A method for predicting atmospheric visibility based on physical diagnostic model

Abstract

This paper discloses a method for predicting atmospheric visibility based on a physical diagnostic model. This method, based on a physical diagnostic model in fog, analyzes visibility and can generate visibility forecasts based on various mainstream numerical model products, such as the Global Forecasting System (GFS) and the European Central Meteorological Organization (ECMWF). This method boasts fast computational speed, minimal storage requirements, the absence of a large sample size, and strong scalability, providing theoretical and technical support for the development of refined fog forecasting and early warning technologies.

Description

Technical Field

[0001] The present invention belongs to the technical field of meteorological disaster prevention, and in particular relates to an atmospheric visibility prediction method. Background Art

[0002] Fog is a typical low-visibility weather phenomenon that forms suddenly and develops rapidly, severely impacting transportation and causing disasters and economic losses. With the improvement of atmospheric science theories and the development of computer technology, numerical models have been widely used to simulate and forecast fog. Current operational numerical forecast models typically do not output fog and visibility, requiring statistical methods or artificial intelligence to calculate visibility. Establishing statistical or artificial intelligence models requires a large amount of historical observation and forecast product data as training samples to obtain accurate visibility calculations, which consumes significant computing and storage resources, and cannot guarantee satisfactory results from a single training session. When applying an existing statistical or artificial intelligence model to another numerical model product, retraining is also required, significantly increasing the R&D cycle of numerical product fog forecasting technology.

[0003] At present, statistical models and artificial intelligence models are generally used in existing technologies to output visibility forecasts, and it is not possible to directly establish and obtain ground visibility forecast output results based on numerical forecast products. Summary of the Invention

[0004] Purpose of the Invention: To address the aforementioned existing problems and shortcomings, the present invention provides a method for predicting atmospheric visibility based on a physical diagnostic model. Based on the fog physics diagnostic equation, the present invention analytically derives a visibility model. This model, applied to mainstream numerical model products such as the Global Forecasting System (GFS) and the European Central Meteorological Organization (ECMWF), can produce visibility forecasts. This method offers the advantages of fast computational speed, minimal storage requirements, the absence of a large sample size, and strong scalability, providing theoretical and technical support for the development of refined fog forecasting and early warning technologies.

[0005] Technical solution: To achieve the above-mentioned purpose, the present invention adopts the following technical solution: a method for predicting atmospheric visibility based on a physical diagnostic model, comprising the following steps:

[0006] S1, obtaining numerical model forecast product data, including surface meteorological elements and isobaric surface meteorological elements, wherein the surface meteorological elements include temperature, dew point, 10m wind speed, and air pressure, and the isobaric surface meteorological elements include temperature, absolute humidity, wind speed, and geopotential height;

[0007] S2: Construct a fog path variation model. Considering the influence of temperature changes and surface droplet deposition on the fog path, a differential equation for the time-varying fog path is established. Based on the linear relationship between the fog path and ground fog concentration in meteorological studies, algebraic equations for the time-varying rate of the fog path and ground fog concentration are established, respectively. These two equations are then combined to obtain an ordinary differential equation for the time-varying fog concentration q.

[0008] S3, assuming that the initial fog concentration q1 = 0, the fog concentration q at the n+1th moment is obtained based on the ordinary differential equation of the fog concentration in step S2 n+1 , and the visibility VISn+1 at the n+1th moment is obtained by the following formula:

[0009] .

[0010] Furthermore, the ordinary differential equation of the time-varying mist concentration q in step S2 is as follows:

[0011] ,

[0012] Where α is the fog settling rate constant, which is 0.062, H is the fog top height, and β represents the amount of water vapor condensation caused by temperature drop.

[0013] Furthermore, the mist concentration qn+1 in step S3 is obtained by the following formula:

[0014] ,

[0015] And when season ;

[0016] In the above formula, It represents the amount of water vapor condensation caused by the temperature drop at the nth moment; Indicates the relative size of water vapor condensation and fog water deposition at the nth moment, Indicates the height of the fog top at the nth moment.

[0017] Furthermore, the amount of water vapor condensed due to the temperature drop at the nth moment is and the relative size of water vapor condensation and fog deposition λ n , are calculated by the following formulas:

[0018] ,

[0019] Where Lv represents the latent heat constant of water vapor condensation, which is 2.5×10 6J / kg; Rv represents the water vapor ratio gas constant, which is 461.5 J / kg; α is the fog water deposition rate constant, which is 0.062; basic meteorological quantities include air pressure p, temperature T, 1000 hPa isobaric surface height z1000 hPa, and time interval Δt, all of which can be directly read from numerical forecast products;

[0020] represents the condensation rate function with respect to air pressure p and T;

[0021] β n represents the amount of water vapor condensation caused by the temperature drop at the nth moment, λ n Indicates the relative size of water vapor condensation and fog water deposition at the nth moment, and are the condensation rate functions at 1000 hPa and the ground, respectively. and Respectively represent the temperature change values ​​at 1000hPa and the ground. and Respectively represent the temperature at 1000hPa at the n+1th moment and the nth moment, and Represent the ground temperature at the n+1th moment and the nth moment respectively.

[0022] Furthermore, the numerical model forecast product data in step S1 is collected from the ECMWF model, and the spatial resolution of the product data is 0.25 ∘ ×0.25 ∘ , select surface, 1000hPa, 925hPa, 850hPa, 500hPa for vertical levels; the forecast time interval is 3h, select forecast product data at 12, 15, 18, 21, 24, 27, 30 o'clock.

[0023] Beneficial Effects: Compared with existing technologies, this method uses a fog physics diagnostic model to derive a visibility model. This model, applied to mainstream numerical model products such as the Global Forecasting System (GFS) and the European Central Meteorological Organization (ECMWF), can produce visibility forecasts. This method offers the advantages of fast computational speed, minimal storage requirements, a lack of sample size, and strong scalability, providing theoretical and technical support for the development of refined fog forecasting and warning technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a flow chart of the atmospheric visibility prediction method based on the physical diagnostic model described in the present invention. DETAILED DESCRIPTION

[0025] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0026] This method establishes a physical diagnostic model for fog based on various numerical models, such as the Global Forecasting System (GFS) and the European Conference on Meteorological and Molecular Observation (ECMWF). This model simulates and predicts visibility forecasts, eliminating the need for extensive historical samples and minimizing computational and storage requirements. The method is applicable not only to mainstream numerical model products like the GFS and ECMWF, but also to any other numerical model products, saving significant computational and storage resources.

[0027] like Figure 1 As shown, the present invention innovatively proposes an atmospheric visibility prediction method based on a physical diagnostic model. The specific process steps are as follows:

[0028] S1, obtain numerical model forecast product data

[0029] (1) Taking the ECMWF model as an example, the corresponding data are obtained based on the current forecast time. The product data is in GRIB format, covers the entire world, has a spatial resolution of 0.25°×0.25°, and selects the surface, 1000 hPa, 925 hPa, 850 hPa, and 500 hPa vertical levels. The forecast time interval is 3 hours, and the forecasts for 12, 15, 18, 21, 24, 27, and 30 o'clock are selected. The variables are selected as surface meteorological elements (temperature, dew point, 10-meter wind speed, and air pressure) and isobaric surface meteorological elements (temperature, absolute humidity, wind speed, and geopotential height).

[0030] S2. Construct a model for the variation of the fog path (the total amount of fog concentration in the vertical direction). Considering the influence of temperature changes and surface droplet deposition on the fog path, establish a differential equation for the variation of the fog path over time. Based on the linear relationship between the fog path and ground fog concentration established in meteorological research, establish an algebraic equation for the time rate of change of the fog path and ground fog concentration. Combine these two equations and eliminate the common term to obtain an ordinary differential equation for the variation of ground fog concentration q over time. The specific process is as follows:

[0031] First, establish the physical model of fog water concentration, as shown in the following formula:

[0032] ,

[0033] Where LWC(z) is the fog water concentration at height z; K is the turbulent diffusion coefficient; α is the fog water settling rate constant (0.062); p and T represent the air pressure and temperature, respectively; γ is the condensation rate function with respect to p and T; Lv represents the water vapor condensation latent heat constant (2.5×106 J / kg; Rv represents the specific gas constant of water vapor, which is 461.5 J / kg; C represents the rate of temperature change. The boundary conditions of the equation are 0 < z < H, where H is the fog top height, which can be defined as the maximum height above the ground where the relative humidity is continuously greater than 95%, and LWC(H) is fixed at 0.

[0034] The key of the equation lies in: the fog water concentration LWC(0) at the ground, denoted as q. The fog water concentration q is the quantity to be solved in the present invention, and it is a quantity that varies with time.

[0035] Integrate this equation vertically from 0 to H. The left - hand side term LWC(z) integrated gives the liquid water path LWP (the definition of LWP in meteorology, which represents the total amount of fog water concentration in the vertical direction); the first term on the right - hand side is turbulent diffusion. According to meteorological theory, it is assumed that turbulent diffusion only changes the vertical distribution of fog water and does not change the total amount of fog water. Therefore, this term is considered to be 0 after integration; the second term on the right - hand side After integration, with the boundary conditions LWC(0) = q and LWC(H) = 0, the result is easily obtained as -αq 2 ; the third term on the right - hand side After integration, it represents the amount of water vapor condensation caused by the temperature decrease of the whole layer, denoted as β. Greater than 0 indicates condensation, and less than 0 indicates evaporation.

[0036] .

[0037] Since the fog layer is usually thin and its occurrence range is basically from the ground to the 1000 hPa height, the integration range is replaced by the surface to 1000 hPa. γ and C are represented by the averages of these two layers. C represents the rate of temperature change and is calculated using the temperature change values of two adjacent moments. Therefore, β is calculated by the following formula

[0038] ,

[0039] where γ 1000hpa and γ sfc respectively represent the condensation rate values at 1000 hPa and the ground, ΔT represents the temperature change value between two adjacent moments, ΔT 1000hpa and ΔT sfc respectively represent the ΔT at 1000 hPa and the ground, Δt is the time interval, and z 1000hpa is the 1000 hPa height.

[0040] After the above - mentioned processing, the equation (1) is obtained, and combined with the model of the liquid water path (LWP) and the ground fog water concentration (q) (as shown in Equation 2),

[0041] (1)

[0042] (2)

[0043] Among them, the adiabatic parameter a eq and function Γ ad These two quantities will not be used later. H is also the height of the fog top. Assuming that only the time variation of q is considered and the time variation of H and other variables is ignored, (1) and (2) are combined and the time derivative of equation (2) is obtained.

[0044] ,

[0045] The ordinary differential equation of the time-varying fog water concentration q is obtained, as shown in formula (3):

[0046] (3)

[0047] Equation (3) can be solved analytically for each time interval of the numerical forecast product. Let the forecast time of the numerical model be t1, t2, ..., t n , the interval is Δt, and the corresponding q is q1,q2,…,q n , and let q1 corresponding to the first moment t1 be 0. Taking t1 to t2 as an example, take q1 as the known quantity and q2 as the quantity to be solved, and calculate q2 according to the following detailed derivation steps. Then for t2 to t3, t3 to t4, ..., t n-1 to t n , using the same solution method, we can get q at all moments. The specific process is shown in step S3.

[0048] S3, for the ordinary differential equation obtained in S2, let the fog water concentration q1=0 (initial condition) at the first moment, and find the analytical solution to obtain the fog water concentration q at the next moment n+1 and the current q n The recursive relationship, and the visibility VIS at the corresponding moment n+1 The calculation is as follows:

[0049] ,

[0050] The intermediate variables are as follows:

[0051] ,

[0052] In the above formula, the constants include α, L v 、R v , L v The latent heat constant of water vapor condensation is 2.5×10 6 J / kg, R vrepresents the water vapor ratio gas constant of 461.5 J / kg, α is the fog deposition rate constant of 0.062; basic meteorological quantities include air pressure p, temperature T, 1000 hPa isobaric surface height z1000 hPa, and time interval Δt, all of which are variables that can be directly read in numerical forecast products; γ is a condensation rate function related to p and T in meteorology; the intermediate calculation quantity is 、 、 、 、 、 、 、 、 、 , , their subscript n represents the current moment, and n+1 represents the next moment, The meaning of is the amount of water vapor condensation caused by temperature drop. The meaning of is the relative size of water vapor condensation and fog water deposition. and Indicates the γ value at 1000hPa and the ground, and Indicates the temperature change value between 1000hPa and the ground. and Indicates the temperature at 1000hPa at the current moment n and the next moment n+1, and represents the ground temperature at the current time n and the next time n+1, H n is the fog top height, which can be defined as the maximum height from the ground where the relative humidity is continuously greater than 95%. The final result is q n+1 and VIS n+1 , indicating the fog concentration and visibility at the next moment.

[0053] Example: Based on the atmospheric visibility prediction method of the present invention, a heavy fog forecast for Hebei Province on December 29-30, 2023, was tested. The TS score of the fog forecast was quantitatively calculated. The results showed that the official visibility forecast from ECMWF had a TS score of only 0.17, while using the method of the present invention, the TS score increased to 0.38, indicating that the forecast and the measured visibility were significantly better.

[0054] This study developed a visibility prediction model based on numerical modeling and a physical diagnostic model for fog. This model was applied to mainstream numerical model products, such as the Global Forest Service (GFS) and the European Central Meteorological Organization (ECMWF), to generate visibility forecasts. This method offers the advantages of fast computational speed, minimal storage requirements, a lack of sample size, and strong scalability, providing theoretical and technical support for the development of refined fog forecasting and warning technologies.

[0055] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solutions and technical concepts of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for predicting atmospheric visibility based on a physical diagnostic model, characterized in that The following steps are involved: S1, obtaining numerical model forecast product data, including surface meteorological elements and isobaric surface meteorological elements, wherein the surface meteorological elements include temperature, dew point, 10m wind speed, and air pressure, and the isobaric surface meteorological elements include temperature, absolute humidity, wind speed, and geopotential height; S2: Construct a fog path variation model. Considering the influence of temperature changes and surface droplet deposition on the fog path, a differential equation for the time-varying fog path is established. Based on the linear relationship between the fog path and ground fog concentration in meteorological studies, algebraic equations for the time-varying rate of the fog path and ground fog concentration are established, respectively. These two equations are then combined to obtain an ordinary differential equation for the time-varying fog concentration q. S3, assuming that the initial fog concentration q1 = 0, the fog concentration q at the n+1th moment is obtained based on the ordinary differential equation of the fog concentration in step S2 n+1 , and the visibility VIS at the n+1th moment is obtained by the following formula n+1 , The ordinary differential equation of the time-varying mist concentration q in step S2 is as follows: Where α is the fog settling rate constant, which is 0.062, H is the fog top height, and β represents the amount of water vapor condensation caused by temperature drop.

2. The atmospheric visibility prediction method based on the physical diagnostic model according to claim 1 is characterized in that: The mist concentration q in step S3 n+1 It is obtained by the following formula: And when q n+1 When q n+1 =0; In the above formula, β n Indicates the amount of water vapor condensation caused by the temperature drop at the nth moment; λ n Indicates the relative size of water vapor condensation and fog water deposition at the nth moment, H n Indicates the height of the fog top at the nth moment.

3. The atmospheric visibility prediction method based on the physical diagnostic model according to claim 2 is characterized in that: The amount of water vapor condensation β caused by the temperature drop at the nth moment n and the relative size of water vapor condensation and fog deposition λ n , are calculated by the following formulas: Where, L v represents the latent heat constant of water vapor condensation, which is 2.5×10 6 J / kg; R v represents the water vapor ratio gas constant, which is 461.5 J / kg; α is the fog water deposition rate constant, which is 0.062; Basic meteorological quantities include air pressure p, temperature T, 1000hPa isobaric surface height z1000hPa, and time interval Δt, all of which can be directly read from numerical forecast products; γ(p,T) represents the condensation rate function with respect to air pressure p and T; β n represents the amount of water vapor condensation caused by the temperature drop at the nth moment, λ n Indicates the relative size of water vapor condensation and fog water deposition at the nth moment, and are the condensation rate functions at 1000 hPa and the ground, respectively. and Respectively represent the temperature change values ​​at 1000hPa and the ground. and Respectively represent the temperature at 1000hPa at the n+1th moment and the nth moment, and Represent the ground temperature at the n+1th moment and the nth moment respectively.

4. The atmospheric visibility prediction method based on the physical diagnostic model according to claim 2 is characterized in that: The numerical model forecast product data described in step S1 is collected from the ECMWF model, the spatial resolution of the product data is 0.25°×0.25°, and the vertical levels are selected as surface, 1000hPa, 925hPa, 850hPa, and 500hPa; the forecast time interval is 3h, and the forecast product data at 12, 15, 18, 21, 24, 27, and 30 o'clock are selected.

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