution slowly dissipated. The pollution ended on December 26th. The entire process clearly demonstrates the complete lifecycle of this pollution event on a quasi-biweekly scale.

[0064] Compared with the prior art, the present invention has the following significant advantages:

[0065] (1) The invention is the first to systematically apply the Fourier filtering method to extract the quasi-bi-weekly oscillation signal of pollution events, which can reveal the inherent periodic life rhythm hidden behind complex changes and driven by large-scale climate dynamics, thus deepening the understanding of the causes of pollution processes.

[0066] (2) Adaptive frequency band selection: Step S2 acts as a "pre-test checkpoint" to ensure that the subsequent filtering and lifetime identification are performed on data that actually have quasi-bicycle oscillation signals, thus avoiding the forced application of this method on data that does not have this periodic characteristic, and improving the reliability and persuasiveness of the results.

[0067] (3) Power spectrum analysis can help determine the exact period of the most significant oscillation, so that the filter band can be finely adjusted in S3 according to the characteristics of the data itself, which enhances the adaptability of the method.

[0068] (4) Objective Quantification: Through Fourier transform and phase calculation, the identification process of pollution life cycle is transformed from subjective experience judgment to objective and quantitative data analysis, which improves the accuracy and comparability of the results.

[0069] (5) Strong technical universality: This method does not rely on complex numerical models, but is based solely on conventional observation data. The calculation process is clear and can be widely applied to different regions and different pollutants (such as PM2.5). 2.5 PM 10 Periodic analysis of (O3, etc.).

[0070] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and technical concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for identifying quasi-biweekly life cycle of atmospheric pollution based on Fourier filtering, characterized in that The method comprises the following steps: S1, atmospheric pollution time screening: obtaining daily observation data of atmospheric pollutant concentration in a target area, and screening and confirming a period in which the pollutant concentration continuously exceeds a threshold value as an independent pollution event; S2, quasi-biweekly cycle significance test: performing Fourier transform on the daily observation data to calculate a power spectrum to test whether there is a significant quasi-biweekly cycle signal; when there is a significant quasi-biweekly cycle signal, step S3 is entered, otherwise the method is terminated; S3, atmospheric pollutant concentration filtering analysis: on the basis of confirming that there is a significant quasi-biweekly cycle signal, performing Fourier filtering on the daily observation data to extract a quasi-biweekly scale component sequence; S4, quasi-biweekly life cycle identification: for each pollution event, phase positioning is performed to realize quasi-biweekly life cycle identification of the pollutant event; Step S3 specifically comprises the following steps: S3.1, constructing a frequency filter function As shown in the following formula, ， wherein denotes a frequency filter function, denotes the kth frequency component, denotes the minimum of the exact frequency band of the quasi-double periodic oscillation, denotes the maximum of the exact frequency band of the quasi-double periodic oscillation; S3.2, applying a filter function to the Fourier transformed result to obtain a filtered frequency signal , ； S3.3, based on the filtered frequency signal performing an inverse Fourier transform to reconstruct the quasi-biweekly scale component sequence in the time domain , ， wherein denotes the quasi-biweekly scale component sequence. 2.The method of claim 1, wherein the method is characterized by: In step S1, a threshold value of atmospheric pollutant concentration for identifying a pollution event is determined based on an environmental air quality standard or historical statistical data, and by traversing the daily observation data, a period in which the pollutant concentration continuously exceeds the threshold value is screened out, and the period is taken as an independent pollution event. 3.The method of claim 2, wherein: The atmospheric pollutant concentration uses average daily concentration data of all observation sites in the target area. 4.The method of claim 1, wherein the method further comprises: The specific process of the quasi-biweekly cycle significance test in step S2 is as follows: S2.1 The power spectrum is calculated for the entire time series of daily observations by Fourier transforming the data using the formula , ， wherein P(k) denotes the power spectrum at the kth frequency component P(k) denotes the power spectrum at the kth frequency component P(k) denotes the power spectrum at the kth frequency component P(k) denotes the power spectrum at the kth frequency component P(k) denotes the power spectrum at the kth frequency component S2.2, the power spectrum In the 8-30 day band, if the red noise test calculation reaches 95% confidence level or above, it is determined that the preset significance level is exceeded. S2.3, when there is a spectrum peak value exceeding a preset significance level, it is determined that the time sequence has a significant quasi-biweekly oscillation, and step S3 is entered; otherwise, the method is terminated.

5. The method of claim 1, wherein the method is characterized by: In step S4, the quasi-biweekly phase of the atmospheric pollutant event is determined according to the quasi-biweekly scale component sequence of the pollutant concentration, and quasi-biweekly life cycle identification of the pollution event is realized, and the specific process is as follows: S4.1, comparing and analyzing the original concentration sequence of each day in the duration of the pollution event and the corresponding quasi-biweekly scale component sequence: taking the evolution process of the quasi-biweekly scale component sequence as a reference period, defining the date in which the quasi-biweekly component value is 0 in the reference period as the 1st phase, defining the date corresponding to the maximum value of the quasi-biweekly component in the reference period as the 3rd phase, defining the date in which the quasi-biweekly component value is 0 after the original concentration reaches the peak in the reference period as the 5th phase, defining the date corresponding to the minimum value of the quasi-biweekly component in the reference period as the 7th phase, defining the date in which the quasi-biweekly component value is 1 / 2 of the maximum value between the 1st and 3rd phases as the 2nd phase, defining the date in which the quasi-biweekly component value is 1 / 2 of the maximum value between the 3rd and 5th phases as the 4th phase, defining the date in which the quasi-biweekly component value is 1 / 2 of the minimum value between the 5th and 7th phases as the 6th phase, and defining the date in which the quasi-biweekly component value is 1 / 2 of the minimum value after the 7th phase as the 8th phase. S4.2, according to the phase determined in step S4.1, mapping the entire duration of the target pollution event into the reference cycle, specifically as follows: the 1-8 phases are divided into the removal period, the cleaning period, the accumulation period, the transition period, the development period, the peak period, the attenuation period and the dissipation period respectively corresponding to the pollution event and the cleaning stage before the occurrence of the pollution event, thereby realizing the identification of the quasi-biweekly life cycle of the pollution event. 6.The method of claim 1, wherein the method further comprises: The atmospheric pollutants include PM 2.5 , PM 10 , ozone, nitrogen oxides, carbon monoxide.

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