A method for simulating hail growth trajectory

Abstract

The invention discloses a method for simulating the growth trajectory of hail, comprising calculating the movement trajectory of hail; calculating in detail the collision and merging of supercooled raindrops and raindrops, condensation, sublimation, melting and other processes of each hailstone according to an environmental field and a cloud microphysical field, as well as the process of unfrozen supercooled water on the surface of the hailstone penetrating into the gaps between the hailstones and falling off the surface of the hailstones, thereby predicting the parameter changes of the particle size, mass and density of the hailstones; the invention can reflect the influence of different environments and different parent storms on the diameter of hailstones, and is consistent with actual observation data, reflecting the accuracy of hail growth simulation.

Description

Technical Field

[0001] The invention relates to the technical field of hail growth trajectory simulation, and in particular to a hail growth trajectory simulation method. Background Art

[0002] In the field of meteorology and disaster prevention and mitigation, simulation of hail growth trajectory has always been a hot topic and difficulty in research. At present, the most commonly used hail growth trajectory simulation methods are mainly based on numerical weather prediction models (NWP). These models predict the formation, growth and movement trajectory of hail by solving the atmospheric dynamics equations and combining microphysical process parameterization schemes. Although such methods can simulate the basic characteristics of hail to a certain extent, they still have significant deficiencies in dealing with the complex physical mechanisms in the growth process of hail (such as the interaction between hail and surrounding water vapor, updrafts and other particles). When simulating the growth trajectory of hail, the existing NWP models are often difficult to accurately capture the key physical processes of hail growth due to computational resource limitations and simplified physical processes, resulting in a large deviation between the simulation results and the actual situation. The complex numerical calculation process makes the output speed of the simulation results slow, which is difficult to meet the needs of real-time warning and decision support. The hail formation conditions in different regions are significantly different. When dealing with hail simulation in specific regions or under specific weather conditions, the existing models have a large workload of parameter adjustment and calibration, and are not adaptable.

[0003] When calculating the growth of hail through cold cloud droplets (hcm), existing methods usually use a relatively simplified model, which fails to fully consider the combined effects of cloud droplet size distribution, wind speed, and humidity environmental factors. The calculation of hail surface temperature is crucial for predicting the melting and splitting processes of hail, but existing methods often ignore the influence of internal heat conduction of hail and external environmental changes during calculation. In the process of hail growth, dry growth (i.e. hail growth in a moisture-free environment) is an important link, but existing technical solutions often fail to effectively judge and process it. Therefore, a method for simulating hail growth trajectory is needed. Summary of the invention

[0004] The purpose of the invention is to provide a method for simulating hail growth trajectory.

[0005] To achieve the above object, the present invention is implemented according to the following technical solutions:

[0006] The present invention comprises the following steps:

[0007] A Calculate hail particle trajectories by Lagrangian method;

[0008] B. Calculate various microphysical processes of hail based on environmental fields and microphysical fields, especially consider the wet growth and melting process of hail in detail, so as to predict parameters such as hail diameter, density, mass, surface supercooled water content, etc.

[0009] Specifically, when:

[0010] 1) Ambient temperature>=273.15K. Considering the melting process, if the water Mmelt melted out during the melting process exceeds the maximum water content Mcrit that the hail surface can withstand, the excess water will be thrown away, otherwise it will remain on the hail surface;

[0011] 2) When the temperature is less than 273.15K, first calculate the content hcw of the colliding supercooled cloud droplets and raindrops, and then recalculate the hail surface temperature Tsfc. If the hail surface temperature is still less than 273.15K, dry growth occurs, and then the condensation and sublimation process hdiff on the hail surface is calculated, and finally the mass and density of the hail are updated; if the calculated hail surface temperature Tsfc>273.15K, then Tsfc is set to 273.15, the hail undergoes wet growth, and the condensation and evaporation process hdiff on the hail surface is calculated. At the same time, the freezing rate Ff is calculated, and the mass and density of the supercooled water that can be frozen are updated to the mass and density of the hail, and then the unfrozen (1-Ff) supercooled water is considered; if there is still some left after filling the internal gaps of the hail, it is necessary to consider whether the remaining amount exceeds the maximum water content Mcrit on the hail surface, and the excess part is thrown away, otherwise it is retained on the hail surface, and the mass and density of the hail are updated.

[0012] Further, the parameter changes of the particle size, mass and density of the hail are predicted through the collision of the hail particles and the supercooling of raindrops and raindrops, condensation, sublimation, melting, immersion in the gaps of the hail and the shedding process;

[0013] The formula for the growth of hail collision and supercooled cloud droplets and raindrops is:

[0014]

[0015] in, is the change in hail mass per unit time, D h is the hail diameter, E cc and E cr are the collision efficiencies of hail droplets and raindrops, respectively, and v h and are the final falling velocity of hail and the mass-weighted falling velocity of raindrops, ω c and ω r are the mass contents of supercooled cloud droplets and raindrops, respectively;

[0016] The formula for calculating the final falling velocity of hail is:

[0017]

[0018] where ρ h is the density of hail, ρa is the air density, ρ a,0 is the reference air density, C D is the drag coefficient

[0019] The mass-weighted final falling velocity of a raindrop is:

[0020]

[0021] Where D r is the equivalent volume diameter of raindrops;

[0022] The formula for the growth of hailstones, ice crystals and snow is:

[0023]

[0024] where ω i is the total mass content of ice crystals and snow, E ci is the collision efficiency of hail ice crystals and snow, which is set to 1 under wet growth conditions and 0 under dry growth conditions.

[0025] The formula for the hail sublimation process is:

[0026]

[0027] Where Re is the Reynolds number, Sc is the Schmidt number, and D v is the diffusion coefficient of water vapor, χ is the conversion coefficient of heat and mass, ρ v,∞ is the water vapor density in the environment, ρ v,sfc is the water vapor density on the hail surface;

[0028] The calculation formula of hail surface temperature is:

[0029]

[0030] in, are the mass changes of the hail mentioned above through the collision of supercooled cloud droplets, raindrops, condensation and sublimation, collision of ice crystals and snow growth, respectively. f is the latent heat of freezing, F f is the freezing rate of supercooled cloud droplets and raindrops after collision, Pr is the Prandtl number, k t is the thermal diffusion coefficient of air, T ∞ is the ambient temperature;

[0031] The calculation formula of the freezing rate is:

[0032]

[0033] Among them, T0 is 273.15K.

[0034] Furthermore, when dry growth occurs, the calculation formula for hail density is: ρ rime =300A 0.44 , when A<1.6 and the surface temperature of the hail is below -5℃,

[0035] ρ rime =1000.0exp(-0.03115-1.7030A+0.9116A 2 -0.1224A 3 );

[0036] When wet growth occurs, the density of hail is: ρ ′ h =(1-0.08F f )F f ×10 3 ;

[0037] in D m,cloud is the average diameter of cloud droplets.

[0038] 4. The method for simulating hail growth trajectory according to claim 1 is characterized in that: when hail grows wetly, when unfrozen supercooled water can completely fill the internal gaps of the hail, the excess supercooled water will cover the surface of the hail, and the maximum supercooled water content that the hail surface can withstand has an upper limit, and if the upper limit is exceeded, the hail will fall off, and the formula for the upper limit of the supercooled water content is:

[0039] m w,crit =2.68×10 -4 kg+0.1390(m ice +m soaked )

[0040] Among them, m ice and m soaked It is the content of ice phase in hail and supercooled water that has penetrated into the internal gaps of hail.

[0041] Furthermore, in the movement of hail particles in the trajectory mode, the grid wind field is interpolated to the location of the particles. The particles move according to the wind field at their location, follow the horizontal wind in the horizontal direction, and move in the vertical wind direction according to the combined speed of the vertical speed and the final falling speed. The specific formula is as follows:

[0042] X t+1 =X t +U×dt

[0043] Y t+1 =Y t +V×dt

[0044] Z t+1 =Z t+(WV h )×dt

[0045] Among them, X, Y, Z are the three-dimensional positions of the hailstones, U, V, W are the three-dimensional wind speeds interpolated to the hailstones’ positions, and V h is the final velocity of the hailstone falling.

[0046] The beneficial effects of the present invention are:

[0047] 1. The present invention improves the accuracy and reliability of temperature judgment by comprehensively considering the complex influence of temperature on the growth rate and mode of hail.

[0048] 2. The present invention adopts a more sophisticated model to calculate hail growth, fully considering the combined effects of various environmental factors, thereby improving the accuracy and precision of hail growth simulation.

[0049] 3. The new heat conduction model of the present invention not only takes into account the influence of the external environment, but also takes into account the effect of heat conduction inside the hail, thereby more accurately calculating the temperature of the hail surface.

[0050] 4. The present invention monitors the humidity changes in the environment surrounding the hail and the state and mass changes of the hail itself, effectively determines whether the hail is in a wet growth state, and adjusts the relevant parameters in the growth model accordingly, thereby improving the integrity and accuracy of the hail growth simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a logic relationship diagram of a hail growth trajectory simulation method of the present invention;

[0052] Figure 2 It is a comparative schematic diagram of an implementation of a hail growth trajectory simulation method of the present invention;

[0053] in Figure 2 (a) Figure 2 (b) Figure 2 (c) Simulated pulse storm and Figure 2 (d) Figure 2 (e) Figure 2 (f) The trajectories of the simulated supercell hail. Figure 2 (a) Figure 2 (d) small hail, Figure 2 (b) and Figure 2 (e) large hailstones, Figure 2 (c) and Figure 2 (f) shows the overall situation. The color of the lines in the figure indicates the liquid water content of the environment in which the hail particles were located at that time.

[0054] Figure 3The present invention is a schematic diagram of a hail trajectory with a maximum diameter exceeding 10 mm, which is implemented in a hail growth trajectory simulation method.

[0055] in Figure 3 (a) is a three-dimensional trajectory diagram, Figure 3 (b) is the echo intensity and airflow structure; Figure 3 (c) is the distribution of supercooled water content; the white thin line is the hail trajectory, and the blue dot indicates the moment when the hail reaches the maximum diameter. DETAILED DESCRIPTION

[0056] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0057] Hail microphysical process flow Figure 1 As shown, the present invention includes the following steps:

[0058] A Calculate hail particle trajectories by Lagrangian method;

[0059] B. Calculate various microphysical processes of hail based on environmental fields and microphysical fields, especially consider the wet growth and melting process of hail in detail, so as to predict parameters such as hail diameter, density, mass, surface supercooled water content, etc.

[0060] The basic principle of the hail trajectory model is: in terms of dynamics, hail particles move horizontally following the wind field, and move vertically according to the vertical velocity and the terminal velocity of the hail falling.

[0061] The calculation of the microphysical process of hail is relatively complicated. First, we need to judge based on the ambient temperature.

[0062] 1) Ambient temperature>=273.15K. The melting process needs to be considered. If the water Mmelt melted out during the melting process exceeds the maximum water content Mcrit that the hail surface can withstand, the excess water will be thrown away, otherwise it will remain on the hail surface.

[0063] 2) When the temperature is <273.15K, first calculate the content hcw of colliding supercooled cloud droplets and raindrops, and then recalculate the hail surface temperature Tsfc. If the hail surface temperature is still <273.15K, dry growth will occur, and then calculate the condensation and sublimation process hdiff on the hail surface, and finally update the mass and density of the hail. If the calculated hail surface temperature Tsfc>273.15K, set Tsfc to 273.15, the hail will grow wetly, calculate the condensation and evaporation process hdiff on the hail surface, and calculate the freezing rate Ff at the same time, update the mass and density of the supercooled water that can be frozen to the mass and density of the hail, and then consider the unfrozen (1-Ff) supercooled water. First, the unfrozen supercooled water will penetrate into the internal gaps of the hail, and the mass and density of the hail will change accordingly. If there is any remaining water after filling the internal gaps of the hail, it is also necessary to consider whether the remaining water exceeds the maximum water content Mcrit on the surface of the hail. The excess water is thrown away. Otherwise, it remains on the surface of the hail, and the mass and density of the hail are updated.

[0064] (1) Hail collision and supercooled cloud droplets increase

[0065] The formula for the growth of hailstones, supercooled cloud droplets and raindrops is:

[0066]

[0067] in, is the change in hail mass per unit time, D h is the diameter of the hailstone, E cc and E cr are the collision efficiencies of hail droplets and raindrops, respectively, and v h and are the final falling velocity of hail and the mass-weighted falling velocity of raindrops, ω c and ω r are the mass contents of supercooled cloud droplets and raindrops, respectively.

[0068] The formula for calculating the final falling velocity of hail is:

[0069]

[0070] where ρ h is the density of hail, ρ a is the air density, ρ a,0 is the reference air density, C D The mass-weighted final falling velocity of the raindrop is:

[0071]

[0072] Where D r is the equivalent volume diameter of a raindrop.

[0073] (2) Hail collision and ice crystal and snow growth

[0074] The formula for the growth of hailstones, ice crystals and snow is:

[0075]

[0076] where ω i is the total mass content of ice crystals and snow, E ci is the collision efficiency of hail ice crystals and snow, which is set to 1 under wet growth conditions and 0 under dry growth conditions.

[0077] (3) Hail condensation and sublimation process

[0078] The formula for the hail sublimation process is:

[0079]

[0080] Where Re is the Reynolds number, Sc is the Schmidt number, and D v is the diffusion coefficient of water vapor, χ is the conversion coefficient of heat and mass, ρ v,∞ is the water vapor density in the environment, ρ v,sfc is the water vapor density on the hail surface.

[0081] (4) Hail surface temperature:

[0082] The calculation formula of hail surface temperature is:

[0083]

[0084] in, are the mass changes of the hail mentioned above through the collision of supercooled cloud droplets, raindrops, condensation and sublimation, collision of ice crystals and snow growth, respectively. f is the latent heat of freezing, F f is the freezing rate of supercooled cloud droplets and raindrops after collision, Pr is the Prandtl number, k t is the thermal diffusion coefficient of air, T ∞ is the ambient temperature.

[0085] The calculation formula of the freezing rate is:

[0086]

[0087] Among them, T0 is 273.15K.

[0088] (5) Hail density

[0089] When dry growth occurs, the calculation formula for hail density is: ρ rime =300A 0.44, when A<1.6 and the surface temperature of the hail is below -5℃,

[0090] ρ rime =1000.0exp(-0.03115-1.7030A+0.9116A 2 -0.1224A 3 )

[0091] in D m,cloud is the average diameter of cloud droplets.

[0092] When wet growth occurs, the density of hail is: ρ ′ h =(1-0.08F f )F f ×10 3 .

[0093] (6) Treatment of unfrozen liquid water on the surface during hail growth

[0094] When hailstones grow wet, the supercooled liquid water that collides with each other will not freeze completely. The unfrozen part will first penetrate into the internal gaps of the hailstones and freeze, increasing the mass and density of the hailstones. When the unfrozen supercooled water can completely fill the internal gaps of the hailstones, the excess supercooled water will cover the surface of the hailstones. There is an upper limit to the maximum supercooled water content that the hailstone surface can withstand. If this limit is exceeded, it will fall off. The upper limit of the supercooled water content is:

[0095] m w,crit =2.68×10 -4 kg+0.1390(m ice +m soaked )

[0096] Among them, m ice and m soaked It is the content of ice phase in hail and supercooled water that has penetrated into the internal gaps of hail.

[0097] (7) Hail melting process

[0098] The trajectory model takes into account the melting process of hail. The melting of hail is a very complex process due to the combined effects of dynamics and thermodynamics, as well as the coexistence of solid and liquid states during the melting process. The melting rate of hail particles is determined by particle thermodynamics, especially by the heat influx at the particle ice-water surface. The melting rate is related to the Reynolds number, and the specific relationship is shown in Table 1 below:

[0099] Table 1 Empirical formula and theoretical formula of melting rate

[0100]

[0101]

[0102] (8) Particle movement

[0103] In trajectory mode, particles move according to the wind field at their location (the grid wind field must be interpolated to the particle location first). They move horizontally following the horizontal wind and vertically following the combined speed of the vertical velocity and the final falling velocity. The specific formula is as follows:

[0104] X t+1 =X t +U×dt

[0105] Y t+1 =Y t +V×dt

[0106] Z t+1 =Z t +(WV h )×dt

[0107] Among them, X, Y, Z are the three-dimensional positions of the hailstones, U, V, W are the three-dimensional wind speeds interpolated to the hailstones’ positions, and V h is the final velocity of the hailstone falling.

[0108] Example 2 Application of Hail Track Model

[0109] Depend on Figure 2 It can be seen that the hail track pattern can reflect the difference between the hail tracks in pulse hail storms and supercells. In pulse hail storms, the hail mainly shows a single up and down growth, while in supercell cases, the hail track is more complicated. In supercell cases, the maximum diameter of ground hail can reach 58mm, while in pulse storms the maximum diameter of ground hail can only reach 5.1mm, both of which are close to observations. Therefore, the hail track pattern can not only reflect the difference in hail track patterns in the two cases, but also reproduce the difference in hail size under the two conditions.

[0110] Figure 3 The hail trajectories and positions in pulse storms are shown. It can be seen that hail with a maximum diameter of more than 10 mm mainly appears near the main rising area in the pulse storm, and reaches the maximum hail diameter below the supercooled water area, which is consistent with the findings in observations.

[0111] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0112] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for simulating hail growth trajectory, characterized by: The following steps are included: A Calculate hail particle trajectories by Lagrangian method; B. Calculate various microphysical processes of hail, consider the wet growth and melting process of hail, and predict the diameter, density, mass, and surface supercooled water content parameters of hail; Specifically, when: 1) The ambient temperature is greater than or equal to 273.15 K. Considering the melting process, if the water Mmelt melted out during the melting process exceeds the maximum water content Mcrit that the hail surface can withstand, the excess water will be thrown away, otherwise it will remain on the hail surface; 2) When the temperature is less than 273.15 K, first calculate the content hcw of the collided supercooled cloud droplets and raindrops, and then recalculate the hail surface temperature Tsfc. If the hail surface temperature is still less than 273.15 K, dry growth occurs, and then the condensation and sublimation process hdiff on the hail surface is calculated, and finally the mass and density of the hail are updated; if the calculated hail surface temperature Tsfc>273.15 K, then Tsfc is set to 273.15 K, the hail undergoes wet growth, and the condensation and evaporation process hdiff on the hail surface is calculated. At the same time, the freezing rate Ff is calculated, and the mass and density of the supercooled water that can be frozen are updated to the mass and density of the hail, and then the amount of supercooled water that has not been frozen is considered; if there is still some left after filling the internal gaps of the hail, it is necessary to consider whether the remaining amount exceeds the maximum water content Mcrit on the hail surface, and the excess part is thrown away, otherwise it is retained on the hail surface, and the mass and density of the hail are updated; The parameter changes of the particle size, mass and density of the hail are predicted through the collision of the hail particles with the supercooled raindrops and raindrops, condensation, sublimation and melting process, and the infiltration of the unfrozen supercooled water on the surface of the hail into the gaps of the hail and the falling process; The formula for the growth of hail collision and supercooled cloud droplets and raindrops is: in, is the change in hail mass per unit time, is the hail diameter, and are the collision efficiencies of hail droplets and raindrops, respectively. and are the final falling velocity of hail and the mass-weighted final falling velocity of raindrops, and are the mass contents of supercooled cloud droplets and raindrops, respectively; The formula for calculating the final falling velocity of hail is: in is the density of hail, is the air density, is the reference air density, is the drag coefficient The mass-weighted final falling velocity of a raindrop is: in is the equivalent volume diameter of raindrops; The formula for the growth of hailstones, ice crystals and snow is: in is the total mass content of ice crystals and snow, is the collision efficiency of hail ice crystals and snow, which is set to 1 under wet growth conditions and to 0 under dry growth conditions; The formula for the hail sublimation process is: in, is the Reynolds number, is the Schmidt number, is the diffusion coefficient of water vapor, is the conversion factor between heat and mass, is the water vapor density in the environment, is the water vapor density on the hail surface; The calculation formula of hail surface temperature is: in, , , are the mass changes of the hail mentioned above through the collision of supercooled cloud droplets, raindrops, condensation and sublimation, collision of ice crystals and snow growth, is the latent heat of freezing, is the freezing rate of supercooled cloud droplets and raindrops after collision, is the Prandtl number, is the thermal diffusion coefficient of air, is the ambient temperature; The calculation formula of the freezing rate is: in is 273.15 K.

2. The method for simulating hail growth trajectory according to claim 1, characterized in that: When dry growth occurs, the formula for calculating hail density is: ,when When the surface temperature of the hail is below -5℃, ; When wet growth occurs, the density of hail is: ; in , is the average diameter of cloud droplets.

3. The hail growth trajectory simulation method according to claim 1, characterized in that: When hailstones grow wet, when the unfrozen supercooled water can completely fill the internal spaces of the hailstones, the excess supercooled water will cover the surface of the hailstones. There is an upper limit to the maximum supercooled water content that the hailstone surface can withstand. If the upper limit is exceeded, the hailstone will fall off. The formula for the upper limit of the supercooled water content is: in, and It is the content of ice phase in hail and supercooled water that has penetrated into the internal gaps of hail.

4. A method for simulating hail growth trajectory according to claim 1, characterized in that: In the movement of hail particles in the trajectory mode, the grid wind field is interpolated to the location of the particles. The particles move according to the wind field at their location. They move horizontally following the horizontal wind and vertically according to the combined speed of the vertical speed and the final falling speed. The specific formula is as follows: Among them, X, Y, Z are the three-dimensional positions of the hail, U, V, W are the three-dimensional wind speeds interpolated to the position of the hail, is the final velocity of the hailstone falling.

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