Method and system for calculating oceanic sea spray heat flux contribution based on lagrangian transport coupling microphysical processes

Abstract

The application discloses a method and system for calculating ocean sea spray heat flux contribution based on coupling microphysical processes by Lagrangian transport, and belongs to the technical field of marine atmospheric boundary layer physics and air-sea interaction. The application couples a Lagrangian stochastic transport model with sea spray droplet microphysical processes: the evolution law of sea spray droplet temperature and radius with time is pre-calculated, and the mass and relaxation time of the sea spray droplet are updated according to the flight time of the sea spray droplet during the Lagrangian transport process; for each sea spray droplet, the termination time when the sea spray droplet stops being tracked due to falling back to the sea surface, complete evaporation of liquid water or reaching a preset vertical transport height threshold is recorded, and the final state temperature and final state radius of the sea spray droplet are determined according to the time, so that the cumulative sensible heat and the cumulative latent heat of a single sea spray droplet are quantitatively calculated; and the average sensible heat flux contribution and the average latent heat flux contribution of the ocean sea spray with the initial radius are obtained. The application improves the physical authenticity and reliability of the calculation of the ocean sea spray heat flux contribution.

Description

Technical Field

[0001] This invention belongs to the field of marine atmospheric boundary layer physics and air-sea interaction technology, specifically relating to a method and system for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes. This invention is applicable to the quantitative calculation of the heat flux contribution of a single marine droplet under high wind speed conditions. Background Technology

[0002] Sea spray consists of seawater droplets ejected from the sea surface into the atmosphere when waves break apart, with particle sizes ranging from approximately 0.01 micrometers to several millimeters. Under strong wind conditions (wind speeds greater than 15 m / s at 10 m / s), sea spray plays a crucial role in momentum, sensible heat, and latent heat exchange at the sea-air interface. During their suspension, individual droplets exchange heat and water vapor with the surrounding atmosphere; the cumulative effect of this exchange significantly enhances the heat flux at the sea-air interface, thereby influencing tropical cyclone intensity development, the upper ocean heat budget, and regional climate simulation results.

[0003] For a single ocean droplet, the calculation of its heat flux contribution depends on two core elements: (1) the microphysical processes of the droplet, including its temperature adjustment and radius change due to evaporation; and (2) the residence time of the droplet, which is the suspension time of the droplet from being ejected into the atmosphere to falling back to the sea surface (or completely evaporating). Among these, the residence time of the droplet directly determines the effective duration of heat and mass exchange between a single ocean droplet and the atmosphere, and is a key parameter controlling the magnitude of the heat flux contribution of a single ocean droplet.

[0004] The core of the widely used methods for calculating the contribution of marine droplet heat flux internationally is derived from the microphysical timescale framework (hereinafter referred to as the A92 framework) proposed by Andreas (1992). This framework describes the evolution of the temperature and radius of a single droplet over time using an exponential relaxation function, which represents the time scale of a single droplet within its existence. The cumulative sensible heat exchanged between the interior and the atmosphere depends on the temperature change of the droplets. The product of heat capacity and cumulative latent heat depends on the product of mass loss caused by droplet evaporation and latent heat of vaporization. The duration of the droplet's existence is also a factor. Parameterized as the time required for a droplet to fall from its significant wave height to the sea surface:

[0005] (1)

[0006] in, Let be the initial radius of the droplet. For the effective wave height, For effective wave amplitude, Let be the terminal settling velocity of the droplet. This scheme assumes that the droplet is falling vertically in still air, and its existence time depends only on the effective wave amplitude and the settling velocity.

[0007] Temperature change at the end of the droplet's existence time and final state radius They are respectively:

[0008] (2)

[0009] in, The equilibrium temperature at which droplets reach thermal equilibrium with their surroundings. This refers to the sea surface temperature, which is the initial temperature of the droplets. e-folding timescale for temperature adjustment; The equilibrium radius of droplets when they reach humidity equilibrium with the environment. The e-folding timescale for radius evolution; exp() represents the exponential function.

[0010] Subsequent studies have made several improvements based on the A92 framework, but the physical treatment of the heat flux contribution of a single marine droplet has never deviated from the basic ideas of the A92 framework. Fairall et al. (1994) constructed a new marine droplet generation function based on the droplet spectrum parameterization described by A92 and introduced the white crown coverage dependence. This function continued the existence time parameterization of A92 in the treatment of single droplets, but further simplified the heat exchange of single droplets through the limiting assumptions of complete sensible heat exchange and constant latent heat evaporation. Andreas et al. (2015) proposed an improved overall flux algorithm based on the A92 framework, introducing three empirical tuning coefficients and basing it on the "bellwether" droplet radius (sensible heat...). Latent heat extraction A fast approximation algorithm was established to avoid radius-wise integration. The above work uses the existence-time parameterization of the A92 framework for calculating the heat flux contribution of individual ocean droplets, without changing the physical treatment of the droplet transport process or the physical description of the droplet's final state parameters.

[0011] The A92 framework has the following technical limitations in calculating the contribution of heat flux from a single ocean droplet:

[0012] (1) The existence time calculation ignores the transport effect of the ocean-atmospheric boundary layer. Existing schemes simplify the existence time of ocean droplets to the vertical settling time of droplets in still air. However, in reality, droplets are transported and diffused by mean wind, gusts, and high-frequency turbulence (usually collectively referred to as boundary layer turbulence) in the ocean-atmospheric boundary layer. The Lagrange stochastic simulation study by Mueller and Veron (2014) shows that boundary layer turbulence can significantly prolong the existence time of ocean droplets, and the existence time does not show the clear proportional relationship assumed by Andreas (1992) between the existence time and the significant wave height. Since the heat flux contribution of a single ocean droplet directly depends on the existence time, its deviation will be transmitted to the calculation results.

[0013] (2) The coupling effect between transport and microphysics is not considered. During transport, ocean droplets undergo evaporation, which reduces their radius, leading to a decrease in their settling velocity and an increase in their turbulent following ability, thereby prolonging their existence time. The extended existence time, in turn, allows the droplets to undergo more thorough evaporation. The existing scheme fails to consider this real physical feedback mechanism, further leading to calculation errors. Summary of the Invention

[0014] To address the aforementioned technical problems, this invention provides a method and system for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled with microphysical processes. This invention couples the Lagrange random transport model with the microphysical processes of droplets: by pre-calculating the evolution of droplet temperature and radius over time, and updating the droplet's mass and relaxation time based on its flight time during Lagrange transport; for each droplet, the termination time when it stops tracking due to falling back to the sea surface, complete evaporation of liquid water, or reaching a preset vertical transport height threshold is recorded, referred to as the effective existence time, and its final state temperature and final state radius are determined based on this time, quantitatively calculating the cumulative sensible heat and cumulative latent heat of a single marine droplet; further... The calculation results of droplets with the same initial radius are ensembled and averaged to obtain the average sensible heat flux contribution and average latent heat flux contribution of marine droplets with that initial radius. In this invention, the cumulative sensible heat (or cumulative latent heat) of a single marine droplet refers to the total amount of sensible heat (or latent heat) exchanged with the atmosphere from the time of ejection to the end of tracking, expressed in joules (J). This cumulative heat, combined with the droplet generation function and integrated over the droplet size, yields the air-sea heat flux (W / m). Therefore, the cumulative heat of a single (or ensemble-averaged) droplet is called the contribution of a single marine droplet to the air-sea heat flux, or simply the (average) heat flux contribution. This invention can solve the problem of heat flux deviation caused by the simplification of droplet existence time calculation in existing technologies, and improve the physical accuracy and reliability of marine droplet heat flux contribution calculation.

[0015] To achieve the above objectives, the present invention adopts the following technical solution:

[0016] A method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes includes the following steps:

[0017] S1: Establish the Lagrange transport equation for droplets to describe the motion of droplets in the turbulent field of the ocean-atmospheric boundary layer. The transport equation includes deterministic gravity terms, mean wind and gust terms, and stochastic turbulence terms.

[0018] S2: Establish a set of equations for the microphysical processes of droplets, including the temperature evolution equation and radius evolution equation of droplets, to describe the temperature adjustment, evaporation cooling and radius change of droplets during the transport process;

[0019] S3: Given environmental parameters and an initial radius, perform pre-calculation on the microphysical process equations of the droplets to obtain the evolution law of the temperature and radius of the droplets with the flight time under the initial radius, and establish a corresponding pre-calculation lookup table;

[0020] S4: Couple the Lagrange transport equation with the temperature and radius evolution laws pre-calculated in S3. Within each time step of the Lagrange transport, obtain the current radius based on the flight time of the droplet, and update its mass and relaxation time, simultaneously updating the droplet position and velocity, until the droplet falls back to the sea surface, the liquid water completely evaporates, or the preset vertical transport height is reached. ;

[0021] S5: Yes Each of the droplets with the same initial radius executes S4, recording the... The time from the ejection of a droplet to the termination of tracking The effective existence time is determined based on the pre-calculated lookup table established in S3. The final temperature of a droplet corresponding to its effective existence time. and final state radius ;

[0022] S6: Based on the final temperature of each droplet and final state radius Calculate its cumulative sensible heat and cumulative latent heat respectively, and then... The calculation results of droplets with the same initial radius are ensembled and averaged to obtain the average sensible heat flux contribution and average latent heat flux contribution of marine droplets with that initial radius.

[0023] Further, in S1, the Lagrange transport equation includes a velocity control equation and a position control equation for droplets. The velocity control equation describes that the acceleration of droplets is determined by both air resistance and gravity terms. The air resistance term is the product of the ratio of the drag correction factor to the relaxation time and the difference between the local atmospheric air velocity and the droplet velocity. The drag correction factor is a function of the droplet Reynolds number. The gravity term acts on the vertical component. The position control equation describes that the rate of change of droplet position is equal to its velocity. The local atmospheric air velocity is the sum of the average atmospheric velocity, the gust velocity, and the turbulent fluctuation velocity (excluding the turbulent fluctuation velocity in the horizontal direction). The turbulent vertical fluctuation velocity is described using the generalized Langevin model.

[0024] Furthermore, in S2, the droplet temperature evolution equation describes the rate of temperature change over time as determined by the sensible heat exchange term and the evaporative cooling term between the atmosphere and the droplets, wherein the evaporative cooling term is related to the latent heat of vaporization and the difference between the ambient water vapor density and the saturated water vapor density on the droplet surface; the radius evolution equation describes the rate of radius change over time as driven by the difference between the ambient water vapor density and the saturated water vapor density on the droplet surface, and is affected by the modified water vapor molecule diffusion coefficient, the modified atmospheric thermal conductivity coefficient, the droplet radius, and the seawater density.

[0025] Furthermore, in S3, the process of establishing the pre-calculation lookup table includes: given environmental parameters and an initial radius, performing time integration on the microphysical process equations to obtain a discrete time series of the temperature and radius of the droplets as a function of the flight time at the given initial radius; the environmental parameters include atmospheric temperature, sea surface temperature, relative humidity, and water vapor density; the pre-calculation lookup table stores at least the flight time, the corresponding droplet temperature and radius, and the temperature and radius when the droplets are completely evaporated or reach a steady state.

[0026] Further, in S4, the coupled solution adopts a prediction-update format, and performs the following operations sequentially within each time step: obtain local atmospheric state parameters based on the current droplet position; based on the pre-calculation lookup table established in step S3, obtain the current radius by interpolation of the droplet's flight time, and update the mass and relaxation time accordingly; generate turbulence and gust velocity increments, and solve the Lagrange transport equation in combination with the updated relaxation time to update the position and velocity; determine whether the termination condition is met, the termination condition including the droplet height being less than or equal to zero, the radius being less than or equal to the dry salt core radius, or the height being greater than or equal to a preset vertical transport height threshold.

[0027] Furthermore, in S5, the effective existence time is the time elapsed from the moment the i-th droplet is ejected until it meets any of the following conditions: falling back to the sea surface, complete evaporation of liquid water, or reaching a preset vertical transport height threshold; the final state temperature and final state radius are the temperature and radius values ​​at the corresponding time obtained by querying or interpolating the pre-calculated lookup table established in step S3 using the recorded effective existence time as an index.

[0028] Furthermore, in S6, the cumulative sensible heat is calculated based on the initial mass of the droplet, the specific heat of the seawater, and the difference between the final temperature and the sea surface temperature; the cumulative latent heat is calculated based on the latent heat of vaporization, the density of the seawater, and the difference between the initial volume and the final volume of the droplet; if the liquid water in the droplet completely evaporates, the final radius is taken as the dry salt core radius.

[0029] Further, in S6, the ensemble average refers to the arithmetic average of the cumulative sensible heat and cumulative latent heat calculated for N droplets with the same initial radius, to obtain the average sensible heat flux contribution and average latent heat flux contribution of the marine droplets with that initial radius; where N is the total number of simulated droplets and N is not less than 1000.

[0030] This invention also provides a system for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes, comprising:

[0031] The Lagrange transport module is used to establish and solve the equations of motion of droplets in the turbulent field of the ocean-atmospheric boundary layer. The equations of motion include deterministic gravity terms, mean wind and gust terms, and stochastic turbulence terms.

[0032] The microphysics process module is used to establish the temperature evolution equation and radius evolution equation of droplets, describing the temperature adjustment, evaporative cooling and radius change process of droplets;

[0033] The pre-calculation module is used to pre-calculate the microphysical process equations given environmental parameters and an initial radius, obtain the evolution of the temperature and radius of the droplet with the flight time, and establish a pre-calculation lookup table.

[0034] The coupled solution module is used to perform time-step coupled solution of the Lagrange transport module and the pre-calculation module. Within each time step, it obtains the current radius based on the flight time of the droplet, updates the mass and relaxation time, and synchronously updates the position and velocity until the droplet falls back to the sea surface, the liquid water completely evaporates, or a preset vertical transport height threshold is reached, and records the result. The effective existence time of each droplet ;

[0035] The heat flux contribution calculation module is used to calculate the contribution based on the first... The effective existence time of each droplet The pre-calculation module is called to obtain the corresponding final temperature. and final state radius Calculate the first one respectively The cumulative sensible heat and cumulative latent heat of each droplet;

[0036] The statistical processing module is used for... Two with the same initial radius The cumulative sensible heat and cumulative latent heat calculated from the droplets are aggregated and averaged to obtain the average sensible heat flux contribution and average latent heat flux contribution of the marine droplets at the initial radius.

[0037] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the above-described method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes.

[0038] Beneficial effects:

[0039] 1. This invention simultaneously considers the mean flow field, gusts, gravity settling, and random turbulent diffusion effects in the Lagrange transport equation, overcoming the shortcomings of existing methods that simplify the existence time to the vertical settling time in still air, and can more realistically describe the transport process of ocean droplets in the ocean-atmospheric boundary layer.

[0040] 2. This invention first pre-calculates the temperature evolution and radius evolution, and then, during the Lagrange transport process, calls the pre-calculation results based on the flight time of the droplets to synchronously update the mass and relaxation time, thereby reflecting the influence of the radius change caused by evaporation on the motion response of the droplets, and avoiding the need to repeatedly solve the complete microphysical equations in each transport time step.

[0041] 3. This invention determines the final temperature and final radius based on the effective existence time of each droplet, and calculates the cumulative heat drop by drop before performing a ensemble average, thus avoiding the approximate errors caused by using the average time to back-calculate the average final state and using a single exponential temperature relaxation method.

[0042] 4. This invention decomposes Lagrange transport, microphysics pre-computation, coupled solution, dropwise final state extraction, and heat flux set statistics into interconnected modules, which can provide environmental fields based on observation data, reanalysis data, or boundary layer model outputs, and are also easy to implement in computer-readable storage media and computing systems. Attached Figure Description

[0043] Figure 1 This is a schematic diagram illustrating the process of marine droplet transport and heat exchange in the marine atmospheric boundary layer according to the present invention.

[0044] Figure 2 This is a flowchart illustrating the method for calculating the heat flux contribution of a single ocean droplet based on Lagrange transport coupled with microphysical processes, as described in this invention.

[0045] In the attached figures, the following labels are used: 1 represents the ocean-atmospheric boundary layer; 2 represents mean wind and gust transport; 3 represents random turbulent diffusion; 4 represents the Lagrange trajectory of droplets; 5 represents sensible heat exchange; 6 represents evaporation and latent heat exchange; 7 represents the sea surface; and 8 represents the preset vertical transport height. . Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0047] like Figure 1 The diagram illustrates the complete transport and evolution process of marine droplets in the ocean-atmospheric boundary layer 1: After being generated by wave breaking and ejection, the movement of marine droplets is driven by both deterministic and stochastic components of the flow field—mean wind and gusts provide systematic horizontal transport and lifting (represented in the diagram as mean wind and gust transport 2), while high-frequency stochastic turbulence leads to the stochastic diffusion of droplet trajectories (represented in the diagram as stochastic turbulent diffusion 3). Their trajectories are represented by the Lagrange trajectories of the droplets 4. During transport, the droplets continuously undergo sensible heat exchange 5 and evaporation and latent heat exchange 6, resulting in temperature changes and mass reduction; some droplets can rise to a predetermined vertical transport height. 8; Some of the unevaporated droplets fall back to the sea surface 7, completing the entire life cycle from generation, transport, thermodynamic evolution to sedimentation or complete evaporation.

[0048] like Figure 2 As shown, the present invention provides a method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes, comprising the following steps:

[0049] S1: Establish the Lagrange transport equation for droplets to describe the motion of droplets in the turbulent field of the ocean-atmospheric boundary layer. The transport equation includes deterministic gravity terms, mean wind and gust terms, and stochastic turbulence terms.

[0050] S2: Establish a set of equations for the microphysical processes of droplets, including the temperature evolution equation and radius evolution equation of droplets, to describe the temperature adjustment, evaporation cooling and radius change of droplets during the transport process;

[0051] S3: Given environmental parameters and an initial radius, perform pre-calculation on the microphysical process equations of the droplets to obtain the evolution law of the temperature and radius of the droplets with the flight time under the initial radius, and establish a corresponding pre-calculation lookup table;

[0052] S4: Couple the Lagrange transport equation with the temperature and radius evolution laws pre-calculated in S3. Within each time step of the Lagrange transport, obtain the current radius based on the flight time of the droplet, update its mass and relaxation time, and synchronously update its position and velocity until the droplet falls back to the sea surface, the liquid water completely evaporates, or the preset vertical transport height is reached. ;

[0053] S5: Yes Each of the droplets with the same initial radius executes S4, recording the... The time from the ejection of a droplet to the termination of tracking (Effective existence time); Based on the pre-calculated lookup table established in S3, determine the first... The final temperature of a droplet corresponding to its effective existence time. and final state radius ;

[0054] S6: Based on the final temperature of each droplet and final state radius Calculate its cumulative sensible heat and cumulative latent heat respectively, and then... The calculation results of droplets with the same initial radius are ensembled and averaged to obtain the average sensible heat flux contribution and average latent heat flux contribution of marine droplets with that initial radius.

[0055] Specifically, in S1, the Lagrange transport equation for the droplets is:

[0056] (3)

[0057] (4)

[0058] in, Let be the velocity components of the droplets in a three-dimensional coordinate system. For the corresponding three-dimensional position coordinates, , and The mean velocity, gust velocity, and vertical turbulent fluctuation velocity of the ocean-atmospheric boundary layer flow field are given. This is the drag correction factor. For time, It is the acceleration due to gravity. The relaxation time of droplets; the stated Gust speed obtained from actual observations or numerical model data The vertical turbulent pulsation velocity is obtained through parameterization based on analysis of actual observation data. It is described using the generalized Langevin equation.

[0059] Specifically, in S2, the set of equations for the microphysical processes of the droplets includes:

[0060] (5)

[0061] (6)

[0062] in, , , and The temperature, radius, density, and specific heat of the droplet. Atmospheric temperature, and To correct for atmospheric thermal conductivity and water vapor molecule diffusion coefficient, For latent heat of vaporization, For the density of water vapor in the environment, The density of saturated water vapor on the droplet surface. For ambient relative humidity, The surface saturation ratio of the droplet. This is the universal gas constant. The molar mass of water, This is the saturated water vapor pressure at ambient temperature.

[0063] Specifically, in S3, the pre-calculation includes:

[0064] Given standard environmental parameters and initial radius By integrating the microphysical process equations over time, the temperature of the droplet with the initial radius can be obtained. and radius A pre-calculated lookup table is established based on the evolutionary patterns over time; the standard environmental parameters include atmospheric temperature. Sea surface temperature Ambient relative humidity and ambient water vapor density .

[0065] Specifically, in S4, the coupled solution adopts a prediction-update format, which is executed sequentially within each time step:

[0066] (1) Input the local atmospheric conditions based on the current droplet position;

[0067] (2) Based on the radius evolution law obtained by S3 pre-calculation, combined with the flight time of the droplet, the current radius is obtained and its mass and relaxation time are updated;

[0068] (3) Generate turbulence and gust speed increments and update droplet position and speed until droplets fall back to the sea surface, liquid water evaporates completely, or the preset vertical transmission height threshold is reached.

[0069] Specifically, S5 includes:

[0070] right Two with the same initial radius The droplets were executed in S4, and the number of droplets was recorded. The tracking termination time for each droplet from its ejection to its return to the sea surface, complete evaporation of the liquid water, or reaching a preset vertical transport height threshold. (Effective existence time), and based on the temperature evolution law and radius evolution law pre-calculated in step S3, determine the first... The final temperature and final radius of each droplet:

[0071] (7)

[0072] in, This represents the total number of droplets, and .

[0073] Specifically, S6 includes:

[0074] Based on the final temperature and final radius of each droplet, first calculate its cumulative sensible heat and cumulative latent heat, then... The calculation results of droplets with the same initial radius are ensembled and averaged to obtain the average sensible heat flux contribution and the average latent heat flux contribution:

[0075] (8)

[0076] (9)

[0077] (10)

[0078] (11)

[0079] in, and The first The cumulative sensible heat and cumulative latent heat of each droplet; and These represent the average sensible heat flux contribution and the average latent heat flux contribution of the droplet at the initial radius, respectively. The density of seawater; The specific heat of seawater; Sea surface temperature; For the first The temperature of a droplet at the end of its effective existence time; The initial radius of the droplet; Latent heat of vaporization; For the first The radius of a droplet at the end of its effective existence time, if its liquid water has completely evaporated, then Take the radius of the dry salt nucleus; Pi is the mathematical constant of a circle.

[0080] This invention also provides a system for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes, comprising:

[0081] The Lagrange transport module is used to establish and solve the equations of motion of droplets in the turbulent field of the ocean-atmospheric boundary layer. The equations of motion include deterministic gravity terms, mean wind and gust terms, and stochastic turbulence terms.

[0082] The microphysics process module is used to establish the temperature evolution equation and radius evolution equation of droplets, describing the temperature adjustment, evaporative cooling and radius change process of droplets;

[0083] The pre-calculation module is used to pre-calculate the microphysical process equations given environmental parameters and an initial radius, obtain the evolution of the temperature and radius of the droplet with the flight time, and establish a pre-calculation lookup table.

[0084] The coupled solution module is used to perform time-step coupled solution of the Lagrange transport module and the pre-calculation module. Within each time step, it obtains the current radius based on the flight time of the droplet, updates its mass and relaxation time, and synchronously updates its position and velocity until the droplet falls back to the sea surface, the liquid water completely evaporates, or a preset vertical transport height threshold is reached, and records the result. The effective existence time of each droplet ;

[0085] The heat flux contribution calculation module is used to calculate the contribution based on the first... The effective existence time of each droplet The pre-calculation module is called to obtain the corresponding final temperature. and final state radius Calculate the first one respectively The cumulative sensible heat and cumulative latent heat of each droplet;

[0086] The statistical processing module is used for... Two with the same initial radius The cumulative sensible heat and cumulative latent heat calculated from the droplets are aggregated and averaged to obtain the average sensible heat flux contribution and average latent heat flux contribution of the marine droplets at the initial radius.

[0087] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the above-described method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes.

[0088] Example:

[0089] The calculation of the marine droplet heat flux contribution in this embodiment includes six interconnected steps: establishing the Lagrange transport equation, establishing a set of microphysical process equations, performing microphysical process pre-calculation, performing coupled solution of transport and pre-calculation results, extracting effective existence time and final state parameters drop by drop, and calculating cumulative heat drop by drop and performing ensemble averaging.

[0090] The calculation input includes: initial radius of the droplet. Sea surface temperature Atmospheric temperature Ambient relative humidity Environmental water vapor density Air pressure, mean velocity field of ocean-atmospheric boundary layer, parameterized variables of gust wind, statistics of vertical velocity of turbulence, and total number of simulated particles. Time step and preset vertical transmission height threshold The calculated output is the average sensible heat flux contribution of the droplet with this initial radius. and the contribution of average latent heat flux .

[0091] Establishing the Lagrange transport equations includes:

[0092] This embodiment is based on the Lagrange stochastic model constructed from equations (3) and (4), taking its value in... A two-dimensional representation in a plane, used to describe the motion of droplets in the turbulent field of the ocean-atmospheric boundary layer. Droplet velocity. and location The governing equations are in two-dimensional form, as shown in equations (3) and (4), respectively. Among them, the average velocity... Obtained from actual observations, reanalysis data, or numerical model output; gust speed Obtained by a parameterization scheme based on actual observation data; turbulent vertical fluctuation velocity It is described using the generalized Langevin equation.

[0093] relaxation time of droplets Calculated based on droplet inertial response time:

[0094] (12)

[0095] in, The density of droplets. Where is the droplet radius, Aerodynamic viscosity. Drag correction factor. To characterize drag correction under non-Stokes flow conditions, this embodiment uses the droplet Reynolds number. Functional representation:

[0096] (13)

[0097] in, air density, The fluid velocity at the location of the droplet is denoted as . For droplet velocity, a value of is used. For small-diameter droplets in the Stokes region, a value of is used. For larger droplets, resistance correction is performed according to formula (13).

[0098] Turbulent vertical pulsation velocity The stochastic evolution is represented as:

[0099] (14)

[0100] in, The drift coefficient, Where is the diffusion coefficient. The increment is the Wiener process value. The drift coefficient and diffusion coefficient are determined based on local turbulence statistics as follows:

[0101] (15)

[0102] (16)

[0103] in, Kolmogorov's constant, The turbulent kinetic energy dissipation rate, This represents the vertical velocity variance. Turbulence statistics can be provided by air-sea coupled boundary layer observation data or model simulation outputs; when using near-surface similarity relationships for estimation, a value can be taken as... ,in The corresponding fluid Lagrangian timescale is: .

[0104] Establishing the system of equations for microphysical processes and conducting preliminary calculations of microphysical processes include:

[0105] The microphysical processes include droplet temperature adjustment and radius change. This embodiment uses equations (5) and (6) to describe the droplet temperature. With radius Evolution over time. For given environmental parameters and initial radius... Before the Lagrange transport simulation begins, the microphysical equations are integrated over time to obtain the temperature evolution sequence corresponding to the initial radius. and radius evolution sequence .

[0106] Pre-calculation uses discrete time series Storage, in This is the time step for microphysics integration. The pre-computed lookup table includes at least: the flight time. Droplet temperature and radius The lookup table stores both the final temperature and final radius of the droplet when it has completely evaporated or reached a steady state.

[0107] When environmental conditions employ a height-nonuniform profile, multiple pre-calculated lookup tables can be established for different height ranges or combinations of environmental parameters. During the coupled solution process, the matching lookup table is invoked based on the local atmospheric state corresponding to the current position of the droplet. If the local state lies between adjacent lookup tables, linear interpolation can be performed on the temperature and radius evolution sequences.

[0108] The coupled solution of transport and microphysics pre-calculation results includes:

[0109] This embodiment employs a prediction-update scheme for coupled solution. For each droplet, the following steps are performed:

[0110] Step 1: Initialization. Given the initial position of the droplets. , initial velocity , initial radius and initial temperature and set the flight time of droplets to .

[0111] Step 2: Input local atmospheric conditions. Based on the current droplet location, obtain the average velocity, gust velocity parameters, turbulence statistics, and environmental parameters used to select the microphysics lookup table from observational data, reanalysis data, or numerical model output.

[0112] Step 3: Retrieve pre-calculated results. Based on the flight time of the droplets. Read the current radius from the pre-calculated lookup table and update the droplet mass and relaxation time .

[0113] Step 4: Calculate the transmission increment. Update the drag correction coefficient according to equation (13). The gust velocity component and the random pulsating velocity increment of the generalized Langevin equation are generated and substituted into equations (3) and (4) to update the droplet velocity and position.

[0114] Step 5: Termination Criterion. If the updated droplet height... If the current radius is [missing information], then it is determined that the droplet falls back to the sea surface; if [missing information If the radius of the dry salt nucleus is less than or equal to the radius of the dry salt nucleus, it is determined that the liquid water has completely evaporated and formed a residual dry salt nucleus; if the height of the renewed droplet is... If the droplet reaches a preset vertical transport height threshold, the tracking termination time is recorded. (Valid existence time) and terminate tracking.

[0115] Step 6: Time Progression. If the termination condition is not met, then let... Then return to step 2 until the termination condition or the maximum simulation time is reached.

[0116] Droplet-by-drop final-state parameter extraction, cumulative heat calculation, and ensemble averaging include:

[0117] For the same initial radius release Each droplet After completing the tracking of all droplets, record the effective existence time of each droplet. And read its final temperature from the microphysics pre-calculation lookup table according to equation (7). and final state radius In this embodiment, take .

[0118] Then, calculate the cumulative sensible heat of each droplet according to formula (8), and calculate the cumulative latent heat of each droplet according to formula (10); then calculate the cumulative latent heat of each droplet according to formulas (9) and (11). The average sensible heat flux contribution and the average latent heat flux contribution are obtained by ensemble averaging of the calculation results of each droplet.

[0119] In this embodiment, an adaptive Lagrangian transport time step is used to accurately and stably solve for the motion of droplets. ,in For fluid Lagrangian timescales. Generally speaking... It is small enough; this embodiment adopts a more stringent approach. .

[0120] The initial ejection height of ocean droplets is set at the effective wave height of the ocean waves. In actual calculations, the initial height and initial velocity distribution can also be given based on observations or ocean droplet generation experiments.

[0121] To verify the computational effectiveness of the method of the present invention, a typical typhoon boundary layer environment can be selected as an example: 10-meter wind speed. Sea surface temperature Atmospheric temperature relative humidity of the environment The corresponding effective wave height is approximately The initial radii are selected as follows: and The initial temperature of the droplets was taken as the sea surface temperature. .

[0122] Under the same environmental parameters and initial conditions, the effective existence time, final temperature, final radius, sensible heat flux contribution, and latent heat flux contribution of a single marine droplet were calculated using the A15 (Andrease et al., 2015) settling time method and the method of this invention, respectively. The results of this invention in Table 1 are ensemble averages of N droplets. In this embodiment, the preset vertical transport height threshold is only an optional protection condition and does not change the comparison results in Table 1. The calculation results are shown in Table 1.

[0123] Table 1 Comparison of Calculation Results for Key Parameters

[0124]

[0125] As shown in Table 1, for an initial radius of 100... For droplet droplets, the original A15 method estimated the existence time to be 8.20 s, while the method of this invention yielded an effective existence time of 599 s, approximately 73.0 times that of the original method; for an initial radius of 50... The original method estimated the existence time of droplets at 23.53 s, while the method of this invention yields an effective existence time of 1952 s, approximately 83.0 times that of the original method. The significant difference lies in the fact that the original method (A15) estimates existence time solely based on significant wave height and droplet terminal settling velocity, neglecting the effects of ocean-atmospheric boundary layer transport and the influence of droplet microphysical processes. The method of this invention explicitly describes the combined transport and diffusion effects of mean wind, gusts, and high-frequency turbulence using the Lagrange transport equation, enabling droplets to be entrained, lifted, and transported over long distances, thus significantly extending their effective existence time in the ocean-atmospheric boundary layer. Simultaneously, droplets continuously evaporate during transport, their radius and mass decreasing, and their relaxation time decreasing accordingly, making them more susceptible to airborne motion and less prone to rapid return to the sea surface. The transport effect of the ocean-atmospheric boundary layer on droplets and the enhanced following ability caused by evaporation are coupled, forming a process of "evaporation → radius reduction → mass and relaxation time reduction → settling velocity reduction, enhanced turbulent following ability → extended effective existence time." Therefore, the effective existence time obtained by the method of the present invention is significantly longer than that of the original method, and the initial radius is smaller than 50. The impact on droplets is more significant.

[0126] For an initial radius of 100 For marine droplets, the final temperature calculated by the original method (A15) was 17.07 ℃, while the final temperature calculated by the method of this invention was 17.33 ℃. The initial temperature of the marine droplets upon leaving the sea surface was 20 ℃, 18 ℃ higher than the ambient temperature. Initially, they rapidly cooled to near the minimum temperature of the wet-bulb temperature through sensible heat exchange and evaporative cooling. Subsequently, as evaporation continued, the salinity of the droplets increased, the surface equilibrium vapor pressure decreased, evaporative cooling weakened, and the sensible heat absorbed by the droplets from the surrounding air exceeded the latent heat of evaporation, causing the temperature to gradually rise and tend towards the quasi-equilibrium temperature determined by the ambient temperature and humidity conditions and the droplet salinity. Because the effective existence time obtained by the method of this invention is longer, the droplets have more time to rise from the minimum temperature to the quasi-equilibrium temperature, therefore their final temperature is higher than the temperature obtained by the original method at 8.20 s. Accordingly, according to the notation conventions used in Table 1, the sensible heat flux contribution of a single marine droplet calculated by the original method and the method of this invention are respectively... and The absolute value of the result obtained by the method of the present invention is reduced by approximately 8.7%. This result is consistent with the microphysical process in which the final temperature of droplets gradually approaches the quasi-equilibrium temperature.

[0127] For an initial radius of 50 The final radius of the marine droplets calculated using the original A15 method is 45.76. The final radius is only slightly smaller than the initial radius; the final radius calculated by the method of this invention is 32.00. This represents a reduction of approximately 30.1% compared to the original method. Based on droplet volume estimation, the evaporation volume ratio corresponding to the original method is approximately 23.3%, while the evaporation volume ratio corresponding to the method of this invention is approximately 73.8%, the latter being approximately 3.16 times the former. Correspondingly, the latent heat flux contribution per marine droplet calculated by the original method and the method of this invention are 3.07 × 10⁻⁶, respectively. -4 J and 9.64×10 -4 J. The method of this invention is approximately 3.14 times more efficient than the original method. The increase in latent heat is basically consistent with the increase in the proportion of evaporation volume, indicating that the method of this invention maintains good mass conservation and physical consistency among effective existence time, radius evolution, and latent heat contribution.

[0128] The above embodiments demonstrate that estimating the existence time of marine droplets solely based on significant wave height and terminal settling velocity significantly underestimates the actual existence time of marine droplets in the ocean-atmospheric boundary layer, further underestimating their evaporation and latent heat flux contributions, while also leading to calculation errors in sensible heat flux contributions. The method of this invention, by coupling the microphysical evolution of droplets during Lagrangian transport, can more reasonably describe the physical relationship between the extended effective existence time, adjusted final temperature, reduced final radius, and enhanced latent heat flux contribution, thereby improving the physical accuracy and reliability of calculating the heat flux contribution of individual marine droplets.

Claims

1. A method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes, characterized in that, Includes the following steps: S1: Establish the Lagrange transport equation for droplets to describe the motion of droplets in the turbulent field of the ocean-atmospheric boundary layer. The transport equation includes deterministic gravity terms, mean wind and gust terms, and stochastic turbulence terms. S2: Establish a set of equations for the microphysical processes of droplets, including the temperature evolution equation and radius evolution equation of droplets, to describe the temperature adjustment, evaporation cooling and radius change of droplets during the transport process; S3: Given environmental parameters and an initial radius, perform pre-calculation on the microphysical process equations of the droplets to obtain the evolution law of the temperature and radius of the droplets with the flight time under the initial radius, and establish a corresponding pre-calculation lookup table; S4: Couple the Lagrange transport equation with the temperature and radius evolution laws pre-calculated in S3. Within each time step of the Lagrange transport, obtain the current radius based on the flight time of the droplet, and update its mass and relaxation time. Simultaneously update the position and velocity of the droplet until the droplet falls back to the sea surface, the liquid water completely evaporates, or the preset vertical transport height is reached. ; S5: Yes Each of the droplets with the same initial radius executes S4, recording the... The time from the ejection of a droplet to the termination of tracking , as the effective existence time; based on the pre-calculated lookup table established in S3, determine the first The final temperature of a droplet corresponding to its effective existence time. and final state radius ; S6: Based on the final temperature of each droplet and final state radius Calculate its cumulative sensible heat and cumulative latent heat respectively, and then... The calculation results of droplets with the same initial radius are ensembled and averaged to obtain the average sensible heat flux contribution and average latent heat flux contribution of marine droplets with that initial radius.

2. The method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes according to claim 1, characterized in that, In S1, the Lagrange transport equation includes a velocity control equation and a position control equation for droplets. The velocity control equation describes that the acceleration of droplets is determined by both air resistance and gravity terms. The air resistance term is the product of the ratio of the drag correction factor to the relaxation time and the difference between the local atmospheric air velocity and the droplet velocity. The drag correction factor is a function of the droplet Reynolds number. The gravity term acts on the vertical component. The position control equation describes that the rate of change of droplet position is equal to the droplet velocity. The local atmospheric air velocity is the sum of the average atmospheric velocity, the gust velocity, and the turbulent fluctuation velocity, and the turbulent vertical fluctuation velocity is described using the generalized Langevin model.

3. The method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes according to claim 1, characterized in that, In S2, the droplet temperature evolution equation describes the rate of change of droplet temperature over time, which is jointly determined by the sensible heat exchange term and the evaporative cooling term between the atmosphere and the droplets. The evaporative cooling term is related to the latent heat of vaporization and the difference between the ambient water vapor density and the saturated water vapor density on the droplet surface. The radius evolution equation describes the rate of change of droplet radius over time, which is driven by the difference between the ambient water vapor density and the saturated water vapor density on the droplet surface, and is affected by the modified water vapor molecule diffusion coefficient, the modified atmospheric thermal conductivity, the droplet radius, and the seawater density.

4. The method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes according to claim 1, characterized in that, In S3, the process of establishing the pre-calculation lookup table includes: given environmental parameters and an initial radius, performing time integration on the microphysical process equations to obtain a discrete time series of the temperature and radius of the droplets as a function of the flight time at the given initial radius; the environmental parameters include atmospheric temperature, sea surface temperature, relative humidity, and water vapor density; the pre-calculation lookup table stores at least the flight time, the corresponding droplet temperature and radius, and the temperature and radius when the droplets are completely evaporated or reach a steady state.

5. The method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes according to claim 1, characterized in that, In S4, the coupled solution adopts a prediction-update format, and performs the following operations in sequence within each time step: obtain local atmospheric state parameters based on the current droplet position; based on the pre-calculation lookup table established in step S3, obtain the current radius by interpolation of the droplet's flight time, and update the mass and relaxation time accordingly. The system generates turbulence and gust velocity increments, and solves the Lagrange transport equations using the updated relaxation time to update the position and velocity. It then determines whether the termination conditions are met, including droplet height being less than or equal to zero, radius being less than or equal to the dry salt nucleus radius, or height being greater than or equal to a preset vertical transport height threshold.

6. The method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes according to claim 1, characterized in that, In S5, the effective existence time is the time elapsed from the moment the i-th droplet is ejected until it meets any of the following conditions: falling back to the sea surface, complete evaporation of liquid water, or reaching a preset vertical transport height threshold. The final state temperature and final state radius are the temperature and radius values ​​at the corresponding time obtained by querying or interpolating the pre-calculated lookup table established in step S3 using the recorded effective existence time as an index.

7. The method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes according to claim 1, characterized in that, In S6, the cumulative sensible heat is calculated based on the initial mass of the droplet, the specific heat of the seawater, and the difference between the final temperature and the sea surface temperature; the cumulative latent heat is calculated based on the latent heat of vaporization, the density of the seawater, and the difference between the initial volume and the final volume of the droplet; if the liquid water in the droplet completely evaporates, the final radius is taken as the dry salt core radius.

8. The method for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes according to claim 1, characterized in that, In S6, the ensemble average refers to the arithmetic average of the cumulative sensible heat and cumulative latent heat calculated for N droplets with the same initial radius, to obtain the average sensible heat flux contribution and average latent heat flux contribution of the marine droplets with that initial radius; where N is the total number of simulated droplets and N is not less than 1000.

9. A system for calculating the contribution of marine droplet heat flux based on Lagrange transport coupled microphysical processes, characterized in that, include: The Lagrange transport module is used to establish and solve the equations of motion of droplets in the turbulent field of the ocean-atmospheric boundary layer. The equations of motion include deterministic gravity terms, mean wind and gust terms, and stochastic turbulence terms. The microphysics process module is used to establish the temperature evolution equation and radius evolution equation of droplets, describing the temperature adjustment, evaporative cooling and radius change process of droplets; The pre-calculation module is used to pre-calculate the microphysical process equations given environmental parameters and initial radius, obtain the evolution of temperature and radius of droplets with flight time at that initial radius, and establish a pre-calculation lookup table. The coupled solution module is used to perform time-step coupled solution of the Lagrange transport module and the pre-calculation module. Within each time step, it obtains the current radius based on the flight time of the droplet, updates its mass and relaxation time, and synchronously updates its position and velocity until the droplet falls back to the sea surface, the liquid water completely evaporates, or a preset vertical transport height threshold is reached, and records the result. The effective existence time of each droplet ; The heat flux contribution calculation module is used to calculate the contribution based on the first... The effective existence time of each droplet The pre-calculation module is called to obtain the corresponding final temperature. and final state radius Calculate the first one respectively The cumulative sensible heat and cumulative latent heat of each droplet; The statistical processing module is used for... Two with the same initial radius The cumulative sensible heat and cumulative latent heat calculated from the droplets are aggregated and averaged to obtain the average sensible heat flux contribution and average latent heat flux contribution of the marine droplets at the initial radius.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for calculating the contribution of marine droplet heat flux based on the Lagrange transport coupled microphysical process as described in any one of claims 1-8.

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