Calculation method for maximum height of catalyst diffusion based on optimal number concentration of ice nuclei in cloud

Abstract

The present disclosure provides a calculation method based on the maximum height of catalyst diffusion when the optimal number concentration of ice nuclei in the cloud, comprising establishing a diffusion calculation coordinate system; constructing a wind field model describing the distribution of horizontal wind speed and vertical airflow with height, deriving the lifting trajectory of the center line of the smoke plume with the downwind distance; establishing a concentration distribution analytical model describing the three-dimensional space of the catalyst in the coordinate system; simplifying the concentration distribution analytical model, and solving to obtain the predicted height based on the concentration dilution criterion; based on the vertical airflow velocity distribution model in the wind field model and the preset vertical airflow decay threshold, the critical height based on the limit of dynamic lifting ability is solved; taking the minimum value of the predicted height and the critical height as the maximum height of the catalyst diffusion, the method can comprehensively consider the vertical airflow lifting effect, and the calculation is simple and fast, solving the problems of large prediction deviation caused by ignoring the vertical airflow in the existing model and poor practicability caused by complex calculation.

Description

Technical Field

[0001] This disclosure relates to the field of weather modification technology, and in particular to a method for calculating the maximum diffusion height of a catalyst based on the optimal number concentration of ice nuclei in clouds. Background Technology

[0002] In weather modification operations, the study of catalyst diffusion height plays a crucial role. It not only tracks the diffusion range of catalysts but also provides a scientific basis for determining the conditions for weather modification operations, enabling catalysts to maximize their catalytic efficiency within the operational potential zone and providing reliable theoretical support for the implementation of weather modification operations. In the study of catalyst diffusion problems, using mathematical models to simulate and predict the catalyst transport and diffusion process is a commonly used and effective technique. In existing technologies, the basic form of diffusion prediction for continuous point sources under windy conditions generally adopts the Gaussian flue gas diffusion model. This model describes the concentration distribution of the flue gas in space through specific mathematical expressions, can calculate the catalyst concentration at any point in space, and can also infer the lateral or vertical diffusion distance reached when the catalyst diffuses to a specific concentration.

[0003] However, the Gaussian diffusion model upon which existing technologies rely has the following limitations: First, in terms of physical mechanisms, this model typically simplifies the wind field to the prevailing horizontal wind, neglecting the dynamic lifting effect of vertical airflow in the actual atmosphere, which may lead to biases in its prediction of the vertical diffusion range of plumes. Second, at the engineering application level, when solving the key problem of "maximum diffusion height at a specific ice core concentration," this model, due to its mathematical limitations, usually cannot obtain a directly calculable explicit solution. In practice, numerical methods are often required, involving iterative searches through spatial coordinates, which is complex and time-consuming, making it difficult to meet the needs of rapid pre-assessment and real-time judgment in weather modification operations.

[0004] Therefore, there is an urgent need for a method to calculate the maximum height of catalyst diffusion that can comprehensively consider the vertical airflow lifting effect and is simple and fast to solve the problems of large prediction deviations caused by neglecting vertical airflow in existing models and poor practicality caused by computational complexity. Summary of the Invention

[0005] In view of this, in order to solve the problems caused by the prior art, this application provides a method for calculating the maximum height of catalyst diffusion based on the optimal number concentration of ice nuclei in clouds.

[0006] In a first aspect, this disclosure provides a method for calculating the maximum diffusion height of a catalyst based on the optimal number concentration of ice nuclei in clouds, the method comprising:

[0007] S1: Calculate the smoke intensity of continuous point sources and establish a diffusion calculation coordinate system with the smoke source projection as the origin and the prevailing wind direction as the x-axis;

[0008] S2: Construct a wind field model that describes the distribution of horizontal wind speed and vertical airflow with height, and derive the lifting trajectory of the plume centerline as it changes with the downwind distance based on the wind field model;

[0009] S3: Using the aforementioned lifting trajectory as the central axis and combining turbulent diffusion parameters, establish an analytical model describing the concentration distribution of the catalyst in the three-dimensional space of the coordinate system.

[0010] S4: Substitute the preset target value of the optimal ice nucleus number concentration into the concentration distribution analytical model for simplification, and combine it with the maximum downwind distance limited by the emission time to obtain the predicted height based on the concentration dilution criterion; at the same time, based on the vertical airflow velocity distribution model in the wind field model and the preset vertical airflow attenuation threshold, obtain the critical height based on the dynamic lift capability limit; take the minimum value between the predicted height and the critical height as the maximum height of catalyst diffusion.

[0011] Optionally, the calculation of smoke source intensity in step S1 specifically involves:

[0012] Based on the mass, combustion time, and quantity of the flame catalyst, the total number of ice nuclei released per unit time is calculated using a formula.

[0013] Optionally, the wind field model in S2 includes:

[0014] A logarithmic distribution model describing the variation of horizontal wind speed with height, and a parabolic distribution model describing the variation of vertical airflow speed with height.

[0015] Optionally, the derivation of the plume centerline lifting trajectory in S2 specifically involves:

[0016] By combining the logarithmic law distribution model and the parabolic distribution model, and solving the differential equation reflecting the ratio of vertical to horizontal wind speed, the lifting trajectory defined by the analytical expression of the change of plume center height with downwind distance can be obtained.

[0017] Optionally, in step S3, an analytical model for concentration distribution is established, specifically as follows:

[0018] Under the steady assumption, the governing equations, which include advection transport and turbulent diffusion terms, are solved to obtain the concentration analytical formula with the analytical expression of the lifting trajectory as the vertical center and a Gaussian distribution on the cross section, thereby establishing the analytical model of the concentration distribution.

[0019] Optionally, the calculation of the predicted height based on the concentration dilution criterion in S4 specifically involves:

[0020] In the concentration distribution analytical model, the horizontal coordinate is set to zero, and the concentration value is set to the preset target value of the optimal number concentration of ice nuclei, and the relationship between vertical height and downwind distance is derived.

[0021] The maximum downwind distance that the plume can reach is determined based on the combustion time and average wind speed.

[0022] The maximum downwind distance is substituted into the formula for calculation. The plume center lifting height, which is the basis of the formula, is calculated using different methods depending on whether the vertical airflow velocity at the smoke source exceeds the vertical airflow attenuation threshold, thereby obtaining the predicted height.

[0023] Optionally, in step S4, based on the vertical airflow distribution in the wind field model and a preset vertical airflow attenuation threshold, the critical height based on the dynamic lift capability limit is calculated, specifically as follows:

[0024] When the vertical airflow velocity at the smoke source Not greater than the attenuation threshold At that time, the critical height is equal to the emission height of the smoke source, that is... ;

[0025] When the vertical airflow velocity at the smoke source Greater than the attenuation threshold At that time, by solving the equation Obtain the critical height ,in, The parameter for maximum vertical airflow velocity. , The attenuation threshold is... For feature height, This refers to the height of the smoke source emission.

[0026] Optionally, the step of using different calculation methods based on whether the vertical airflow velocity at the smoke source exceeds the vertical airflow attenuation threshold to obtain the predicted height includes:

[0027] ,

[0028] Where Q is the smoke source intensity, The horizontal wind speed at the height of the smoke source. The vertical airflow velocity at the smoke source. The smoke source emission height is t, and the flame burning time is t. and These are the lateral and vertical turbulent diffusion coefficients, respectively. For feature height, The parameter for maximum vertical airflow velocity. , This is the threshold for vertical airflow attenuation.

[0029] In a second aspect, this disclosure provides an electronic device including a memory and at least one processor, the memory storing a computer program, and the processor executing the computer program to implement the method of the first aspect described above.

[0030] Thirdly, this disclosure provides a computer storage medium storing a computer program that, when executed, implements the method described in the first aspect.

[0031] The beneficial effects of this disclosure are that, compared with the prior art, this disclosure has the following advantages:

[0032] 1) By constructing a wind field model that simultaneously includes the logarithmic distribution of horizontal wind speed and the parabolic distribution of vertical airflow, and deriving the analytical expression of the dynamic lifting trajectory of the plume centerline, the limitation of the traditional Gaussian diffusion model in ignoring the dynamic lifting effect of vertical airflow is effectively overcome. This enables the prediction of the catalyst diffusion range to more realistically reflect its actual movement and lifting behavior in the three-dimensional atmospheric wind field, and significantly improves the physical authenticity and accuracy of the diffusion height prediction.

[0033] 2) By focusing on the key indicator of optimal ice nucleus number concentration, the synthesized three-dimensional diffusion model is reasonably simplified. The problem of solving for the maximum diffusion height, which originally required complex numerical iterations traversing spatial coordinates, is transformed into a direct analytical calculation based on explicit observation and operational parameters. The resulting piecewise explicit calculation formula avoids the time-consuming numerical search process of traditional methods, enabling rapid acquisition of calculation results. This greatly satisfies the urgent need for rapid pre-assessment and real-time judgment of operational conditions in weather modification operations.

[0034] 3) By calculating the height limit from two physical dimensions, namely concentration diffusion and dilution and vertical airflow dynamic attenuation, and taking the minimum of the two as the final maximum diffusion height, the calculation results are ensured to conform to both atmospheric diffusion laws and dynamic constraints. This ensures that the predicted height value not only indicates that the catalyst has reached an effective ice-forming concentration, but also does not exceed the lifting capacity of the actual airflow, thus providing a more scientific, reliable and comprehensive basis for key parameters in the formulation of operational plans.

[0035] 4) All input parameters involved in this method, such as smoke source intensity, wind speed, airflow velocity, combustion time, and turbulent diffusion coefficient, are derived from actual operational settings, routine meteorological observations, or standard atmospheric parameters, without relying on unconventional or difficult-to-obtain data. The entire calculation process is clear, the parameters have explicit meanings, and it is easy to integrate into operational systems, effectively improving the operability and standardization of weather modification operation design. Attached Figure Description

[0036] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0037] Figure 1 A flowchart illustrating the calculation method for the maximum catalyst diffusion height based on the optimal number concentration of ice nuclei in clouds, provided in an embodiment of this disclosure, is shown.

[0038] Figure 2 A flowchart illustrating the calculation and integrated judgment process for the maximum catalyst diffusion height provided in an embodiment of this disclosure is shown.

[0039] The accompanying drawings have illustrated specific embodiments of this disclosure, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this disclosure to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0040] The present disclosure will be further described below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solutions of the present disclosure more clearly, and should not be used to limit the scope of protection of the present disclosure.

[0041] The components of the embodiments of the invention described and illustrated herein can typically be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0042] In the following, the terms “comprising,” “having,” and their cognates, which may be used in various embodiments of the invention, are intended only to indicate a particular feature, number, step, operation, element, component, or combination thereof, and should not be construed as excluding, firstly, the presence of one or more other features, numbers, steps, operations, elements, components, or combinations thereof, or adding the possibility of one or more features, numbers, steps, operations, elements, components, or combinations thereof.

[0043] Unless otherwise specified, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of the invention pertain. Terms (such as those defined in commonly used dictionaries) shall be interpreted as having the same meaning as in their contextual meaning in the relevant technical field and shall not be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of the invention.

[0044] Figure 1 A flowchart illustrating the calculation method for the maximum catalyst diffusion height based on the optimal number concentration of ice nuclei in clouds, as provided in this embodiment of the disclosure, is shown below. Figure 1 As shown, the process may include the following steps:

[0045] S1: Calculate the smoke intensity of continuous point sources and establish a diffusion calculation coordinate system with the smoke source projection as the origin and the prevailing wind direction as the x-axis.

[0046] This step transforms the basic parameters of the catalyst flames used in weather modification operations into quantitative source inputs necessary for subsequent diffusion model calculations. By establishing explicit mathematical relationships, macroscopic operational parameters such as the number of flames, catalyst content, and combustion time are calculated and defined as continuous point source intensities in the model. Simultaneously, a matching spatial diffusion calculation coordinate system is established, providing accurate initial conditions and a spatial reference for the entire simulation. This is achieved through the following sub-steps.

[0047] S1.1: Obtain and confirm the basic parameters of the flame strips used in the catalytic operation, including catalyst mass, combustion time, and the number of flame strips ignited simultaneously.

[0048] First, the basic parameters of the flame strips used in this catalytic operation need to be obtained and confirmed from the work plan. These parameters include the mass of catalyst contained in a single flame strip, denoted as M, usually in grams; the time from ignition to complete combustion of a single flame strip, denoted as t, usually in seconds; and the total number of flame strips ignited simultaneously in one ignition operation, denoted as N, in units of strips. If N flame strips are ignited simultaneously in one operation, and assuming that all flame strips have the same burning time, the total effective emission time of the smoke source is still t. The catalyst mass M is determined by the flame strip product specifications, the combustion time t can be obtained through experimental measurement or the product manual, and the number of simultaneously ignited flame strips N is specifically determined by the work design. These parameters are the basis for characterizing the source strength and need to be clarified and confirmed before calculation.

[0049] S1.2: Calculate the total number of ice nuclei released per unit time based on the basic parameters of the flame strip using a formula, i.e., the smoke source intensity.

[0050] Based on the confirmed parameters mentioned above, the smoke source intensity Q is calculated using a predetermined conversion formula. The physical meaning of smoke source intensity Q is the total number of effective ice nuclei released from the smoke source per unit time, and its calculation formula is as follows: The calculation result is in units of units per second. In this formula, This is a key conversion factor that represents a typical number of ice nuclei produced per gram of a particular type of catalyst under ideal conditions. The specific value of this factor should be determined based on laboratory nucleation efficiency measurements of the catalyst used or relevant industry standards. In the embodiments of this disclosure, a typical value for a common catalyst is used. The calculation is performed per gram. Through this calculation, macroscopic operational parameters such as the number of flames, catalyst content, and combustion time used in actual operations are transformed into microscopic model input parameters Q that describe the particle release rate.

[0051] S1.3: Establish a three-dimensional rectangular coordinate system with the smoke source projection as the origin and the prevailing wind direction as the x-axis.

[0052] To facilitate the subsequent construction and solution of the catalyst diffusion model, a three-dimensional Cartesian coordinate system associated with the smoke source location and wind direction needs to be established. This coordinate system uses the projection point of the smoke source onto the horizontal plane as its origin, and defines the positive x-axis along the dominant horizontal wind direction at the time of operation, i.e., the main transport direction of the smoke plume; the direction perpendicular to the x-axis on the horizontal plane is defined as the y-axis; and the direction perpendicular to the horizontal plane upwards, i.e., the direction of increasing altitude, is defined as the z-axis. Thus, the position of any point in space can be uniquely determined by the coordinates (x, y, z), where x represents the downwind distance, y represents the lateral offset distance, and z represents the altitude.

[0053] S1.4: Model the smoke source as a point source with continuous and stable emissions and set the emission height, while making simplified assumptions about the steady state and diffusion direction.

[0054] In the established coordinate system, the smoke source is modeled as a continuously and steadily emitting point source. The emission rate of this point source is the smoke source intensity Q calculated in step S1.2, with units of particles / second. The initial emission height of the point source is set to... This refers to the actual altitude of the smoke generator or launching device at the work site, which is provided by the geographical location data of the work site.

[0055] Furthermore, two fundamental assumptions are made regarding the diffusion process to be involved later in order to simplify the model. First, the diffusion process is assumed to be in a steady state. This means that during the period of stable emission from the smoke source, the atmospheric wind field and turbulent structure are relatively stable, resulting in the catalyst concentration at any point in space not changing with time. Mathematically, this is expressed as the partial derivative of concentration c with respect to time t being zero, i.e. Therefore, the concentration c is only a function of the spatial coordinates (x, y, z). Second, based on the general laws of atmospheric diffusion, under the advection transport dominated by horizontal winds, the turbulent diffusion effect along the x-axis (downwind direction) is much smaller than the average wind transport effect, and is therefore ignored in the model; instead, it is considered that turbulent diffusion mainly plays a significant role in the horizontal transverse (y-direction) and vertical (z-direction) directions, which is the main reason for the broadening of the plume in the cross-section and the mixing in the vertical direction.

[0056] In the technical solution of this disclosure, by systematically determining the smoke source intensity and establishing a matching spatial coordinate system, a precise and standardized input basis is provided for the subsequent diffusion model. Calculating the smoke source intensity based on the basic parameters of the flame ensures the physical reality of the source terms in the model; while the clearly defined three-dimensional coordinate system and the steady diffusion assumption allow for a mathematical description of the complex real-world diffusion process within a reasonably simplified framework. This step transforms actual operational parameters into quantifiable inputs that the model can process, fundamentally improving the reliability and repeatability of the entire calculation method and avoiding calculation deviations caused by ambiguity in the definition of source intensity or inconsistent spatial reference systems.

[0057] S2: Construct a wind field model that describes the distribution of horizontal wind speed and vertical airflow with height, and derive the lifting trajectory of the plume centerline as it changes with downwind distance based on the wind field model.

[0058] A wind field model consistent with actual atmospheric physics is established for catalyst diffusion simulation. Traditional Gaussian diffusion models only consider the dominant transport effect of horizontal winds, while this method innovatively introduces both a horizontal wind speed model varying with altitude and a vertical airflow model to more realistically reflect the diffusion and lifting behavior of the plume under the combined effects of a three-dimensional wind field. This step, by constructing two mathematical models and establishing the correlation between them, provides a theoretical foundation for subsequent derivation of the diffusion model in the direction of the synthetic wind and the calculation of the plume's lifting trajectory. Specifically, this is achieved through the following sub-steps.

[0059] S2.1: Establish a logarithmic law distribution model of horizontal wind speed with height under neutral conditions.

[0060] First, it is necessary to establish the variation law of horizontal wind speed in the vertical direction. Under neutral atmospheric stability conditions, the horizontal wind speed from the near-surface to the boundary layer generally follows a logarithmic distribution with increasing height. This model describes the horizontal wind speed u as a function of height z, and its expression is: In this formula, u(z) represents the horizontal wind speed at height z, in meters per second. represents the ground wind speed, and its value is usually much smaller than the logarithmic term, so it can be ignored in subsequent simplified calculations; k is a constant related to atmospheric friction speed and the Karman constant, and its specific value can be estimated based on the actual atmospheric boundary layer characteristics or the known wind speed at the smoke source. This is the surface roughness length, expressed in meters. Its value depends on the type of underlying surface of the smoke source, such as flat grassland, crops, forest, or urban buildings. Different underlying surface types correspond to different roughness lengths. Typical value; z is the vertical height above the ground in meters. This model characterizes the classic boundary layer feature where horizontal wind gradually increases with altitude, providing a basis for calculating the variation of the advection transport velocity of a plume in the leeward direction with altitude.

[0061] S2.2: Establish a parabolic distribution model of vertical airflow velocity as a function of height.

[0062] Secondly, a distribution model of vertical airflow velocity needs to be established. Vertical airflow is a key factor leading to the dynamic lifting of the plume. This method uses a parabolic function to describe the typical distribution of vertical airflow velocity w from the ground to the tropopause, and its expression is: In this formula, w(z) represents the vertical airflow velocity at height z, in meters per second, with a positive value indicating an updraft. The maximum vertical airflow velocity across the entire distribution is a key parameter of the model. To describe the characteristic height of the vertical airflow profile, an approximate height of the tropopause in the operating area is typically used; in common calculations in mid-latitude regions, a value of 8000 meters is commonly adopted. z represents altitude in meters. This parabolic model reflects that the vertical airflow velocity tends to zero near the ground and at the tropopause, while reaching its maximum value at a certain intermediate height. The general laws governing this can reasonably simulate the lifting effect of rising airflow on the plume.

[0063] S2.3: Key parameters in the vertical airflow distribution model are retrieved based on vertical airflow observations at the smoke source height.

[0064] Key parameters in vertical airflow models It is usually impossible to obtain directly from observation, but it can be indirectly determined through vertical airflow observations at the height of the smoke source. Assume that the smoke source emission height has been obtained through automatic weather stations or other detection methods. Vertical airflow velocity at the location The height of the smoke source and its corresponding vertical velocity observations Substitute the general formula for vertical airflow distribution established in step S2.2 In, that is, let one of them , The equation is obtained as follows:

[0065] ;

[0066] By solving this problem... The equation can be used to deduce the maximum vertical airflow velocity. The value of is calculated using the following formula: This calculation establishes a bridge between local observations and the parameters of the entire vertical profile model, enabling the model to deduce the true vertical airflow structure applicable to the entire computational domain based on practically available single-height observation data. This refers to the peak velocity in the vertical airflow velocity distribution. For smoke source height The measured vertical velocity at the location is related to the above formula.

[0067] S2.4: Solve the analytical expression of the lifting trajectory of the plume center height as the downwind distance changes by combining horizontal and vertical airflow models.

[0068] In a combined wind field where horizontal transport and vertical lift coexist, the central axis of the plume does not remain horizontal but continues to rise in the leeward direction. Its lifting rate is determined by the ratio of the local vertical airflow velocity to the horizontal wind speed. Consider a infinitesimal element on the plume's central axis; the time required for it to move an infinitesimal distance dx along the horizontal wind direction is... During the same time period, the height to which it is lifted vertically by the airflow is Therefore, the height of the plume center The rate of change of downwind distance x can be described by a differential equation:

[0069] ;

[0070] This equation shows that for every unit distance the plume centerline travels downwind, the increase in its height is equal to the ratio of the vertical wind speed to the horizontal wind speed at that point.

[0071] The specific expressions for u(z) and w(z) established in steps S2.1 and S2.2, and the inversion obtained in step S2.3, are used to... Substitute into the above differential equation. To solve for the plume center height... As an explicit function of the downwind distance x, this differential equation needs to be solved. Considering the initial conditions: at the smoke source location, i.e., x=0, the plume center height is equal to the smoke source emission height. By integrating, we can obtain the analytical expression describing the trajectory of the plume's centerline rise:

[0072] ;

[0073] in, For smoke source height The horizontal wind speed at the given location is used as a known input parameter. This formula quantitatively describes the three-dimensional spatial path of the catalyst plume concentration core as it drifts and rises downwind over time under the influence of a given horizontal and vertical wind field.

[0074] In the technical solution of this disclosure, by constructing a logarithmic distribution model of horizontal wind speed and a parabolic distribution model of vertical airflow, and establishing the correlation between the two, the physical realism and completeness of the wind field description are significantly enhanced. Introducing a vertical airflow model and utilizing source observation data to invert key parameters effectively compensates for the inherent defect of traditional Gaussian models that neglect dynamic lifting effects. The derived analytical expression for the plume center lifting trajectory can accurately characterize the spatial motion path of the catalyst cloud under the combined action of a three-dimensional wind field, laying a crucial theoretical foundation for the subsequent coupling of lifting effects in the diffusion model, thus upgrading the model from a static, horizontally dominated framework to a dynamic, three-dimensional synthetic framework.

[0075] S3: Using the aforementioned lifting trajectory as the central axis and combining turbulent diffusion parameters, establish an analytical model describing the concentration distribution of the catalyst in the three-dimensional space of the coordinate system.

[0076] Based on established horizontal wind speed distribution, vertical airflow distribution, and plume center lifting trajectory, a catalyst diffusion concentration distribution model dominated by the synthetic wind field is constructed. This model aims to overcome the limitations of traditional Gaussian diffusion models that only consider horizontal wind transport. By combining the vertical airflow lifting effect with the turbulent diffusion effect, it achieves a more accurate description of the catalyst distribution in three-dimensional space. The model derivation follows the basic principles of atmospheric diffusion theory and, with reasonable simplification, yields an analytical expression that is easy to apply. This is achieved through the following sub-steps.

[0077] S3.1: Establish the three-dimensional concentration transport control equations considering advection transport and turbulent diffusion under steady conditions.

[0078] Under conditions of continuous point source emission and stable wind field, the transport and diffusion of the catalyst in the atmosphere can be considered as a steady state. In this case, the concentration at any point in space does not change with time, and its distribution is determined by both advection transport and turbulent diffusion. Based on the principle of mass conservation, a governing equation describing the spatial variation of concentration can be established. This equation is mathematically expressed as:

[0079] ;

[0080] Where c represents the catalyst concentration, which is a function of spatial coordinates x, y, z; u and w represent the horizontal wind speed and vertical airflow velocity, respectively, both of which are functions of height z, and their specific forms have been given in step S2; and These represent the turbulent diffusion coefficients in the lateral and vertical directions, respectively. The two terms on the left side of the equation represent the advection transport effect of the horizontal wind along the downwind direction (x) and the vertical airflow along the height direction (z) on the concentration, respectively; the two terms on the right side represent the diffusion effects in the lateral and vertical directions due to turbulent mixing, respectively. This equation forms the theoretical basis for characterizing the diffusion behavior of catalysts in the synthetic wind field from a physical mechanism perspective.

[0081] S3.2: Establish a quantitative relationship between diffusion parameters and downwind distance.

[0082] In practical applications, the turbulent diffusion coefficient is used directly. and Often inconvenient, it is more common to use diffusion parameters. and This describes the spread width of the plume in the lateral and vertical directions. The diffusion parameter is essentially the standard deviation of the concentration distribution, and its squared value has a definite integral relationship with the turbulent diffusion coefficient and wind field conditions. Specifically, the lateral diffusion parameter... and vertical diffusion parameters satisfy:

[0083] ;

[0084] ;

[0085] The integral is performed downwind from the smoke source location 0 to the target point x, with dx' being the integration variable. To obtain an explicit expression that facilitates calculation, the above relationship is usually parameterized based on atmospheric diffusion experimental data. A widely adopted simplification is to assume that, under neutral atmospheric stability conditions, the turbulent diffusion coefficient... and It can be considered a constant, while the horizontal wind speed u is the wind speed at the smoke source. An approximate representation. With this simplification, integration can be performed directly, yielding a straightforward relationship between the diffusion parameter and the downwind distance x:

[0086] ;

[0087] ;

[0088] in, and This coefficient characterizes the intensity of atmospheric turbulence diffusion, and its value is determined by atmospheric stability. For neutral conditions, The typical value range is approximately 50 to 100m. 2 / s, The typical value range is approximately 5 to 10m. 2 / s. Let be the horizontal wind speed at the smoke source height, and be a known input parameter. This relationship directly links the increase in diffusion range to downwind distance, providing a key element for the concentration distribution formula.

[0089] S3.3: The analytical formula for catalyst concentration, which is centered on the dynamic lifting trajectory and follows a Gaussian distribution in the cross section, is derived.

[0090] In step S2, we have obtained the height of the plume centerline. The analytical expression for the variation of downwind distance x describes the lifting effect of vertical airflow on the entire plume. Based on the classical solution of continuous point source diffusion in atmospheric diffusion theory, and considering the characteristic of plume center lifting, it can be assumed that the catalyst concentration follows a two-dimensional Gaussian distribution on the cross section perpendicular to the centerline. Based on the governing equations of step S3.1, combined with steady state and uniform horizontal wind speed (taken as...),... Assuming that the turbulent diffusion coefficient is constant and the plume centerline rises with the vertical airflow, the classical two-dimensional Gaussian distribution analytical solution for the concentration can be obtained by solving this equation. The specific form of this analytical formula for catalyst concentration distribution is:

[0091] ;

[0092] Where Q is the smoke source intensity calculated in step S1; The horizontal wind speed at the smoke source; and These are the lateral and vertical diffusion parameters that vary with downwind distance; The formula represents the plume center height, which varies with leeward distance. The exponential terms in the formula describe the concentration in the horizontal direction with the plume axis y=0 as the axis of symmetry, and in the vertical direction, with a dynamically changing center height. The model employs a Gaussian decay law with the axis of symmetry as its axis. The core of this model lies in the fact that the center of symmetry for the concentration distribution is no longer at a fixed height, but rather follows the trajectory of the plume's ascent. The changes organically incorporate the dynamic lifting effect of vertical airflow into the diffusion model.

[0093] S3.4: Explain the physical meaning of each parameter in the concentration model and how to obtain it in actual operations.

[0094] To ensure the operability and practicality of the derived diffusion model, it is essential to clarify the physical meaning of each parameter in the model and its acquisition methods in actual operations. The smoke source intensity Q is the source term of the model, its value calculated in step S1 based on the catalyst content, combustion time, and quantity of the flame strip, reflecting the total number of ice nuclei released per unit time. The horizontal wind speed at the smoke source... and vertical airflow velocity This is a key parameter describing the initial wind field, and it can usually be obtained directly from automatic weather stations, wind profiler radar, or radiosonde observations deployed near the work site. Smoke source height The altitude of the working device is determined by the geographical information of the work site. (Diffusion coefficient) and The value depends on the atmospheric stability conditions at the time of the operation. Under neutral conditions, the given typical value range can be used, or a more refined calibration can be performed based on local historical diffusion test data or empirical formulas. Maximum vertical airflow velocity Instead of direct observation, the formula in step S2.3 is used. From the observed values and This is derived by reverse engineering. All parameters are derived from actual measurable or calculable quantities, ensuring that the entire model is built upon real observational data.

[0095] In the technical solution of this disclosure, a substantial innovation over the traditional diffusion model is achieved by deriving an analytical model of catalyst concentration distribution dominated by the syngas field and centered on the dynamic lifting trajectory. This model organically integrates the vertical lifting effect described in step S2 into the core symmetry axis of the concentration distribution, allowing the concentration field to evolve in accordance with the actual movement of the plume. Simultaneously, by establishing an explicit relationship between diffusion parameters and downwind distance and clarifying the physical meaning and acquisition methods of all model parameters, the theoretical model possesses good operability and adaptability to actual operating conditions, providing a rigorous and practical mathematical tool for solving key indicators from the perspective of concentration distribution.

[0096] S4: Substitute the preset target value of the optimal ice nucleus number concentration into the concentration distribution analytical model for simplification, and combine it with the maximum downwind distance limited by the emission time to obtain the predicted height based on the concentration dilution criterion; at the same time, based on the vertical airflow velocity distribution model in the wind field model and the preset vertical airflow attenuation threshold, obtain the critical height based on the dynamic lift capability limit; take the minimum value between the predicted height and the critical height as the maximum height of catalyst diffusion.

[0097] Based on the analytical model of concentration distribution established in step S3, this step calculates the maximum vertical height that the catalyst can reach when it diffuses to the optimal number concentration of ice nuclei in the cloud. This maximum height is a key indicator for evaluating the effectiveness of weather modification operations and determining whether the catalyst can effectively cover the supercooled water region in the cloud. To achieve efficient calculation, this step makes targeted and reasonable simplifications to the analytical model of concentration distribution established in S3, ultimately deriving a set of explicit formulas that can be directly calculated, thus avoiding the complexity and large amount of computation brought about by traditional numerical iterative methods. Figure 2 The flowchart for calculating and integrating the determination of the maximum diffusion height of the catalyst provided in the embodiments of this disclosure is as follows: Figure 2 As shown, this is achieved through the following sub-steps.

[0098] S4.1: Unify the target value of the optimal ice nucleus number concentration, and set the calculation premise and the criterion for the effect of vertical airflow.

[0099] First, the target concentration value for calculation needs to be clearly defined. Based on the scientific principles and practical experience of weather modification, the catalyst achieves optimal ice-forming efficiency when the number of effective ice nuclei per unit volume in a cloud reaches a specific value; this value is called the optimal ice nucleus number concentration. This method adopts a widely accepted empirical reference value in this field, namely 1 unit per liter. To ensure consistency with the International System of Units (SI) in the model, it needs to be converted to the standard unit per cubic meter. The conversion relationship is: 1 unit per liter equals... per cubic meter. Therefore, the target concentration Set as Units per cubic meter. This value will serve as the benchmark for determining whether the plume has diffused to an effective working concentration.

[0100] Secondly, to focus on the core issue of maximum vertical diffusion height, the concentration distribution analytical model in step S3 needs to be appropriately focused and simplified. The maximum diffusion height necessarily corresponds to the upper edge of the plume in the vertical direction. At this position, the influence of lateral diffusion is relatively minor; to simplify the calculation, the lateral center section of the plume can be taken, i.e., the lateral coordinate y=0 can be set. Simultaneously, we are concerned with the concentration decreasing to the target value. The height at that time, this height z will be greater than the height of the plume center at the corresponding leeward distance. Based on these two premises, the analytical formula for catalyst concentration distribution c(x,y,z) in step S3 can be simplified to a form that retains only the Gaussian distribution term in the vertical direction, which greatly reduces the complexity of subsequent solutions.

[0101] To objectively determine whether vertical airflow has an effective dynamic lifting effect on the plume, a physical threshold needs to be set. Based on statistical analysis of typical vertical airflow observation data, this method defines an empirical vertical airflow attenuation threshold. When the vertical airflow velocity at the smoke source At that time, the airflow was considered too weak, and its dynamic lifting effect could be ignored in subsequent calculations; when In this case, the lifting effect of vertical airflow must be fully considered. This threshold will serve as the criterion for selecting different model branches in subsequent calculations.

[0102] Thus, the complex problem of "finding the maximum height at which the concentration reaches the target value in three-dimensional space" has been transformed into two more feasible sub-problems: first, on the transverse central section of the plume (y=0), solving the functional relationship between the upper edge height z satisfying the concentration condition and the downwind distance x; second, determining the maximum downwind distance that the plume can influence within a finite emission time t. This transformation is the key design element that enables this method to achieve efficient analytical computation.

[0103] S4.2: Derive the functional relationship between vertical height and downwind distance when the target concentration is achieved on the transverse central section of the plume.

[0104] The simplified concentration distribution analytical formula and the target concentration value are compared. Combining these, an equation for solving the height z can be established. Specifically, by combining y=0 and Substitute into the concentration formula of step S3

[0105] ;

[0106] Among them, diffusion parameters and Use the expression in step S3.2 and Replace it.

[0107] Through a series of algebraic transformations, the above equation can be rearranged into the equation about Explicit expression:

[0108] ;

[0109] This formula clearly shows that the upper edge of the plume is relative to the center height. The square of the offset, and the vertical diffusion parameter And it is proportional to the logarithmic term. The logarithmic term is the ratio of the source strength Q to the "baseline concentration" after diffusion and dilution at a downwind distance x.

[0110] Since we are solving for the height of the upper edge of the plume, which satisfies... Therefore, taking the positive root of both sides of the above equation is necessary. Thus, the expression for the height z of the upper edge of the plume is:

[0111] ;

[0112] This expression indicates that, for any given downwind distance x, the height z at which the target concentration is achieved can be determined by the elevation height from the center of the plume. It is obtained by directly adding to an explicit offset based on diffusion parameters and a logarithmic term. This eliminates the need for concentration traversal and iterative comparisons in 3D space for height calculation, providing a concise mathematical foundation for the core maximum height calculation.

[0113] S4.3: Determine the downwind distance of the maximum influence of the smoke plume based on the flame burning time and the average wind speed.

[0114] In actual operation, the emission of catalyst smoke is not continuous indefinitely; its duration is determined by the total combustion time t of the flame. This means that the maximum horizontal distance the smoke plume can spread is finite. Therefore, it is necessary to determine the maximum horizontal distance the smoke plume can travel under the influence of average wind within the combustion time t, i.e., the maximum downwind distance. .

[0115] Since the horizontal wind speed u varies with altitude, it is necessary to calculate the wind speed from the ground to the top of the troposphere. Average wind speed between Taking ground wind speed into account The contribution was small, so it was ignored. The simplified wind speed model after the term For its altitude range Integral average:

[0116] ;

[0117] in, This refers to the surface elevation. Under typical boundary layer conditions (such as...) much smaller And the height of the smoke source (Located within the logarithmic law layer), the integral result can be approximated as the wind speed at the smoke source height. 1.5 times, that is .

[0118] Therefore, the maximum downwind distance that the plume may affect during the combustion time t. It can be calculated using the following formula:

[0119] = .

[0120] This distance This represents the limiting horizontal scale that needs to be considered in plume diffusion calculations. By substituting it into the relevant formulas, the diffusion state that may be reached during the effective emission period of the smoke source can be obtained.

[0121] S4.4: Integrating the above relationships, derive the explicit calculation formula for the maximum height segment based on the target concentration.

[0122] The aforementioned derivation yielded a functional relationship between the height z of the upper edge of the plume and the downwind distance x. However, in actual operation, the duration of catalyst emission is determined by the total combustion time t of the flame strip, and the plume has a maximum influence distance in the horizontal direction. Therefore, it is necessary to... Substitute the values ​​to obtain the predicted maximum height that may be reached during the emission period. .

[0123] First, determine the maximum downwind distance. As described in step S4.3, during the combustion time t, the plume is at the average horizontal wind speed Under conveying conditions, the maximum horizontal distance reached is = .

[0124] Secondly, Substitute into the formula for the plume center lifting trajectory and vertical diffusion parameter formula .in, As given in step S2.4.

[0125] However, whether the plume center can rise depends on the vertical airflow at the source. According to the threshold defined in step S4.1 :

[0126] when At this time, the vertical airflow lifting effect is negligible, and the plume center remains at the source height throughout the diffusion process. That is, at this time .

[0127] when At that time, the vertical airflow has a significant effect, and the center of the plume moves along the trajectory. Lifting requires the use of a complete expression.

[0128] Under the above different conditions Expressions and Substitute these values ​​into the formula for the height z of the upper edge of the plume, and replace x with... After sorting and simplification, the predicted maximum height based on the target concentration condition is obtained. The formula for segmented calculation is as follows:

[0129] ;

[0130] S4.5: Calculate the critical limit height of dynamic lift based on the vertical airflow attenuation threshold.

[0131] The maximum height was estimated from the perspective of concentration diffusion, but the actual rise of the plume is also subject to the rigid constraint of the dynamic attenuation of the vertical airflow itself. According to the model established in step S2.2, the vertical airflow velocity w(z) follows a parabolic distribution with height, and will attenuate to a point at which it cannot overcome the gravity of the plume and environmental resistance.

[0132] According to step S4.1, set when When the airflow lift capacity is exhausted, it is determined that the lift capacity is weakening. The height corresponding to this critical condition is the limit height of the dynamic lift. .

[0133] Vertical airflow velocity distribution with height is as follows To solve for the critical height ,make That is, to establish the equation: ,in, Treat this equation as a quadratic equation in z and solve it, while also... Substituting the values, we can obtain the critical height. The calculation formula.

[0134] Similarly, its calculation needs to be based on the source conditions. Perform branching decisions:

[0135] when At this time, the airflow at the source is already below the lift threshold, and the plume cannot be effectively lifted from the beginning. Therefore, its dynamic lift limit height is the source height itself, i.e. .

[0136] when When: There is sufficient lifting force at the source, the above quadratic equation needs to be solved to obtain the result. During the solution process, After substituting and rearranging, the constant 0.4 appearing within the radical in the formula comes from solving the quadratic equation. The calculation result of the item, i.e. .

[0137] The critical height is obtained by comprehensive analysis. The formula for segmented calculation is as follows:

[0138] ;

[0139] S4.6: The final maximum diffusion height is determined by taking the minimum value of the overall concentration and dynamic constraints.

[0140] The maximum height that a catalyst plume can actually reach is constrained by both concentration dilution (diffusion capacity) and airflow dynamics (lifting capacity). Therefore, the final maximum diffusion height... The height should be based on concentration calculations. Critical height based on aerodynamic calculations The minimum of the two:

[0141]

[0142] This principle ensures that the calculation results not only meet the requirements for the catalyst to reach an effective concentration, but also conform to the objective physical laws of atmospheric dynamics, thus making the predicted maximum diffusion height more scientific, reliable and practical, providing accurate key parameters for the formulation of artificial operation plans.

[0143] As a specific application example of this method, in the pre-evaluation of an artificial rain enhancement operation, the known parameters are: pcs / second , , , , , , The calculation process is as follows:

[0144] 1. Judgment: Because Therefore, the branch with the vertical lifting effect is adopted in the formula.

[0145] 2. Calculation .

[0146] 3. Substitute each parameter into step S4.4. corresponding Formula, calculated .

[0147] 4. Substitute the parameters into S4.5 corresponding Formula, calculated .

[0148] 5. Final maximum diffusion height .

[0149] This example demonstrates that, by simply substituting the observation and design parameters into a fixed formula, the maximum diffusion height can be estimated within minutes, a process that previously required complex numerical simulations. This significantly improves the efficiency and practicality of pre-assessment.

[0150] In the technical solution of this disclosure, by focusing on core issues, implementing key simplifications, and conducting systematic analytical derivations, a complex concentration field model is successfully transformed into a set of explicit piecewise formulas that can directly calculate the maximum diffusion height. By cleverly transforming the three-dimensional search problem into a one-dimensional calculation along the downwind distance, and strictly considering the dual constraints of limited emission time and vertical airflow dynamic attenuation, the final output calculation formula simultaneously takes into account the physical limits of concentration dilution and dynamic lift. This method overcomes the shortcomings of traditional numerical iterative methods, which are computationally complex and time-consuming. It enables operators to quickly, easily, and scientifically predict the maximum diffusion height of catalysts based on conventional observation data, greatly improving the efficiency and reliability of weather modification operation condition prediction.

[0151] According to embodiments of this disclosure, an electronic device is also provided, which may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, the communications interface, and the memory communicate with each other via the communication bus. The processor can invoke logical instructions stored in the memory to execute the methods provided in the above embodiments.

[0152] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0153] On the other hand, this disclosure also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the methods provided in the above embodiments.

[0154] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0155] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0156] It should be understood that the above embodiments are only used to illustrate the technical solutions of this disclosure, and not to limit them; although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure.

Claims

1. A method for calculating the maximum diffusion height of a catalyst based on the optimal number concentration of ice nuclei in clouds, characterized in that, The method includes: S1: Calculate the smoke intensity of continuous point sources and establish a diffusion calculation coordinate system with the smoke source projection as the origin and the prevailing wind direction as the x-axis; S2: Construct a wind field model that describes the distribution of horizontal wind speed and vertical airflow with height, and derive the lifting trajectory of the plume centerline as it changes with the downwind distance based on the wind field model; S3: Using the aforementioned lifting trajectory as the central axis and combining turbulent diffusion parameters, establish an analytical model describing the concentration distribution of the catalyst in the three-dimensional space of the coordinate system. S4: Substitute the preset target value of the optimal ice nucleus number concentration into the concentration distribution analytical model for simplification, and combine it with the maximum downwind distance limited by the emission time to obtain the predicted height based on the concentration dilution criterion; at the same time, based on the vertical airflow velocity distribution model in the wind field model and the preset vertical airflow attenuation threshold, obtain the critical height based on the dynamic lift capability limit; take the minimum value between the predicted height and the critical height as the maximum height of catalyst diffusion; The wind field model in S2 includes: A logarithmic distribution model describing the variation of horizontal wind speed with height, and a parabolic distribution model describing the variation of vertical airflow speed with height; The derivation of the plume centerline lifting trajectory in S2 is as follows: By combining the logarithmic law distribution model and the parabolic distribution model, and solving the differential equation reflecting the ratio of vertical to horizontal wind speed, the lifting trajectory defined by the analytical expression of the change of plume center height with downwind distance is obtained. The calculation of the predicted height based on the concentration dilution criterion in S4 is specifically as follows: In the concentration distribution analytical model, the horizontal coordinate is set to zero, and the concentration value is set to the preset target value of the optimal number concentration of ice nuclei, and the relationship between vertical height and downwind distance is derived. The maximum downwind distance that the plume can reach is determined based on the combustion time and average wind speed. The maximum downwind distance is substituted into the formula for calculation. The plume center lifting height, which is the basis of the formula, is calculated in different ways depending on whether the vertical airflow velocity at the smoke source exceeds the vertical airflow attenuation threshold, thereby obtaining the predicted height. In step S4, based on the vertical airflow distribution in the wind field model and a preset vertical airflow attenuation threshold, the critical height based on the dynamic lift capability limit is calculated, specifically as follows: When the vertical airflow velocity at the smoke source Not greater than the attenuation threshold At that time, the critical height is equal to the emission height of the smoke source, that is... ; When the vertical airflow velocity at the smoke source Greater than the attenuation threshold At that time, by solving the equation Obtain the critical height ,in, The parameter is the maximum vertical airflow velocity. , The attenuation threshold is... For feature height, This refers to the height of the smoke source emission.

2. The calculation method for the maximum catalyst diffusion height based on the optimal number concentration of ice nuclei in clouds according to claim 1, characterized in that, The calculation of smoke source intensity in S1 is specifically as follows: Based on the mass, combustion time, and quantity of the flame catalyst, the total number of ice nuclei released per unit time is calculated using a formula.

3. The calculation method for the maximum catalyst diffusion height based on the optimal number concentration of ice nuclei in clouds according to claim 1, characterized in that, The concentration distribution analytical model established in S3 is as follows: Under the steady assumption, the governing equations, which include advection transport and turbulent diffusion terms, are solved to obtain the concentration analytical formula with the analytical expression of the lifting trajectory as the vertical center and a Gaussian distribution on the cross section, thereby establishing the analytical model of the concentration distribution.

4. The calculation method for the maximum catalyst diffusion height based on the optimal number concentration of ice nuclei in clouds according to claim 1, characterized in that, The method of using different calculation methods based on whether the vertical airflow velocity at the smoke source exceeds the vertical airflow attenuation threshold to obtain the predicted height includes: ， Where Q is the smoke source intensity, The horizontal wind speed at the height of the smoke source. The vertical airflow velocity at the smoke source. The smoke source emission height is t, and the flame burning time is t. and These are the lateral and vertical turbulent diffusion coefficients, respectively. For feature height, The parameter for maximum vertical airflow velocity. , This is the threshold for vertical airflow attenuation.

5. An electronic device, characterized in that, The electronic device includes a memory and at least one processor, the memory storing a computer program, and the processor executing the computer program to implement the calculation method for the maximum diffusion height of the catalyst based on the optimal number concentration of ice nuclei in the cloud, as described in any one of claims 1-4.

6. A computer storage medium, characterized in that, It stores a computer program that, when executed, implements the calculation method for the maximum height of catalyst diffusion based on the optimal number concentration of ice nuclei in the cloud, according to any one of claims 1-4.

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