A method for quantitatively characterizing the multi-scale structure features of atmospheric vertical temperature profile

Abstract

The application discloses a method for quantitatively describing multi-scale structure characteristics of an atmospheric vertical temperature profile, comprising the following steps: P1, performing space-time matching on multi-source temperature data; P2, calculating a first significant digit probability distribution of the temperature data; P3, calculating the first significant digit probability distribution of the data under different scales; and P4, testing the first significant digit probability distribution of the temperature data of different data based on the Benford law. The method can fully reflect the overall characteristics of the data at all times, and can distinguish the influence of chaotic processes and random processes in the data. The method promotes the understanding of the space-time scale structure characteristics of temperature elements of different data, and reflects the difference in application performance of different data in the initial state.

Description

Technical Field

[0001] This invention relates to the field of atmospheric profile observation and analysis technology. Specifically, it is a method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles. Background Technology

[0002] Temperature is a key parameter for various atmospheric processes and a very important climatic factor. Currently, the observation and analysis of atmospheric temperature profiles is one of the mainstream tasks in the field of meteorology.

[0003] Conventional radiosonde data, ground-based microwave radiometer (MWR) data, and ERA5 reanalysis data are among the main sources of atmospheric vertical temperature profiles. Radiosonde data is considered the most accurate observational data for real atmospheric conditions, and it has very high vertical resolution, making it widely used in meteorological observation and research. However, radiosonde data requires manual balloon deployment, resulting in limited temporal resolution, and it is also affected by balloon horizontal drift. MWR has the ability to conduct continuous observations unattended for extended periods under most weather conditions, thus possessing high temporal resolution. MWR is often used to supplement radiosonde data and in scientific research operations requiring high temporal resolution. However, this observation is susceptible to environmental factors, resulting in significant uncertainty in profile quality. ERA5 reanalysis data is the fifth-generation global climate reanalysis product provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). It incorporates various observational data during the data assimilation process, resulting in high spatiotemporal resolution and accuracy. However, due to the introduction of geographical unevenness in the distribution of observation stations during the data assimilation process, the reanalysis data may contain certain errors. Meanwhile, the ERA5 reanalysis data provided by ECMWF has a low default vertical resolution, which may sometimes require further processing or the use of data at mode resolution.

[0004] Because different data sets still have some issues and exhibit significant differences in spatial resolution, further understanding of the accuracy and structural characteristics of meteorological data is necessary, which is of great significance for weather and climate research. Current mainstream data comparison and analysis often interpolates different data sets to the same altitude, comparing and analyzing the errors and correlations between them. Other methods use a single weather event or temperature inversion to test the detection capabilities of different data sets. It is evident that current mainstream data comparison and analysis methods often require standardizing the vertical resolution of the data, but this approach may obscure some of the inherent spatiotemporal scale characteristics of the data.

[0005] Therefore, reflecting the spatiotemporal structural characteristics of different data and enriching our understanding of different meteorological data remains an area that needs further exploration. Simon Newcomb was the first to discover that the first digit in many datasets is not uniformly distributed, but rather that smaller digits have a higher probability. Later, Frank Albert Benford summarized that the first digit in many datasets follows the same probability distribution, namely Benford's (BL) Law:

[0006]

[0007] Here, d (d = 1, 2, 3, ..., 9) represents the first digit. This represents the probability of different first digits appearing, as defined by the Black-Scholes law. Currently, the Black-Scholes law is widely used in social and natural sciences to test the reliability of different datasets. Research also indicates that the outcomes of stochastic processes better conform to the Black-Scholes law, thus it can be used as a means to monitor chaotic processes and noise. However, in meteorology, this method is still relatively rare, currently mainly used for detecting typhoon path datasets. Summary of the Invention

[0008] Therefore, the technical problem to be solved by the present invention is to provide a method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles, which solves the problem of masking the spatiotemporal scale features of data during data processing, and thus achieves the quantification and differentiation of scale differences between different data while maintaining the resolution differences between data, thereby further reflecting the differences in data.

[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0010] A method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles includes the following steps:

[0011] Step P1: Perform spatiotemporal matching on the multi-source temperature data;

[0012] Step P2: Calculate the probability distribution of the first significant digit of the temperature data;

[0013] Step P3: Calculate the probability distribution of the first significant figure of the data at different scales;

[0014] Step P4: Test the probability distribution of the first significant digit of temperature data for different data based on Benford's Law.

[0015] The above-mentioned method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles involves matching multi-source temperature data on a time scale in step P1.

[0016] Radiosonde data: Radiosonde balls are released daily at 07:15 and 19:15 Beijing time;

[0017] Ground-based microwave radiometer (MWR) data: MWR inversion results from ground-based microwave radiometers at 07:16 and 19:16 Beijing time daily were selected;

[0018] ERA5 reanalysis data: Temperature data from ERA5 reanalysis data were selected at 08:00 and 20:00 Beijing time each day.

[0019] The above-mentioned method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles involves matching multi-source temperature data on spatial scales in step P1.

[0020] Radiosonde data and ground-based microwave radiometer (MWR) data: are co-located observations;

[0021] ERA5 reanalysis data: Linear interpolation was performed in the horizontal direction using radiosonde data and the 8 closest grid points near the ground-based microwave radiometer station to obtain grid data. The vertical height range was set from the ground to 10 km. The ascent speed of the radiosonde was roughly estimated to be 6 m / s, thus obtaining radiosonde data at layer 1670. Data from the 200 hPa to 1000 hPa height range were selected for analysis in the ERA5 reanalysis data.

[0022] The method described above for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles includes, in step P2:

[0023] Step P201: Calculate the significant figures of the multi-source temperature data;

[0024] Step P202: Obtain the first significant digit of the multi-source temperature data;

[0025] Step P203: Calculate the probability distribution of the first significant digit of the multi-source temperature data.

[0026] The above-mentioned method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles, in step P201, is based on the premise that each temperature profile in the statistical data has H layers of data and N time intervals; firstly, the average value of the temperature of each layer over N time intervals is calculated. Let h represent the data at the nth time interval of the h-th layer, then the mean of the h-th layer. for:

[0027]

[0028] The standard deviation STA of each layer is further calculated using formula (2). h :

[0029]

[0030] Combining formulas (2) and (3), the data is standardized, and the standardized data is denoted as follows:

[0031]

[0032] In the above-mentioned method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles, step P202 involves using the standardized data calculated from formula (4). Extract the first non-zero significant digit, denoted as . This is the first significant digit of the nth time period and hth layer of this temperature data.

[0033] The aforementioned method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles, in step P203, uses the first significant figure set Qt calculated in step P202 to statistically analyze the frequency of the corresponding significant figure d in each layer of the corresponding data. Thus, the probability of the first significant digit of the h-th layer is obtained. (probability) (This represents the probability distribution of the first significant digit at each height (h-th layer):)

[0034]

[0035] Based on the results of formula (5), the probability distribution P of the first significant figure of the overall data (considering the results of all time periods of the corresponding data) is calculated. d :

[0036]

[0037] The method described above for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles involves, in step P2, adjusting the temperature data into a new dataset with a scale of s, where s = 1, 2, 3, ..., 7. The scale of the N data points at each layer is then scaled to obtain the data.

[0038]

[0039] Then, by combining formulas (2) to (6), the probability distribution of the first significant digit of the data under different scales s can be obtained. (Due to the limited length of existing data, the upper limit of the value of s is temporarily set to 7. If the data length is sufficient, the upper limit of the value of s can be increased accordingly according to actual needs, until the value of ΔED in step 10 reaches saturation.)

[0040] The original data is scaled, and then the probability distribution is calculated using formulas (2) to (6). This is because we want to see whether the probability distribution of temperature data changes at different scales, so as to test whether the temperature data can reflect the influence of weather processes on atmospheric temperature at a certain scale.

[0041] In the above-mentioned method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles, step P4 involves analyzing the probability distribution of the first significant figure of the data. The theoretical probability distribution in Benford's Law The actual difference is quantified by calculating the Euclidean distance ED between the two at different scales s:

[0042]

[0043] ED(s) reflects the basic structural characteristics of the atmospheric temperature profile and also demonstrates the consistency of temperature data from different sources.

[0044] The above-mentioned method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles, obtained from formula (8), shows the variation characteristic ΔED of the deviation between the probability distribution of the first significant figure of the data and the theoretical distribution with the largest scale L.

[0045] ΔED(L)=max{ED(s),1≤s≤L}-min{ED(s),1≤s≤L}#(9).

[0046] The maximum scale can be determined based on the duration of the temperature data. However, increasing the scale when the sample size is insufficient can lead to significant errors in the results. Theoretically, when data is plentiful, the scale can be set to twenty or even larger.

[0047] The technical solution of the present invention achieves the following beneficial technical effects:

[0048] 1. This invention uses existing temperature profiles from radiosondes and ground-based microwave radiometers after quality control, as well as temperature data from ERA5 reanalysis data, to match them to the same time period. It then uses Benford's (BL) law to statistically analyze and verify the distribution of the data, thereby distinguishing the structural distribution of different temperature data and reflecting the scale structure characteristics of the data.

[0049] 2. This method can advance the understanding of the spatiotemporal scale structural characteristics of temperature elements in different data, and reflect the differences in application performance of different data in their initial state.

[0050] 3. This method can fully reflect the overall characteristics of data at all time points, while distinguishing the influence of chaotic processes and stochastic processes in the data. In addition to the influence of nonlinear vertical coordinate data (such as the barometric coordinate system of ERA5), the probability distribution of the first significant figure of temperature data deviates further from the Benford (BL) when the scale changes. The degree of this deviation can reflect the sensitivity of the data to chaotic processes at a certain scale (i.e., weather processes at a certain scale).

[0051] 4. This method eliminates the need for linear interpolation to process the vertical resolution of the data during the verification process, thus avoiding excessive interference from artificial signals.

[0052] 5. This method has a certain degree of scalability and can be applied to the verification of more meteorological element data with vertical characteristics, thus possessing a certain degree of universality. Attached Figure Description

[0053] Figure 1 A comparison chart of the probability distribution of the first significant figure of temperature data proposed in this invention and the ideal distribution of Benford's law (Aksu Station, Xinjiang, 51628, 20240101111600-0331231600UTC);

[0054] Figure 2 A comparison chart of the probability distribution of the first significant figure of temperature data proposed in this invention and the ideal distribution of Benford's law (Beijing Station, 54511, 20240101111600-0331231600UTC);

[0055] Figure 3 A comparison chart of the probability distribution of the first significant figure of temperature data proposed in this invention and the ideal distribution of Benford's law (Guangzhou Qingyuan Station, 59280, 20240101111600-0331231600UTC);

[0056] Figure 4 The Euclidean distance between the probability distribution of the first significant digit of temperature data from different sources and the theoretical distribution varies with scale.

[0057] Figure 5 The variation of the maximum Euclidean distance deviation between the first significant digit distribution probability of temperature data from different sources and the theoretical distribution with the largest scale. Detailed Implementation

[0058] The method for quantitatively characterizing the multi-scale structural features of temperature profiles in this embodiment includes the following steps.

[0059] Step P1: Spatiotemporal matching method for multi-source temperature data, that is, matching multi-source temperature data together on both the temporal and spatial scales.

[0060] This embodiment selects three types of temperature data: radiosonde data, ground-based microwave radiometer (MWR) data, and ERA5 reanalysis data.

[0061] Step P101: Match the multi-source data on time scales;

[0062] The daily radiosonde launch times are 07:15 and 19:15 Beijing time. To match the radiosonde launch times, the ground-based microwave radiometer (MWR) data are selected from the inversion results of the MWR at 07:16 and 19:16 Beijing time each day. The ERA5 reanalysis data are the temperature data from the ERA5 reanalysis data at 08:00 and 20:00 within the same time period.

[0063] Step P102: Spatial matching of multi-source data;

[0064] Both radiosonde data and MWR data were observed at the same site, meaning they were located in the same spatial location.

[0065] The ERA5 reanalysis data selected the eight closest grid points near the observation site (the site observed by the ground-based microwave radiometer) and performed linear interpolation in the horizontal direction to obtain grid data. To ensure that all data were largely consistent with the MWR data, the vertical altitude range was set from the ground to 10 km. The ascent velocity of the radiosonde was roughly estimated at 6 m / s, resulting in 1670 layers of radiosonde data. The ERA5 reanalysis data selected data from the altitude range of 200 hPa to 1000 hPa for analysis.

[0066] Step P2: Calculate the probability distribution of the first significant digit of the temperature data.

[0067] Step P201: Calculation of significant figures for multi-source temperature data;

[0068] It is known that each temperature profile in the statistical data has H layers of data and N time intervals. First, calculate the average value of the temperature of each layer over N time intervals. Let h represent the data at the nth time interval of the h-th layer, then the mean of the h-th layer. for:

[0069]

[0070] The standard deviation STA of each layer can be further calculated using formula (2). h :

[0071]

[0072] Combining formulas (2) and (3), the data can be standardized, and the standardized data obtained is denoted as...

[0073]

[0074] Step P202: Obtaining the first significant digit of the multi-source temperature data;

[0075] The first non-zero significant digit is truncated from the standardized data calculated from formula (4), and denoted as . This is the first significant digit of the nth time period and hth layer of this temperature data.

[0076] Step P203: Probability calculation of the distribution of the first significant digit of multi-source temperature data;

[0077] Based on the previously calculated set of first significant digits, Qt statistically analyzes the frequency of occurrence of the corresponding significant digit d (d = 1, 2, 3, ..., 9) in each layer of the corresponding data. Obtain the probability of occurrence at each level

[0078]

[0079] Based on the results of formula (5), the distribution of the first significant figure of the data can be calculated as P. d :

[0080]

[0081] Step P3: Calculate the probability distribution of the first significant figure of the data at different scales;

[0082] Step P301: To adjust the temperature data into a new dataset with a scale of s (s = 1, 2, 3, ..., 7), the scale of N data points at each layer is scaled to obtain the data.

[0083]

[0084] Therefore, by combining formulas (2) to (6), we can obtain the distribution of the first significant figure of the data at different scales s.

[0085] like Figures 1 to 3The figures show a comparison between the average probability distribution of the first significant digit of temperature data from MWR, radiosonde, and ERA5 reanalysis data from Aksu Station in Xinjiang, Beijing Station, and Qingyuan Station in Guangdong from January to March 2024, across seven different scales, and the distribution according to Benford's Law. It can be seen that although the three stations have completely different climatic characteristics, their probability distributions are generally close to Benford's Law, especially the ERA5 (P) data, which has a lower vertical resolution, showing good consistency. This indicates that Benford's Law can be applied to some temperature data analysis to a certain extent. That is, the vertical distribution characteristics of atmospheric temperature are generally close to Benford's Law over the long term. Therefore, by adjusting the time scale, the degree of deviation between the data and the theoretical distribution can be examined, thereby revealing whether the data can represent more chaotic processes, i.e., the multi-scale characteristics of the data.

[0086] Step P4: Test the probability distribution of the first significant digit of temperature data from different sources based on Benford's Law;

[0087] To further analyze the actual difference between the distribution of the first significant figure of the data and the theoretical distribution in Benford's Law, the deviation can be quantified by calculating the Euclidean distance ED between the two at different scales s:

[0088]

[0089] Figure 4 This shows the Euclidean distance (ED) between the probability distribution of the first significant figure of temperature data from different sources and the theoretical distribution, varying with scale. It's worth noting that the ED values ​​of the three datasets remain within 0.1 (i.e., the black, red, and green lines show a consistent trend with small differences), indicating that these datasets can reflect the basic structural characteristics of the atmospheric temperature profile. The standard deviation (std) of the ED values ​​of the MWR and radiosonde data are also relatively consistent (dark green and yellow lines), while the ERA5 reanalysis data (blue line at scale 2) shows greater fluctuations, possibly due to the relatively small amount of data in the original reanalysis dataset.

[0090] Subsequently, based on the results in formula (8), the variation characteristic ΔED of the probability distribution of the first significant figure of the data with respect to the theoretical distribution as a function of the maximum scale L can be obtained:

[0091] ΔED(L)=max{ED(s),1≤s≤L}-min{ED(s),1≤s≤L}. #(9)

[0092] like Figure 5The figure shows the variation of the maximum Euclidean distance deviation ΔED of the three datasets with the maximum scale L. From this, we can better distinguish the scale characteristics of the three datasets. It can be seen that the variation of MWR and radiosonde data is relatively similar. The scale of the original data is s=1, and the maximum scale L=1. The three datasets are located at the same point, that is, under the condition that the scale of the original data is s=1, the three datasets cannot be distinguished. However, the trend of ΔED increasing with L indicates that the higher vertical resolution of these two datasets can reflect more scale characteristics and deviate more from the stochastic process. Figure 5 In the data, MWR and RS show stronger variations with the maximum scale range L, suggesting that these data can capture more information about atmospheric temperature and reflect more scale characteristics. ERA5, on the other hand, shows a weaker trend, indicating that it represents fewer scale characteristics. Therefore, it can be used to analyze problems at specific time scales.

[0093] In theory, when a dataset represents a completely random process and the amount of data is large enough, its first significant figure distribution at each scale should be consistent with Benford's (BL) law; however, when the data is affected by chaotic processes at some scales, it may deviate from the theoretical distribution.

[0094] For example, when atmospheric inversion or convective weather occurs, the temperature at the affected upper altitude will be disturbed to some extent. When the vertical resolution of the data can reflect this disturbance, it is assumed that changing the distribution of the first significant figure of the data at the corresponding scale will deviate from Benford's (BL) law to some extent. In other words, the degree of this deviation can reflect the sensitivity of the data to chaotic processes at a certain scale (here referring to weather processes at a certain scale).

[0095] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of the claims of this patent application.

Claims

1. A method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles, characterized in that, Includes the following steps: Step P1: Perform spatiotemporal matching on the multi-source temperature data; Step P2: Calculate the probability distribution of the first significant digit of the temperature data; Step P3: Calculate the probability distribution of the first significant figure of the data at different scales; Step P4: Test the probability distribution of the first significant digit of temperature data from different sources based on Benford's Law; In step P1, the multi-source temperature data are matched on a spatial scale: Radiosonde data and ground-based microwave radiometer (MWR) data: are co-located observations; ERA5 reanalysis data: Linear interpolation was performed in the horizontal direction using radiosonde data and the 8 closest grid points near the ground-based microwave radiometer station to obtain grid data. The vertical height range was set from the ground to 10 km. The ascent speed of the radiosonde balloon was roughly estimated to be 6 m / s to obtain 1670-layer radiosonde data. ERA5 reanalysis data were selected from the altitude range of 200 hPa to 1000 hPa for analysis; Step P2 includes: Step P201: Calculate the significant figures of the multi-source temperature data; Given that each temperature profile in the statistical data has H layers of data and N time intervals; first calculate the average value of the temperature of each layer over N time intervals. Let h represent the data at the nth time interval of the h-th layer, then the mean of the h-th layer. for: ； The standard deviation of each layer can be further calculated using formula (2). : ； Combining formulas (2) and (3), the data is standardized, and the standardized data is denoted as follows: : ； Step P202: Obtain the first significant digit of the multi-source temperature data; the standardized data calculated from formula (4) Extract the first non-zero significant digit, denoted as . This is the first significant digit of the temperature data at the nth time and the hth layer. Step P203: Calculate the probability distribution of the first significant digit of the multi-source temperature data; Based on the first significant digit set Qt calculated in step P202, the frequency of the corresponding significant digit d in each layer of the corresponding data is statistically analyzed. d=1,2,3,…,9, thus obtaining the probability of the first significant digit of the h-th layer. : ； Based on the results of formula (5), the probability distribution of the first significant digit of the data is calculated. : ； In step P2, the temperature data is resized into a new dataset with a scale of s, where s = 1, 2, 3, ..., 7. The scale of the N data points at each layer is then scaled to obtain the data. : ； Then, by combining formulas (2) to (6), the probability distribution of the first significant digit of the data under different scales s can be obtained. .

2. The method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles according to claim 1, characterized in that, In step P1, the multi-source temperature data are matched on a time scale; Radiosonde data: Radiosonde balls are released daily at 07:15 and 19:15 Beijing time; Ground-based microwave radiometer (MWR) data: MWR inversion results from ground-based microwave radiometers at 07:16 and 19:16 Beijing time daily were selected; ERA5 reanalysis data: Temperature data from ERA5 reanalysis data were selected at 08:00 and 20:00 Beijing time each day.

3. The method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles according to claim 1, characterized in that, In step P4, the probability distribution of the first significant digit of the data is analyzed. The theoretical probability distribution in Benford's Law The actual difference is quantified by calculating the Euclidean distance ED between the two at different scales s: ； ED ( s This reflects the basic structural characteristics of the atmospheric temperature profile and also demonstrates whether temperature data from different sources are consistent.

4. The method for quantitatively characterizing the multi-scale structural features of atmospheric vertical temperature profiles according to claim 3, characterized in that, The variation characteristics of the deviation between the probability distribution of the first significant digit of the data and the theoretical distribution as a function of the maximum scale L are obtained from formula (8). , .

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