A method for estimating and predicting annual average values of the gradient of the refractive index of the atmosphere near the ground or sea surface, which exceed the cumulative probability of 1%

Abstract

The application discloses a method for estimating and predicting the annual average value of the atmospheric refractive index gradient of the near-surface or sea surface exceeding the time cumulative probability of 1%, which comprises the following steps: step 1, based on the ERA5 reanalysis data of the European Centre for Medium-Range Weather Forecasts, the statistical value of the atmospheric refractive index gradient of the near-surface or sea surface of 65m of each grid point of the global equator line exceeding the time cumulative probability of 1% is completed year by year; step 2, the arithmetic average of the statistical values of all grid points along the equator line is carried out on the basis of the statistical value of each grid point of the equator line year by year, and the annual average value of the equator line year by year is formed, and on the basis, a quadratic polynomial is formed according to the trend change. The method disclosed by the application has important significance for estimating the global radio wave propagation effect and evaluating the influence of the radio wave propagation effect on radio information systems, mobile communication systems, navigation positioning systems, radar systems and the like working at different frequency bands.

Description

Technical Field

[0001] This invention belongs to the fields of meteorological forecasting and radio technology, and specifically relates to a method for estimating and predicting the annual average value of the atmospheric refractive index gradient at 65m above the ground or sea surface along the equator with a cumulative probability of more than 1% over time. Background Technology

[0002] In modern electronic information technology, the characteristics of the tropospheric radio wave environment are a crucial factor affecting the effective performance of electronic information systems such as radar, communication, and navigation. The planning and design of radio information systems require research into the statistical characteristics of the radio wave environment. As a vital component of the radio information system environment, the radio wave environment must be considered in the planning, design, and operational support of the system. It is essential to establish and enhance the information-based and networked operational capabilities of the region, as well as the adaptive capabilities of communication, detection, and other electronic systems. Underestimating the impact of radio wave propagation can, at best, affect system reliability, and at worst, lead to system failure. Conversely, overestimating the impact of radio wave propagation increases system load and complexity, resulting in waste, increased technical difficulty, and unnecessary interference with other systems.

[0003] The influence of the troposphere on radio wave propagation depends on the electrical properties of the troposphere itself. Atmospheric refraction is an important radio meteorological parameter characterizing the impact of these electrical properties on radio wave propagation. In the VHF and microwave bands, the tropospheric refractive index depends only on the dielectric constant of the air, which is a function of atmospheric temperature, pressure, and humidity. Therefore, the refractive index can be calculated using atmospheric temperature, pressure, and humidity parameters. The influence of tropospheric refraction on propagation is mainly in the lower atmosphere below 1–2 km. The refractive index gradient of the lower atmosphere is a key parameter used in calculating propagation effects. Line-of-sight propagation, especially at ground or sea, involves the refractive index gradient at 65 m near the ground or sea surface. This 65 km refractive index gradient is a major environmental factor to consider when studying line-of-sight propagation at ground or sea.

[0004] Line-of-sight (LAS) propagation refers to the direct propagation of radio waves from the transmitting point to the receiving point (sometimes including ground reflections) within a distance where the transmitting and receiving antennas can "see" each other. It is also known as direct wave or space wave propagation. LAS can be broadly classified into three categories based on the spatial location of the transmitting and receiving antennas: the first is ground or sea-based LAS, such as relay communication, television, radio broadcasting, and terrestrial mobile communication; the second is ground (sea)-air LAS, such as radar sounding and communication satellites; and the third is air-to-air LAS, such as radio wave propagation between aircraft and spacecraft. These propagation paths involve at least part of the troposphere, causing propagation effects such as refraction. Under normal atmospheric conditions, the farthest direct wave distance between the transmitting and receiving antennas of a radio system is the line-of-sight distance.

[0005] For the planning and demonstration of radio information systems, research on the characteristics of the tropospheric radio wave environment largely depends on the acquisition and statistics of tropospheric radio wave environment parameters. The near-surface or sea-surface 65m atmospheric refractive index gradient exceeding a 1% cumulative time probability is a crucial statistical parameter of the atmospheric refractive index distribution with altitude. It represents the gradient value occurring with a 1% cumulative time probability, signifying an extreme case. This parameter requires extensive statistical analysis of numerous long-term near-surface or sea-surface 65m atmospheric refractive index gradients. Previously, near-surface or sea-surface 65m atmospheric refractive index gradient detection relied solely on meteorological gradiometers, tethered airships, or high-altitude sounding balloons, which was resource-intensive and time-consuming. Furthermore, the long observation time and safety concerns made rapid response time unacceptable. For areas like the ocean, it's impractical to regularly deploy meteorological gradiometers, tethered airships, or high-altitude sounding balloons; the observation conditions are difficult to achieve and do not meet the requirements. Therefore, obtaining a large number of long-term near-surface or sea-surface 65m atmospheric refractive index gradient values ​​is quite challenging.

[0006] Internationally, research on information system planning and design primarily focuses on long-term statistical models of radio wave environmental characteristics and propagation prediction, resulting in statistical models and propagation prediction patterns applicable to different frequency bands and operating modes. These long-term research findings are reflected internationally in recommendations such as the ITU-R (International Telecommunication Union Radiocommunication Sector) ITU-R P.453 series of standards.

[0007] The ITU-R Recommendation P.453-11 specifies the refractive indices N0 and N at sea level. S The statistical calculations utilized surface probing data from approximately 1000 ground stations over a five-year period (1955-1959); N S The calculations of the wet refractive index median and 65m refractive index gradient were performed using initial meteorological data (four times a day) from two years (1992-1993) of numerical weather prediction by the European Centre for Medium-Range Weather Forecasts (ECMWF). The data ranged from 0° to 360° in longitude and from +90° to -90° in latitude, with a resolution of 1.5°. The resolution was improved to 0.75° in ITU-R Recommendation P.453-13. The wet refractive index term at locations different from the grid points was derived by bilinear interpolation using the values ​​of the four nearest grid points. Data files were available from the Radiocommunication Bureau. The calculations of the 1000m and 100m refractive index gradients were performed using upper-air sounding data from 99 radiosonde stations over a period of five years (1955-1959).

[0008] Besides research advancements represented by the International Telecommunication Union (ITU), the work of several internationally renowned figures and their achievements has also had a profound impact. The formula for directly calculating atmospheric refractive index from meteorological parameters was first systematically and comprehensively presented by B.R. Bean and E.J. Dutton in their monograph *Radio Meteorology*. This formula, for electromagnetic waves with frequencies above 30 GHz, maintains an error of less than 0.5% in calculating atmospheric refractive index within the commonly encountered range of air pressure, temperature, and relative humidity. Scientists, in conjunction with the needs of radio information systems, further analyzed the data and discovered that the fundamental factor affecting radio meteorology beyond line-of-sight and microwave propagation is primarily the atmospheric refractive index gradient. Therefore, subsequent work has mainly focused on related research. They discovered that the monthly average value of the ground refractive index... and the refractive index gradient within 1000m above the ground There was a strong correlation, and subsequently, several typical countries, including the United States, Germany, Japan, the United Kingdom, and China, established their own statistical modeling studies. and The exponential relationship.

[0009] In 2010, Abu-Almal analyzed the refractive index gradient and equivalent Earth radius distribution at designated stations in the Arabian region, and their impact on microwave line-of-sight link systems; in 2013, Oluwole analyzed the influence of African meteorological parameters on atmospheric refractive index; in 2014, AbuAlmal analyzed the refractive index gradient below 1 km in the subtropical region using 17 years of meteorological surface and radiosonde data from 1997 to 2013; and in 2015, Daniel Effiong Oku analyzed the seasonal variation of atmospheric refractive index under the tropical monsoon conditions of Calabar in Africa, and presented the variation characteristics during the rainy and dry seasons.

[0010] In radio telegraphy propagation design, the equivalent Earth radius is typically used to estimate line-of-sight propagation conditions. Spatiotemporal variations in atmospheric refractive index cause changes in the equivalent Earth radius. These variations affect propagation clearance and the corresponding antenna heights, angle of arrival, and directional characteristics of the antennas. Since Schelleng first derived the classical formula for calculating the equivalent Earth radius in 1933, extensive research has been conducted on its calculation methods and distribution characteristics. Xiong Hao et al. provided a detailed description of the connotation and expression of the equivalent Earth radius. In recent years, scholars worldwide have conducted numerous studies on the distribution characteristics of the equivalent Earth radius using measured meteorological data. For example, in 2006, Afullo TJ et al. studied the distribution characteristics of the equivalent Earth radius factor in South Africa; in 2011, Naveen Kumar Chaudhary of India analyzed the influence of the Indian semi-desert region on the K-factor, which is closely related to the atmospheric refractive index gradient, in radio propagation; and in 2014, Adediji AT's research presented the impact of the meteorological characteristics of the equivalent Earth radius factor on radio links in the Akure region of Nigeria. In 2016, Etokebe IJ calculated the equivalent Earth radius distribution in Lagos, the capital of Nigeria, under clear-sky conditions and presented the distribution of the equivalent Earth radius factor when the refractive index gradient was within a given range. This indicates that obtaining the distribution characteristics of the equivalent Earth radius using meteorological parameters from different locations can be used to analyze the propagation environment of line-of-sight links in terrestrial radio systems, and further assess the impact of atmospheric refraction on radio system performance.

[0011] Extensive research has been conducted in my country on the characteristics of the tropospheric radio wave environment, yielding a wealth of statistical data, models, and propagation forecasting patterns. The 22nd Research Institute of China Electronics Technology Group Corporation (CETC 22nd Research Institute) is the only specialized research institute in China dedicated to the observation and research of radio wave environmental characteristics, with a long history of research in radio meteorology. It possesses a strong theoretical and experimental foundation in the study of tropospheric radio wave environmental characteristics. Since the 1960s, it has collected a large amount of tropospheric radio wave environmental data, conducted numerous tropospheric radio wave environmental experiments, and performed extensive statistical analysis of the data. This has led to the establishment of various atmospheric structure models and the development of a number of national standards, including the "Tropospheric Radio Wave Corrected Atmospheric Model" and the "Radar Radio Wave Propagation, Refraction, and Correction Handbook." Eight research findings, including tropospheric scattering propagation models, atmospheric absorption models, and worst-case monthly precipitation conversion models, have been adopted by international standards, forming or revising International Telecommunication Union (ITU-R) standards, marking my country's leading position in the field of radio wave environmental characteristics research. In the 1970s and 80s, based on ten years of historical meteorological data, the following publications were compiled, analyzed, and edited: "Atlas of Low-Altitude Atmosphere Refractive Index in China," "Statistical Characteristics of Low-Altitude Atmospheric Waveguides in Typical Regions of China," and "Distribution Characteristics of Typical Low-Altitude Atmosphere Refractive Index in Beijing and the Middle and Lower Reaches of the Yangtze River." Qiu Shengbai and Lin Xiuwan, based on six years of data from 103 meteorological sounding stations in my country, statistically calculated national and regional distribution models of low-altitude atmospheric refractive index gradients and water vapor content gradients. In 1998, using sounding data from 1990-1992, the limiting frequencies and penetration angles of atmospheric waveguides in various parts of my country were calculated, and the occurrence probability and characteristic quantities of low-altitude atmospheric waveguides were statistically analyzed. In 2002, the division of terrestrial atmospheric waveguide climate zones in my country and the study of atmospheric waveguide variations with seasons and months were conducted, resulting in the creation of a map showing the distribution of terrestrial atmospheric waveguides in China. In 1996, Liu Chengguo, Pan Zhongwei, and others from the 22nd Research Institute of China Electronics Technology Group Corporation conducted statistical analysis on the probability of low-altitude atmospheric waveguide occurrence and waveguide characteristics in China, dividing the country's waveguide climate zones into four waveguide-frequented areas and four waveguide-free areas. This marked the beginning of nationwide waveguide research in my country. In 2002, Liu Chengguo, Huang Jiying, Jiang Changyin, and others conducted a month-long atmospheric waveguide structure detection experiment in southeastern coastal my country. Through data processing and analysis, they summarized the occurrence patterns of atmospheric waveguides in the region and analyzed the meteorological conditions and new weather patterns associated with their occurrence. From 2002 to 2011, the Key Laboratory of the China Institute of Radio Wave Propagation, through systematic data processing and theoretical research, established the first statistical distribution database (digital map) of my country's tropospheric radio wave environment. In 2017, Hu Ranran of the institute, based on the global database provided by the European Centre for Mesoscale Weather Forecasting (ECMWF), conducted a preliminary statistical analysis of the near-surface atmospheric refractive index gradient in my country and analyzed the impact of atmospheric refraction on the propagation distance of near-surface radio television in my country.

[0012] The above analysis shows that the statistics on near-surface or sea-surface 65m atmospheric refractive index gradients with a cumulative probability exceeding 1% in international ITU or domestic and international studies are based on spatiotemporally sparse meteorological sounding data from various stations, or early reanalysis data from the European Centre for Mesoscale Weather Prediction (ECMWF), such as ERA40 and ERA-I. The horizontal resolution and accuracy of these reanalysis data need improvement. Furthermore, with global warming, the statistical values ​​of near-surface or sea-surface 65m atmospheric refractive index gradients with a cumulative probability exceeding 1% using early data are no longer accurate, and their values ​​will change with climate change. The above studies also do not provide annual variations and forecasts for the annual average values ​​of near-surface or sea-surface 65m atmospheric refractive index gradients with a cumulative probability exceeding 1% over time, varying with climate and time.

[0013] The atmospheric refractive index environment is of significant scientific importance and practical value for assessing electromagnetic wave propagation. The complex variations in atmospheric refractive environment parameters over time and space lead to various electromagnetic wave propagation phenomena, such as propagation delay, waveguide propagation, scattering propagation, multipath propagation, signal fading, depolarization, and signal fluctuations. These directly affect the operational performance of information systems, including their range, detection probability, positioning accuracy, and communication quality. Atmospheric refractive index is a crucial factor influencing electromagnetic wave propagation, especially its distribution with altitude. Atmospheric waveguides, which propagate under anomalies in refractive index gradients, can alter the propagation path of electromagnetic waves, enabling radar to detect beyond line of sight or creating detection blind spots.

[0014] The atmospheric refractive index gradient at 65m above the near-surface or sea surface with a cumulative probability exceeding 1% over time is a crucial statistical parameter. This parameter requires extensive statistical analysis of the near-surface or sea surface atmospheric refractive index gradient over many years. Previously collected data were primarily from discrete stations, with a predominance of continental data and limited or nonexistent oceanic data, lacking an understanding of the global, particularly oceanic, radio wave environment. Therefore, obtaining the near-surface or sea surface atmospheric refractive index gradient with a cumulative probability exceeding 1% over time is very difficult globally, especially in oceanic regions (including the equatorial region).

[0015] In recent years, significant changes have occurred in the global climate, which in turn have affected the propagation characteristics of radio waves in relevant frequency bands. Existing atmospheric refractive index models supporting radio system design are based on observational data from many years ago, and their predictions differ significantly from current radio meteorological characteristics. This restricts the high-reliability design of radio systems in relevant frequency bands.

[0016] With the continuous development of high technology and computer technology, numerical simulation is becoming increasingly superior. Atmospheric numerical models have gradually become an important method for studying weather processes and regional tropospheric radio wave environment characteristics, especially in areas with no observational data on the vast ocean and land surface. Reanalysis grid data based on global numerical models and fusion of multiple data sources has emerged. Because it can cover the entire globe (including the sparsely dataed ocean) in the form of different grid spacings, and the daily time resolution is no more than 6 hours, it makes up for the shortcomings of traditional discrete station data such as uneven distribution and lack of data in some areas. Therefore, this data has advantages that other data cannot match.

[0017] There is currently no precedent for conducting statistical studies on the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability exceeding 1% based on the latest reanalysis data ERA5 over many years. Furthermore, there are no studies, estimates, or predictions on the interannual variation of this statistical value due to global warming, and no related patents have been formed. Summary of the Invention

[0018] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology in which the average value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% over time along the equator cannot reflect global warming and decadal changes, resulting in a serious deviation of its original average value. The present invention provides a method for estimating and predicting the annual average value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% over time along the equator.

[0019] The present invention adopts the following technical solution:

[0020] An improved method for estimating and predicting the annual average of near-surface or sea-surface atmospheric refractive index gradients exceeding a 1% cumulative probability over time includes the following steps:

[0021] Step 1: Based on the ERA5 reanalysis data from the European Centre for Mesoscale Weather Prediction, complete the statistical values ​​of the near-surface or sea-surface 65m atmospheric refractive index gradient for each grid point along the equator each year, representing the global cumulative probability of exceeding 1% over time.

[0022] Based on ERA5 reanalysis data from the European Centre for Mesoscale Weather Prediction, the atmospheric refractive index gradient parameters at 65m near the ground or sea surface were obtained for several years and several time periods. The horizontal resolution of the ERA5 reanalysis data is 0.25°, which means that the globe is divided into 720*1440 grid points, and along the equator, it is divided into 1*1440 grid points. Each grid point contains temperature, air pressure, and humidity at different altitudes. Using the temperature, air pressure, and humidity at each altitude of the grid point directly provided by the ERA5 reanalysis data, the atmospheric refractive index value at each altitude was calculated based on the atmospheric refractive index calculation formula. Then, the atmospheric refractive index gradient parameters at 65m near the ground or sea surface for each grid point at each time period were obtained by altitude interpolation.

[0023] For a single grid point, the atmospheric refractive index gradient parameters at 65m near the ground or sea surface are accumulated and statistically analyzed for each time of the year to form a statistical value that exceeds the time accumulation probability of 1%. This process is repeated to obtain the annual statistical values ​​of the atmospheric refractive index gradient at 65m near the ground or sea surface for 1*1440 grid points along the equator that exceed the time accumulation probability of 1%.

[0024] Step 2: Based on the statistical values ​​of each grid point along the equator each year, calculate the arithmetic mean of the statistical values ​​of all grid points along the equator to form the annual average value along the equator. Then, fit this value to the trend to form a quadratic polynomial:

[0025] The fitted quadratic polynomial is in the following form:

[0026] y = ax 2 +bx+c

[0027] In the above formula, x and y are the annual average values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface with a cumulative probability of 1% above the time at the center and scale of the predicted data after regularization, respectively. a, b, and c are the coefficients of the corresponding formula.

[0028] The relationship between the center and the proportion of the regularized predicted data and the unprocessed year x1 is as follows:

[0029] x=(x1-mu) / std

[0030] In the above formula, mu and std are the mean and standard deviation of x1, respectively;

[0031] Step 3: Based on the fitted quadratic polynomial of the annual average value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% exceeding the equator, given the year x of interest, the annual average value y of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% exceeding the equator can be estimated or predicted.

[0032] Furthermore, the number of years in step 1 shall not be less than 6 years.

[0033] The beneficial effects of this invention are:

[0034] The method disclosed in this invention performs a detailed analysis of the spatiotemporal distribution characteristics of the global atmospheric refractive environment based on the newly developed, refined global reanalysis data ERA5. Both the resolution and accuracy are significantly improved compared to previous reanalysis data such as FNL, ERA-40, and ERA-I, with a grid spacing resolution of 0.25°. On the one hand, it solves the problem of insufficient spatiotemporal resolution and accuracy of data sources (early reanalysis data and meteorological sounding station data) for obtaining statistical values ​​of the near-surface or sea-surface 65m atmospheric refractive index gradient with a time-cumulative probability exceeding 1%. No one has yet used this data to obtain refractive index statistics. On the other hand, it can estimate and predict the annual average value of the near-surface or sea-surface 65m atmospheric refractive index gradient with a time-cumulative probability exceeding 1% in a given year under the background of global warming. With global warming, the statistical values ​​of the near-surface or sea-surface 65m atmospheric refractive index gradient with a time-cumulative probability exceeding 1% obtained using earlier data are no longer accurate, and their values ​​also change with climate change. The statistical parameters obtained by the method of this invention, which are more representative of climate change and more accurate, can provide more reliable support for the planning and design of radio information systems in hotspot areas, and alleviate the contradictions that restrict the high reliability design of radio systems in relevant frequency bands. It is of great significance for estimating the global radio wave propagation effect and assessing its impact on radio information systems, mobile communication systems, navigation and positioning systems, radar systems and other systems operating in different frequency bands. Attached Figure Description

[0035] Figure 1 This is a map showing the annual average distribution of the atmospheric refractive index gradient at 65m above the ground or sea surface along the equator with a cumulative probability of 1% over time from 1981 to 2020.

[0036] Figure 2 This is a map showing the annual average distribution of the atmospheric refractive index gradient at 65m above the ground or sea surface along the equator with a cumulative probability of 1% over time from 1981 to 2019. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0038] The technical solution of this invention is based on the inventor's own research results (the statistical value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% over time (annual average value) shows a certain annual variation pattern). Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), the statistical value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% over time for each grid point along the equator is obtained. By averaging the statistical values ​​of all grid points along the equator for each year, a quadratic polynomial fitting is performed according to the trend change. Based on the fitted polynomial, the annual average value of the statistical value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% over time for the equator is estimated and predicted for the year of interest.

[0039] As is well known, ERA5 reanalysis data is a newly developed dataset, offering significant improvements in both resolution and accuracy compared to previous reanalysis datasets such as FNL, ERA-40, and ERA-I, with a grid spacing resolution of 0.25°. This dataset represents a major upgrade from its predecessor, ERA-I. Firstly, it boasts a substantial increase in spatiotemporal resolution. Secondly, ERA5 is the first to utilize ensemble reanalysis products to assess atmospheric uncertainties. This new function, based on the data assimilation ensemble system developed by ECMWF, can explain errors in observational and forecasting models, giving users greater confidence when analyzing atmospheric parameters at different times and locations. Thirdly, ERA5 incorporates more historical observational data, especially satellite data, into its advanced data assimilation and modeling systems to estimate more accurate atmospheric conditions.

[0040] The present invention discloses a method for estimating and predicting the annual average value of near-surface or sea-surface atmospheric refractive index gradients exceeding a cumulative probability of 1% over time, comprising the following steps:

[0041] Step 1: Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), complete the statistical values ​​of the near-surface or sea-surface 65m atmospheric refractive index gradient for each grid point along the equator each year, based on the cumulative probability of exceeding 1% over time.

[0042] Based on ERA5 reanalysis data from the European Centre for Mesoscale Weather Prediction, near-surface or sea-surface atmospheric refractive index gradient parameters at 65m depth are obtained for several years and at several time periods. The horizontal resolution of the ERA5 reanalysis data is 0.25°, meaning that the globe is divided into 720*1440 grid points, and along the equator, it is divided into n*1440 grid points (the value of n depends on the width of the area along the north and south latitudes, generally taken as 1). Each grid point contains meteorological parameters such as temperature, air pressure, and humidity at different altitudes. Using the temperature, air pressure, and humidity at each altitude of the grid point directly provided by the ERA5 reanalysis data, the atmospheric refractive index values ​​at each altitude are calculated based on the atmospheric refractive index calculation formula. Then, the near-surface or sea-surface 65m atmospheric refractive index gradient parameters for each grid point at each time period are obtained through altitude interpolation. The data structure, large refractive index calculation formula, and interpolation formula of the ERA5 reanalysis data are well-known public models and techniques, and will not be elaborated here.

[0043] After obtaining the atmospheric refractive index gradient parameters at 65m near the ground or sea surface for each grid point at each time interval over many years (depending on the data collection period; the longer the data period, the more accurate the binomial will be, generally no less than 6 years), the statistical value of the atmospheric refractive index gradient at 65m near the ground or sea surface for each grid point exceeding the cumulative probability of 1% over time can be obtained year by year.

[0044] For a single grid point, the atmospheric refractive index gradient parameters at 65m near the ground or sea surface are accumulated and statistically analyzed for each time period of the year, forming a statistical value with a cumulative probability exceeding 1% over time. This process is repeated to obtain the annual statistical values ​​of the atmospheric refractive index gradient at 65m near the ground or sea surface for 1*1440 grid points along the equator with a cumulative probability exceeding 1% over time. The specific method for calculating the statistical value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability exceeding 1% over time is a well-known and publicly available method, and will not be elaborated here.

[0045] Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), the statistical values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface for each grid point with a cumulative probability of 1% over time have been completed annually, which is something that has never been explored before.

[0046] Step 2: Based on the statistical values ​​of each grid point along the equator each year, calculate the arithmetic mean of the statistical values ​​of all grid points along the equator to form the annual average value along the equator. Then, fit this value to the trend to form a quadratic polynomial:

[0047] After calculating the statistical values ​​of the atmospheric refractive index gradient at 65m above the near-surface or sea surface for each of the 1*1440 grid points along the equator with a cumulative probability exceeding 1% annually, an arithmetic mean was calculated for the statistical values ​​at each grid point along the equator each year, forming the annual average value for the equator. This is because this area contains both ocean and land, has abundant and representative observational data, and because the values ​​at each grid point along the 360° meridian within the same year vary relatively little, the average value can represent the annual changes along the equator primarily caused by climate change.

[0048] For the grid points generated by ERA5 reanalysis data with a horizontal resolution of 0.25°, the 0.125°N zonal grid points are the closest to the equator. The annual average value along the equator is obtained by arithmetically averaging the statistical values ​​of each grid point along the equator from the 0.125°N zonal grid points. Figure 1 This is a scatter plot showing the annual average distribution of the 0.125°N zonal atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability exceeding 1% over time (data for 40 years, 1981-2020). It represents the annual variation of the annual average of the near-surface or sea-surface atmospheric refractive index gradient at 65m near the equator with a cumulative probability exceeding 1% over time. The plot shows that with global warming, the value of the near-surface or sea-surface atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability exceeding 1% over time gradually increases with age, indicating that global climate change has a significant impact on the radio wave environment. Therefore, the demonstration and assessment of related radio wave propagation must use new time-limited data. The annual variation trend is very obvious in the plot. The center and proportion of the data can be predicted by regularization, and a quadratic polynomial can be fitted. The fitted quadratic polynomial is as follows:

[0049] y = ax 2 +bx+c

[0050] In the above formula, x and y are the annual average values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface with a cumulative probability of 1% above the time at the center and scale of the predicted data after regularization, respectively. a, b, and c are the coefficients of the corresponding formula.

[0051] The relationship between the center and the proportion of the regularized predicted data and the unprocessed year x1 is as follows:

[0052] x=(x1-mu) / std

[0053] In the above formula, mu and std are the mean and standard deviation of x1, respectively; the techniques for centering and scaling of regularized forecast data are well-known and will not be elaborated here.

[0054] Step 3: Based on the fitted quadratic polynomial of the annual average value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% exceeding the equator, given the year x of interest, the annual average value y of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% exceeding the equator can be estimated or predicted.

[0055] The following are two examples. Example 1 estimates the annual average of the atmospheric refractive index gradient at 65m near the ground or sea surface along the equator for any year of interest within the 1981-2019 period, specifically 2005, with a cumulative time probability exceeding 1%. Example 2 predicts the future year of interest, 2020, outside the 1981-2019 period, by obtaining the annual average of the atmospheric refractive index gradient at 65m near the ground or sea surface along the equator with a cumulative time probability exceeding 1%.

[0056] Example 1:

[0057] Step 1: Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), complete the statistical values ​​of the atmospheric refractive index gradient at 65m near the ground or sea surface for each grid point along the equator for each year, with a cumulative probability of more than 1% over time.

[0058] Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), this study obtains near-surface or sea-surface 65m atmospheric refractive index gradient parameters at 00, 06, 12, 18, and 24 UTC for 39 years (1981-2019). The ERA5 reanalysis data has a horizontal resolution of 0.25°, meaning the globe is divided into 720*1440 grid points, and along the equator, it can be further divided into n*1440 grid points (n is determined by the width of the area along the north-south latitude, typically 1). Each grid point contains meteorological parameters such as temperature, humidity, and pressure at different altitudes. The near-surface or sea-surface 65m atmospheric refractive index gradient parameters for each grid point at each time point can be obtained directly from the atmospheric temperature, pressure, and humidity at each altitude layer provided by the ERA5 reanalysis data. The maximum refractive index values ​​at each altitude are calculated using the maximum refractive index calculation formula and then obtained through altitude interpolation. The data structure, high refractive index calculation formula, and interpolation formula of ERA5 reanalysis data are well-known public models and techniques, and will not be elaborated here.

[0059] After obtaining the atmospheric refractive index gradient parameters at 00:00, 06:00, 12:00, 18:00, and 24:00 UTC for 39 years (1981-2019), the statistical value of the near-surface or sea-surface atmospheric refractive index gradient exceeding the 1% cumulative probability over time for each grid point can be calculated annually. For a single grid point, the near-surface or sea-surface atmospheric refractive index gradient parameters at 65m for each time of the year are accumulated and statistically analyzed to form a statistical value exceeding the 1% cumulative probability over time. This process is repeated to obtain the annual statistical value of the near-surface or sea-surface atmospheric refractive index gradient exceeding the 1% cumulative probability over time for 1*1440 grid points along the equator. The specific method for calculating the statistical value of the near-surface or sea-surface atmospheric refractive index gradient exceeding the 1% cumulative probability over time is a well-known and publicly available method, and will not be elaborated here.

[0060] Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), the statistical values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface for each grid point exceeding the cumulative probability of 1% over time are unprecedented.

[0061] Step 2: Based on the statistical values ​​of the atmospheric refractive index gradient at 65m near the ground or sea surface that exceed the cumulative probability of 1% for each grid point along the equator each year, the arithmetic mean of the statistical values ​​of each grid point along the equator is calculated to form the total annual average value along the equator each year. Based on this, a quadratic polynomial fitting is performed according to the trend change to form a polynomial.

[0062] After calculating the statistical values ​​of the atmospheric refractive index gradient at 65m above the near-surface or sea surface for each of the 1*1440 grid points along the equator with a cumulative probability exceeding 1% annually, an arithmetic mean was calculated for the statistical values ​​at each grid point along the equator each year, forming the annual average value for the equator. This is because this area contains both ocean and land, has abundant and representative observational data, and because the values ​​at each grid point along the 360° meridian within the same year at this location show relatively small variations. Therefore, the average value can represent the annual changes along the equator primarily caused by climate change.

[0063] For the grid points generated by ERA5 reanalysis data with a horizontal resolution of 0.25°, the 0.125°N zonal grid points are the closest to the equator. The annual average value along the equator is obtained by arithmetically averaging the statistical values ​​of each grid point along the equator from the 0.125°N zonal grid points. Figure 2This is a scatter plot showing the annual distribution of the statistical values ​​of the near-surface or sea-surface 65m atmospheric refractive index gradient exceeding the 1% cumulative probability over 39 years from 1981 to 2019 in the equatorial region (0.125°N). It represents the year-to-year variation of the annual average of the near-surface or sea-surface 65m atmospheric refractive index gradient exceeding the 1% cumulative probability near the equator. The plot shows that with global warming, the near-surface or sea-surface 65m atmospheric refractive index gradient value exceeding the 1% cumulative probability gradually increases over time, indicating that global climate change has a significant impact on the radio wave environment. Therefore, the demonstration and assessment of related radio wave propagation must use new time-limited data. Figure 2 The annual variation trend is very obvious. The center and proportion of the data can be predicted by regularization, and a quadratic polynomial can be fitted to obtain the quadratic polynomial.

[0064] Based on the annual average distribution of statistical data from 1981 to 2019, a quadratic polynomial was fitted, yielding the following quadratic polynomial form:

[0065] y = -0.139x 2 -0.9745x-12.92

[0066] In the above formula, x and y are the annual average values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface with a cumulative probability of 1% exceeding the time limit at 0.125°N in the equatorial region corresponding to the year after the center and scale of the predicted data through regularization.

[0067] The relationship between the center and the proportion of the regularized predicted data and the unprocessed year x1 is as follows:

[0068] x=(x1-mu) / std

[0069] In the above formula, mu and std are the mean and standard deviation of x1, respectively, with values ​​of 2000 and 11.4. The techniques for centering and scaling regularized forecast data are well-known and will not be elaborated upon here.

[0070] Step 3: Based on the fitted quadratic polynomial, give the estimated and predicted years of interest, and obtain the estimated or predicted annual average of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% or more along the equator.

[0071] Based on the fitted binomial formula for the annual average value of the near-surface or sea-surface 65m atmospheric refractive index gradient with a cumulative probability of 1% exceeding the equatorial range, and given the year of interest x, the annual average value y of the near-surface or sea-surface 65m atmospheric refractive index gradient with a cumulative probability of 1% exceeding the equatorial range x can be estimated. For example, if x1 = 2005, then after conversion x = 0.4386, the estimated value y according to the binomial formula is -13.4 N / km. Compared with the actual annual average value of the parameter in 2005, -14.0 N / km, the difference is only 0.6 N / km. It can be seen that this embodiment can estimate the annual change value caused by climate change along the equatorial range with a certain degree of accuracy.

[0072] Example 2:

[0073] Step 1: Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), complete the statistical values ​​of the atmospheric refractive index gradient at 65m near the ground or sea surface for each grid point along the equator for each year, with a cumulative probability of more than 1% over time.

[0074] Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), the atmospheric refractive index gradient parameters at 65m near the surface or sea surface were obtained at 00, 06, 12, 18, and 24 UTC for 40 years (1981-2020). The 2020 data was obtained here, and its annual average value was calculated as the true value for comparison with the predicted values ​​of 2020 for future years outside the 1981-2019 period. The ERA5 reanalysis data has a horizontal resolution of 0.25°, meaning the globe is divided into 720*1440 grid points. Along the equator, it can be further divided into n*1440 grid points (where n depends on the width of the latitudinal region, typically 1). Each grid point contains meteorological parameters such as temperature, humidity, and pressure at different altitudes. The atmospheric refractive index gradient parameter at 65m near the ground or sea surface for each grid point at each time interval can be obtained directly from the atmospheric temperature, pressure, and humidity at each altitude layer provided by the ERA5 reanalysis data. The maximum refractive index value at each altitude is calculated using the maximum refractive index calculation formula and then obtained through altitude interpolation. The data structure, maximum refractive index calculation formula, and interpolation formula of the ERA5 reanalysis data are well-known public models and techniques, and will not be elaborated upon here.

[0075] After obtaining the atmospheric refractive index gradient parameters at 00:00, 06:00, 12:00, 18:00, and 24:00 UTC for 40 years (1981-2020), the statistical value of the near-surface or sea-surface atmospheric refractive index gradient exceeding the 1% cumulative probability over time for each grid point can be calculated annually. For a single grid point, the near-surface or sea-surface atmospheric refractive index gradient parameters at 65m for each time of the year are accumulated and statistically analyzed to form a statistical value exceeding the 1% cumulative probability over time. This process is repeated to obtain the annual statistical value of the near-surface or sea-surface atmospheric refractive index gradient exceeding the 1% cumulative probability over time for 1*1440 grid points in the equatorial region. The specific method for calculating the statistical value of the near-surface or sea-surface atmospheric refractive index gradient exceeding the 1% cumulative probability over time is a well-known method and will not be elaborated here.

[0076] Based on the latest ERA5 reanalysis data developed by the European Centre for Mesoscale Weather Prediction (ECMWF), the statistical values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface for each grid point with a cumulative probability of 1% over time have been completed annually, which is something that has never been explored before.

[0077] Step 2: Based on the statistical values ​​of the atmospheric refractive index gradient at 65m near the ground or sea surface that exceed the cumulative probability of 1% for each grid point along the equator each year, the arithmetic mean of the statistical values ​​of each grid point along the equator is calculated to form the total annual average value along the equator each year. Based on this, a quadratic polynomial fitting is performed according to the trend change to form a polynomial.

[0078] After calculating the statistical values ​​of the atmospheric refractive index gradient at 65m above the near-surface or sea surface for each of the 1*1440 grid points along the equator with a cumulative probability exceeding 1% annually, an arithmetic mean was calculated for the statistical values ​​at each grid point along the equator each year, forming the annual average value for the equator. This is because this area contains both ocean and land, has abundant and representative observational data, and because the values ​​at each grid point along the 360° meridian within the same year at this location show relatively small variations. Therefore, the average value can represent the annual changes along the equator primarily caused by climate change.

[0079] For the grid points generated by ERA5 reanalysis data with a horizontal resolution of 0.25°, the 0.125°N zonal grid points are the closest to the equator. The annual average value along the equator is obtained by arithmetically averaging the statistical values ​​of each grid point along the equator from the 0.125°N zonal grid points. Figure 2This is a scatter plot showing the annual distribution of the statistical values ​​of the near-surface or sea-surface 65m atmospheric refractive index gradient exceeding the 1% cumulative probability over 39 years from 1981 to 2019. It represents the year-to-year variation of the annual average of the near-surface or sea-surface 65m atmospheric refractive index gradient exceeding the 1% cumulative probability near the equator. The plot shows that with global warming, the near-surface or sea-surface 65m atmospheric refractive index gradient value exceeding the 1% cumulative probability gradually increases over time, indicating that global climate change has a significant impact on the radio wave environment. Therefore, the demonstration and assessment of related radio wave propagation must use new time-limited data. Figure 2 The annual variation trend is very obvious. The center and proportion of the data can be predicted by regularization, and a quadratic polynomial can be fitted to obtain the quadratic polynomial.

[0080] Based on the annual average distribution of statistical data from 1981 to 2019, a quadratic polynomial was fitted, yielding the following quadratic polynomial form:

[0081] y = -0.139x 2 -0.9745x-12.92

[0082] In the above formula, x and y are the annual average values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface with a cumulative probability of 1% above the time at the center and scale of the predicted data after regularization, respectively.

[0083] The relationship between the center and the proportion of the regularized predicted data and the unprocessed year x1 is as follows:

[0084] x=(x1-mu) / std

[0085] In the above formula, mu and std are the mean and standard deviation of x1, respectively, with values ​​of 2000 and 11.4.

[0086] The annual average of the 2020 data statistics is calculated and used as the true value for comparison with the predicted values ​​of future years outside the 1981-2019 period. The techniques for centering and scaling the regularized forecast data are well-known and will not be elaborated upon here.

[0087] Step 3: Based on the fitted quadratic polynomial, give the predicted future year of interest, 2020 (in this embodiment, the selected future year is 2020), and obtain the annual average of the predicted year of interest, 2020, for the near-surface or sea surface 65m atmospheric refractive index gradient with a cumulative probability of 1% over time along the equator.

[0088] Based on the fitted annual average of the near-surface or sea-surface 65m atmospheric refractive index gradient with a cumulative probability of 1% exceeding the equator over time and the correlation binomial of the year, given the year of interest 2020, the annual average of the near-surface or sea-surface 65m atmospheric refractive index gradient with a cumulative probability of 1% exceeding the equator over time, y, can be predicted for future years of interest x.

[0089] For example, if we take x1 = 2020, then after conversion, x = 1.7544. According to the binomial formula, the predicted y = -15.1 N / km. Compared with the actual annual average of the parameter in 2020, -16.5 N / km, the difference is only 1.4 N / km. It can be seen that this embodiment can predict the annual change value caused by climate change along the equator, and the accuracy is guaranteed to a certain extent.

Claims

1. A method for estimating and predicting the annual average of near-surface or sea-surface atmospheric refractive index gradients exceeding a time-cumulative probability of 1%, characterized in that, Includes the following steps: Step 1: Based on the ERA5 reanalysis data from the European Centre for Mesoscale Weather Prediction, complete the statistical values ​​of the near-surface or sea-surface 65m atmospheric refractive index gradient for each grid point along the equator each year, representing the global cumulative probability of exceeding 1% over time. Based on ERA5 reanalysis data from the European Centre for Mesoscale Weather Prediction, the atmospheric refractive index gradient parameters at 65m near the ground or sea surface were obtained for several years and several time periods. The horizontal resolution of the ERA5 reanalysis data is 0.25°, which means that the globe is divided into 720*1440 grid points, and along the equator, it is divided into 1*1440 grid points. Each grid point contains temperature, air pressure, and humidity at different altitudes. Using the temperature, air pressure, and humidity at each altitude of the grid point directly provided by the ERA5 reanalysis data, the atmospheric refractive index value at each altitude was calculated based on the atmospheric refractive index calculation formula. Then, the atmospheric refractive index gradient parameters at 65m near the ground or sea surface for each grid point at each time period were obtained by altitude interpolation. For a single grid point, the atmospheric refractive index gradient parameters at 65m near the ground or sea surface are accumulated and statistically analyzed for each time of the year to form a statistical value that exceeds the time accumulation probability of 1%. This process is repeated to obtain the annual statistical values ​​of the atmospheric refractive index gradient at 65m near the ground or sea surface for 1*1440 grid points along the equator that exceed the time accumulation probability of 1%. Step 2: Based on the statistical values ​​of each grid point along the equator each year, calculate the arithmetic mean of the statistical values ​​of all grid points along the equator to form the annual average value along the equator. Then, fit this value to the trend to form a quadratic polynomial: The fitted quadratic polynomial is in the following form: y=ax 2 +bx+c In the above formula, x and y are the annual average values ​​of the atmospheric refractive index gradient at 65m above the ground or sea surface with a cumulative probability of 1% above the time at the center and scale of the predicted data after regularization, respectively. a, b, and c are the coefficients of the corresponding formula. The relationship between the center and the proportion of the regularized predicted data and the unprocessed year x1 is as follows: x=(x1-mu) / std In the above formula, mu and std are the mean and standard deviation of x1, respectively; Step 3: Based on the fitted quadratic polynomial of the annual average value of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% exceeding the equator, given the year x of interest, the annual average value y of the atmospheric refractive index gradient at 65m near the ground or sea surface with a cumulative probability of 1% exceeding the equator can be estimated or predicted.

2. The method for estimating and predicting the annual average value of the near-surface or sea-surface atmospheric refractive index gradient exceeding a time-cumulative probability of 1% as described in claim 1, characterized in that: The number of years in step 1 shall not be less than 6 years.

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