CN115859033B - Weather forecast method and device based on cloud micro-physical process - Google Patents
Weather forecast method and device based on cloud micro-physical process Download PDFInfo
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- FAPWRFPIFSIZLT-UHFFFAOYSA-M Sodium chloride Chemical compound [Na+].[Cl-] FAPWRFPIFSIZLT-UHFFFAOYSA-M 0.000 claims description 36
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- 239000011780 sodium chloride Substances 0.000 claims description 18
- PAWQVTBBRAZDMG-UHFFFAOYSA-N 2-(3-bromo-2-fluorophenyl)acetic acid Chemical compound OC(=O)CC1=CC=CC(Br)=C1F PAWQVTBBRAZDMG-UHFFFAOYSA-N 0.000 claims description 14
- BFNBIHQBYMNNAN-UHFFFAOYSA-N ammonium sulfate Chemical compound N.N.OS(O)(=O)=O BFNBIHQBYMNNAN-UHFFFAOYSA-N 0.000 claims description 14
- 229910052921 ammonium sulfate Inorganic materials 0.000 claims description 14
- 235000011130 ammonium sulphate Nutrition 0.000 claims description 14
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Abstract
The embodiment of the invention discloses a weather forecast method and a weather forecast device based on a cloud micro-physical process, wherein the method comprises the following steps: establishing an aerosol activation parameterized model by fitting a regression equation of the radius of the dry aerosol and the activation radius; establishing a multi-mode cloud drip spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter; establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution; and weather simulation forecasting is carried out by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model. The accuracy of weather forecast is improved, and especially the accuracy of weather forecast of disastrous weather is improved.
Description
Technical Field
The invention relates to the technical field of artificial intelligence, in particular to a weather forecasting method and device based on a cloud micro physical process.
Background
At present, the forecast level of the disastrous weather is low, the forecast of the disastrous weather is realized by a weather forecast mode of a high space-time resolution area which can accurately describe macro and micro physical characteristics, the inaccuracy of the cloud micro physical parameterization scheme in the existing mode on the description of the cloud micro physical process is an important factor which causes that the cloud micro physical process cannot be accurately forecasted, and the following problems exist:
1. According to the aerosol activation Kou La theory, when the environmental supersaturation reaches the critical supersaturation degree of the aerosol Where a is related to the curvature of the droplet and b represents the solution correlation coefficient), the aerosol will activate and its activation radius will reach the critical radius/>However, when the ambient supersaturation reaches the critical supersaturation of the aerosol, the portion of activated particles does not have sufficient time to grow to the critical radius due to kinetic limitations. In other words, the critical radius determined by Kou La theory is greater than the actual wet radius of aerosol activation, particularly megakaryon aerosols.
2. The aerosol is further activated into cloud droplets, and the evolution of the cloud droplet spectrum is often represented by a gamma spectrum distribution function in a cloud microphysics parameterization scheme, wherein the gamma spectrum distribution function comprises three variables including a digital concentration, a spectral shape parameter and a slope parameter. Accurate prediction of particle spectrum is required to be achieved by constructing a system of ordinary differential equations of the number concentration, spectral shape parameters and slope parameters. However, in the current various parameterization schemes, slope parameters are generally calculated by adopting a diagnosis formula, and spectrum shape parameters are set to be fixed values or obtained by an empirical formula, so that the simulated cloud particle spectrum evolution completely deviates from the cloud micro physical change rule.
3. Both observation and numerical simulation show that a second mode of a cloud droplet spectrum formed by small cloud droplets exists at any height above the cloud base, and megakaryon aerosol plays an important role in the formation process of the rain embryo. However, current global parameterization schemes cannot describe the second mode of cloud spectrum and the large cloud mode activated by megakaryon aerosols. This is mainly due to the fact that a single gamma distribution function is used to describe the evolution of the cloud spectrum, where the newly activated cloud must follow the same gamma distribution as the other cloud and is assumed to be immediately distributed in the distribution, which assumption may lead to underestimation of the pattern for large clouds.
4. The transformation of cloud droplets into rain droplets during the formation of warm rain is based on random collision theory. In the warm rain formation parameterization scheme, because double integral of a quasi-random collision equation based on a complex integral domain is difficult to solve, a simplified warm rain formation mechanism is generally adopted at present to parameterize the automatic cloud and rain drop conversion rate, and because simplified processing is carried out in the calculation of the automatic cloud and rain conversion rate, simulation errors on the automatic cloud and rain conversion rate are large.
In summary, how to reasonably describe the cloud micro-physical process, so as to improve accuracy of weather forecast, especially accuracy of weather forecast in disastrous weather, is a problem to be solved by those skilled in the art.
Disclosure of Invention
Therefore, the embodiment of the invention provides a weather forecast method and device based on a cloud micro-physical process, so as to at least partially solve the technical problem of poor weather forecast accuracy in the prior art.
In order to achieve the above object, the embodiment of the present invention provides the following technical solutions:
a weather forecast method based on a cloud micro-physical process, the method comprising:
Establishing an aerosol activation parameterized model by fitting a regression equation of the radius of the dry aerosol and the activation radius;
establishing a multi-mode cloud drip spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter;
Establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution;
and weather simulation forecasting is carried out by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
In some embodiments, fitting a regression equation of dry aerosol radius to activation radius specifically includes:
And fitting regression equations of the radius and the activation radius of the dry aerosols of the sodium chloride, the ammonium nitrate and the ammonium sulfate respectively based on the simulation result of the high-resolution Lagrange classification mode.
In some embodiments, the regression equation fitting the dry aerosol radius to the activation radius of the sodium chloride dry aerosol is:
rwet1＝7.54rdry1 0.8318
where r dry1 is the radius (μm) of the sodium chloride dry aerosol and r wet1 is the radius (μm) of the sodium chloride activation.
In some embodiments, the regression equation fitting the dry aerosol radius to the activation radius of the ammonium nitrate dry aerosol is:
rwet2＝6.58rdry2 0.835
where r dry2 is the radius (μm) of the ammonium nitrate dry aerosol and r wet2 is the ammonium nitrate activation radius (μm).
In some embodiments, the regression equation fitting the dry aerosol radius to the activation radius of the ammonium sulfate dry aerosol is:
rwet3＝5.83rdry3 0.8396
Where r dry3 is the radius (μm) of the ammonium sulfate dry aerosol and r wet3 is the ammonium sulfate activation radius (μm).
In some embodiments, the system of numerical concentration, spectral shape, and slope parameters normal differential equations constructed from cloud droplet concentration, cloud water content, and reflectance factors are:
Where M 0c is the cloud drop concentration, M 1c is the cloud water content, M 2c is the reflectance, and H 0c＝1,H1c＝106,H2c＝1012(πρw/6)-2,ρw is the water density.
In some embodiments, the analytical solutions for the multi-modal cloud droplet self-collection rate, the cloud-to-rain automatic conversion rate, the rain droplet self-collection rate, and the collection cloud droplet rate are:
In the formula, SCC is short for a cloud droplet Self-collecting process (Self-collection of cloud droplets), SCR is short for a rain droplet Self-collecting process (Self-collection of raindrops), AUTO is short for a cloud and rain automatic conversion process (Autoconversion), and ACC is short for a rain droplet collecting cloud droplet process (Accretion). Representing the order moment of the first modality cloud drip spectrum,/>Representing the order moment of the second modality cloud drip spectrum,/>The order moment of the raindrop spectrum is represented, and p=0, 1,2. Subscripts c1, c2, and r represent a first-modality cloud, a second-modality cloud, and a rain drop, respectively ,xm＝5.23×10-7g,kc＝9.44×109cm3g-2s-1,kr＝5.78×103cm3g-1s-1.
The invention also provides a weather forecast device based on the cloud micro physical process, which comprises:
The first modeling unit is used for building an aerosol activation parameterized model by fitting a regression equation of the radius of the dry aerosol and the activation radius;
the second modeling unit is used for establishing a multi-mode cloud droplet spectrum condensation three-parameter model by establishing a normal differential equation set of a digital concentration, a spectrum shape and a slope parameter;
The third modeling unit is used for establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution;
and the result output unit is used for performing weather simulation prediction by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the method as described above when executing the program.
The invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the method as described above.
According to the weather forecast method based on the cloud micro physical process, an aerosol activation parameterized model is established by fitting a regression equation of a radius and an activation radius of dry aerosol; establishing a multi-mode cloud drip spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter; establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution; and weather simulation forecasting is carried out by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
Firstly, constructing a regression formula between the radius of dry aerosol and the wet radius of the dry aerosol when the environmental supersaturation reaches the critical supersaturation calculated by Kou La theory, accurately calculating the actual wet radius of the aerosol during activation, and further accurately giving out the initial cloud water content, the reflectivity factor and the activated cloud droplet concentration; then the activated cloud droplet particle spectrum is expressed by a gamma function, and the cloud droplet spectrum evolution is accurately described by constructing a normal differential equation set of a cloud droplet concentration and a spectrum shape parameter and a slope parameter in the gamma function; furthermore, to characterize the distribution of the multi-modal cloud drip spectrum produced by the first and second activations of the aerosol, it is proposed to use a plurality of gamma distribution functions to characterize the multi-modal cloud drip spectrum; further, a cloud drop self-collection, a cloud drop automatic conversion rate, a rain drop collecting cloud drop rate and a rain drop self-collection rate analysis solution in the warm rain forming process are obtained by solving a cloud drop random collision equation based on a multi-mode cloud drop spectrum. The accuracy of weather forecast is improved, especially the accuracy of weather forecast in disastrous weather is improved, and the technical problem of poor accuracy of weather forecast in the prior art is solved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It will be apparent to those of ordinary skill in the art that the drawings in the following description are exemplary only and that other implementations can be obtained from the extensions of the drawings provided without inventive effort.
The structures, proportions, sizes, etc. shown in the present specification are shown only for the purposes of illustration and description, and are not intended to limit the scope of the invention, which is defined by the claims, so that any structural modifications, changes in proportions, or adjustments of sizes, which do not affect the efficacy or the achievement of the present invention, should fall within the ambit of the technical disclosure.
Fig. 1 to 6 and fig. 8 are comparison diagrams of experimental results of a weather forecast method based on a cloud micro-physical process provided by the invention;
FIG. 7 is a schematic flow chart of a weather forecast method based on a cloud micro-physical process provided by the invention;
FIG. 9 is a block diagram of a weather forecast device based on a cloud micro-physical process according to the present invention;
Fig. 10 is a block diagram of a computer device according to the present invention.
Detailed Description
Other advantages and advantages of the present invention will become apparent to those skilled in the art from the following detailed description, which, by way of illustration, is to be read in connection with certain specific embodiments, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In some techniques, parameterization schemes based on Kou La theory assume that aerosol particles can grow to a Kou La critical radius when the environmental supersaturation exceeds its critical supersaturation as determined by Kou La theory. However, the Kou La critical radius of a large aerosol is much larger than the actual activation radius (as in the 14 sets of point distributions of examples 1-14 in fig. 1-3); during the further coagulation and growth of the activated cloud, compared with the Lagrangian grading scheme, the inaccurate calculation of the spectrum shape parameters by the currently commonly used dual-parameter scheme leads to false broadening of the cloud spectrum, such as the dual-parameter scheme of fixed spectrum shape parameters and the Mo Ruisen scheme of calculating spectrum shape parameters by using an empirical formula (as shown in FIG. 4); meanwhile, the observation of the cloud drip spectrum in the actual atmosphere shows that the cloud drip spectrum is often distributed in a multi-mode, but the single gamma distribution function in the current parameterization scheme cannot actually describe the distribution characteristics of the double peaks and the triple peaks of the cloud drip, and even causes simulation errors of rain embryos (as shown in fig. 5); the rainy embryo is further randomly bumped and grown into raindrops, and because of the complexity of a formula describing a random gravity bumping process, in the current mode, the automatic conversion rate of the rainy cloud and the collection rate of the rainy drops are both an empirical formula or a simplified method, and under the same cloud drop spectrum, compared with a grading scheme (shown as b in fig. 6), the simulation of the automatic conversion rate of the rainy cloud by the existing parameterization scheme (KK 00, XL09, LD04 and SB06 schemes) has great errors, as shown as c, d, e and f in fig. 6.
In order to solve the problems, the invention provides a weather forecasting method and device based on a cloud micro-physical process.
Referring to fig. 7, fig. 7 is a flow chart of a weather forecast method based on a cloud micro-physical process according to the present invention.
In a specific embodiment, the weather forecast method based on the cloud micro-physical process provided by the invention comprises the following steps:
s110: establishing an aerosol activation parameterized model by fitting a regression equation of the radius of the dry aerosol and the activation radius;
s120: establishing a multi-mode cloud drip spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter;
S130: establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution;
s140: and weather simulation forecasting is carried out by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
In step S110, a regression equation of the radius of the dry aerosol and the radius of the activation is fitted, specifically including:
And fitting regression equations of the radius and the activation radius of the dry aerosols of the sodium chloride, the ammonium nitrate and the ammonium sulfate respectively based on the simulation result of the high-resolution Lagrangian step mode.
Specifically, the regression equation of the dry aerosol radius and the activation radius fitting the sodium chloride dry aerosol is:
rwet1＝7.54rdry1 0.8318
where r dry1 is the radius (μm) of the sodium chloride dry aerosol and r wet1 is the radius (μm) of the sodium chloride activation.
Specifically, the regression equation of the dry aerosol radius and the activation radius of the fitting ammonium nitrate dry aerosol is:
rwet2＝6.58rdry2 0.835
where r dry2 is the radius (μm) of the ammonium nitrate dry aerosol and r wet2 is the ammonium nitrate activation radius (μm).
Specifically, the regression equation of the dry aerosol radius and the activation radius of the fitting ammonium sulfate dry aerosol is:
rwet3＝5.83rdry3 0.8396
Where r dry3 is the radius (μm) of the ammonium sulfate dry aerosol and r wet3 is the ammonium sulfate activation radius (μm).
That is, to complete the aerosol activation process, the present invention provides first simulating the actual activation radius of the dry aerosol during activation using a high resolution lagrangian stepped air lock mode. The aerosol activation classification model is characterized in that the change of the surface temperature of liquid drops and the change of the water vapor density are considered, and the complex water vapor diffusion growth of the aerosol with the diameter of more than 20nm can be accurately simulated.
In the high resolution Lagrangian classification model, the aerosol spectrum passesInto 2000 steps, where m a (i) represents the dry aerosol mass of the i-th step. The aerosol spectral distribution in the aerosol activation parameterized model consists of three modes (as shown in fig. 8), which is a typical marine aerosol particle size distribution ：Na1＝133cm-3,μa1＝3×10-6cm,δa1＝1.9;Na2＝70cm-3,μa2＝1×10-5cm,δa2＝1.9;Na3＝3cm-3,μa3＝1×10-4cm,δa3＝2.0.
Each modality obeys a lognormal distribution as shown in equation 1.1:
Where N a is the dry aerosol number concentration, D a is the aerosol diameter, μ a is the average radius of the dry aerosol, and δ a is the standard deviation.
The initial conditions are based on observed examples of shallow sea clouds (RICOs), and the initial temperature and air pressure for a given cloud base are 293.28K and 94479.0Pa, respectively. The rising air block is triggered by 0.25K temperature disturbance, and the relative humidity is 95%; correspondingly, the water vapor density is 1.677 X10-5 gcm-3. Since the temperature profile and the microphysical properties of the aerosol, such as number concentration and spectral distribution, both affect the formation of cloud droplets and rain embryos, 14 sets of experiments were set up in this example, including different temperature reduction rates and aerosol number concentrations, as shown in table 1.
TABLE 1 temperature decrease and aerosol number concentration correspondence table
The invention simulates the 14 groups of cases by using a high-resolution Lagrangian step mode, and outputs the dry aerosol radius and the actual wet radius thereof when the environmental supersaturation reaches the critical supersaturation calculated by Kou La theory under different temperature reduction rates and aerosol number concentrations. Fitting a calculation formula based on the Lagrangian step mode simulation results to describe the relationship between the dry aerosol radius and the actual wet radius when the ambient supersaturation reaches its critical supersaturation calculated by Kou La theory.
First, a regression formula (e.g., formula 1.2, correlation coefficient 0.9978) of the radius of sodium chloride (NaCl) dry aerosol and its activation wet radius was fitted based on the simulation results of examples 1 to 14:
rwet1＝7.54rdry1 0.8318 (1.2)
Where r dry1 is the radius (μm) of the sodium chloride dry aerosol and r wet1 is the sodium chloride activated wet radius (μm).
Next, the activation wet radius fitting formula for the ammonium nitrate (NH 4NO3) aerosol was fitted (e.g., formula 1.3, correlation coefficient 0.9984):
rwet2＝6.58rdry2 0.835 (1.3)
Finally, the wet radius fitting function for the ammonium sulfate ((NH 4)2SO4) aerosol is fitted (as in equation 1.4, correlation coefficient is 0.9987):
rwet3＝5.83rdry3 0.8396 (1.4)
the newly built activation parameterized model also passes the aerosol spectra through Discrete to 2000 steps, and when the environmental supersaturation exceeds the critical supersaturation determined by Kou La theory, the aerosol activation wet radius (r wet) is calculated by fitting equations (1.2) - (1.4). As the aerosol activates into droplets, an initial cloud concentration (M 0c), cloud water content (M 1c), and reflectance factor (M 2c) (related to the sixth order of particle diameter) will be obtained-referring to equations 1.5-1.7, the variation of these three moment amounts over time interval Δt can be written as follows:
where l represents the largest activated aerosol step in time interval Δt and n represents the smallest activated step in time interval Δt, and these three step amounts calculated by equations (1.5) - (1.7) will serve as initial step amounts for the condensation growth of the cloud droplets.
In the above step S120, the normal differential equation set of the number concentration, the spectral shape and the slope parameters constructed by the cloud droplet concentration, the cloud water content and the reflectance factor is:
Where M 0c is the cloud drop concentration, M 1c is the cloud water content, M 2c is the reflectance, and H 0c＝1,H1c＝106,H2c＝1012(πρw/6)-2,ρw is the water density.
Specifically, during the cloud droplet coagulation growth process, the general distribution function used to describe the size distribution of the hydrogel particles is shown in equation 2.1:
Where m is the mass of the individual hydrogel particles, α is the spectral shape parameter, μ is the particle spectral end parameter, β is the slope parameter, N 0 is the intercept parameter, μ is set to 1. The coagulation kinetics equation for the cloud droplet continuity with mass m c can be written in the form of equation 2.2:
Where u i denotes velocity components in x, y and z directions, v (m c) is the falling end velocity of a cloud of mass m c, δ i3 is Kronecker symbol, J describes the source and sink of the cloud, i=1, 2,3. Representing the divergence of f (m c, x, y, x) due to the growth of coagulation. Under the assumption that the velocity divergence is zero and no advection exists, the continuity equation of the cloud drip spectrum in the condensation process can be written as:
the rate of change of cloud concentration during coagulation and activation can be described by the above equation. It has been mentioned above that the present invention employs three moment orders representing the number concentration, cloud water content and reflectivity factors, respectively. Equation 2.4 is a definition of the moment of order:
Wherein p=0, 1,2 represent the number concentration, cloud water content and reflectance factor, respectively, H 0c＝1,H1c＝106,H2c＝1012(πρw/6)-2,ρw is the density of water.
Further using the gamma distribution function f (m c) of the cloud drop mass in equation 2.1, and combining equation 2.4, we can derive the analytical solutions of the three moment orders:
further derivative on both sides of equations 2.6 and 2.7 with respect to time:
The predictive equations for the spectral shape parameters and slope parameters can be derived by combining equations 2.8 and 2.9:
/>
The rate of increase of individual droplets during condensation can be described as:
The second term and the third term at the right end of the formula are respectively called a curvature term and a solute term, and for the cloud drops with the radius smaller than 10 mu m, the curvature term and the solute term have a remarkable influence on the condensation growth process of the cloud drops, and for the cloud drops with the radius larger than 10 mu m, the effect is negligible. Δ s represents the surface tension of the particles. The aerosol mass contained in a cloud can be calculated by tracking both the water and aerosol mass in the cloud using a stepped microphysics scheme, however the aerosol mass contained in a cloud cannot be described by a function of both of these quantities. Since the overall parameterization scheme describes the rate of change of the overall size distribution of the droplets, which is determined by the characteristics of the parameterization scheme, only the overall or average effect can be represented, in this embodiment, the droplet condensation growth three-parameter scheme requires the "solute term" to be averaged, i.e./> Average mass of it and solute/>In relation, i is the ionization degree of the solute, m s is the molecular mass of the solute, s c is the supersaturation degree relative to the liquid surface, and k is related to heat conduction and water vapor diffusion, and the expression is as follows:
Wherein T is the ambient temperature, L c is the latent heat release during condensation, R v is the gas constant, D v is the molecular diffusion coefficient, K a is the thermal conductivity of air, and e s is the saturated water vapor pressure relative to the liquid surface.
The rate of change of cloud concentration (M 0c), cloud water content (M 1c), and reflectance (M 2c) can be found in conjunction with equations 2.1, 2.5, 2.6, 2.7, and 2.12:
/>
Substituting equations 2.14, 2.15 and 2.16 into equations 2.10 and 2.11 yields the predictive equations for the spectral shape parameters and slope parameters:
the initial spectral shape parameters and slope parameters can be derived from equations 2.6 and 2.7:
Intercept parameters can be derived from equation 2.5:
The observation of the cloud drip spectrum in the actual atmosphere shows that the cloud drip spectrum is often distributed in multiple modes. This distribution may be caused by the first and second activation of the multimodal cloud, whereas the bimodal and trimodal distribution characteristics of the cloud can not be practically described by a single gamma distribution function. The use of a single gamma distribution function in the parameterized scheme to describe the evolution of the cloud spectrum can lead to simulation errors for large cloud droplets. To solve this problem, it is proposed to describe the multi-modal characteristics of the cloud spectrum with a plurality of gamma distribution functions. It was found by analysis that the multimodal distribution of droplets comprised mainly a large cloud spectrum formed by a large aerosol, a cloud spectrum formed by the first activation of a relatively small aerosol, and a small cloud spectrum produced by the second activation of the aerosol. For this purpose, it is assumed that a cloud droplet activated by a cloud nodule having a radius of more than 0.55 μm belongs to a first mode of the cloud spectrum, whereas a cloud droplet activated for the first time by a cloud nodule having a radius of less than 0.55 μm belongs to a second mode, and a cloud droplet activated for the second time is regarded as a third mode. The secondary activation was judged on condition that the ambient supersaturation exceeded its first reached maximum and a threshold of 0.55 μm was determined by the dry aerosol radius corresponding to the intersection of the first and second modes of the initial aerosol spectrum (fig. 8).
In S130, the analysis solutions of the multi-mode cloud droplet self-collection rate, the cloud-rain automatic conversion rate, the rain droplet self-collection rate and the collected cloud droplet rate are as follows:
/>
/>
In the formula, SCC is short for a cloud droplet Self-collecting process (Self-collection of cloud droplets), SCR is short for a rain droplet Self-collecting process (Self-collection of raindrops), AUTO is short for a cloud and rain automatic conversion process (Autoconversion), and ACC is short for a rain droplet collecting cloud droplet process (Accretion). Representing the order moment of the first modality cloud drip spectrum,/>Representing the order moment of the second modality cloud drip spectrum,/>The order moment of the raindrop spectrum is represented, and p=0, 1,2. Subscripts c1, c2, and r denote first modality cloud, second modality cloud, and rain drops ,xm＝5.23×10-7g,kc＝9.44×109cm3g-2s-1,kr＝5.78×103cm3g-1s-1., respectively, specifically, during warm rain formation, which is generally considered to be based on random merging theory of cloud drops:
where f (x, t) is the spectral distribution function of the drop mass at time t, K (x, y) is the collection kernel between drops of mass x and mass y, and the collection kernel employed in this example is:
K (x, y) =k c(x2+y2), x and y < x m (3.2)
K (x, y) =k r (x+y), x or y. Gtoreq.x m (3.3)
Wherein ,xm＝5.23×10-7g,kc＝9.44×109cm3g-2s-1,kr＝5.78×103cm3g-1s-1, assumes that the particle mass is less than x m as a cloud drop and greater than x m as a rain drop, and the cloud drop spectrum and the rain drop spectrum are represented by different gamma distribution functions.
/>
Cloud and rain drop momentThe variation of (c) can be written as:
Three moment amounts (p=0, 1, 2) are also employed in the warm rain formation scheme, representing the number concentration, cloud water content, and reflectivity factors, respectively. Substituting equation 3.4 into equation 3.5:
the present invention uses three gamma functions to represent the multi-modal cloud spectrum, but in practice the secondary activation is difficult to occur, i.e. the third modality of the cloud spectrum will not generally occur. The cloud spectrum during warm rain formation is thus represented by two gamma functions (f c1 and f c2):
Where subscript j denotes the modality of the cloud spectrum. j=1 represents the first modality, j=2 represents the second modality, and the raindrop spectrum is:
Mu is set to 1.
The moment of the bimodal cloud (M 0cj,M1cj,M2cj) can be calculated by taking the formula (3.7) into the formula (2.4):
/>
The moment of the raindrop (M 0r,M1r,M2r) can be obtained by carrying out calculation in the formula (2.4) by the formula (3.8):
For bimodal cloud, the total change rate (3.6) of the moment of the cloud and the rain can be written as:
The above is a complete formula based on the total change of three moment amounts of cloud and rain drops in the warm rain forming process of the bimodal cloud drop spectrum. In the warm rain forming process, the cloud drops collide with each other, namely the cloud drops are self-collected, and due to the self-collection of the cloud drops, when two cloud drops collide with each other and generate the cloud drops with the mass larger than x m, the cloud drops are converted into the rain drops, and the process is an automatic cloud rain conversion process. Raindrops generated in the automatic cloud and rain conversion process can be collected automatically, and meanwhile, the raindrops can be collected. Thus, the process of forming warm rain includes the processes of Self-collection of cloud droplets (Self-collection of cloud droplets, abbreviated as SCC), self-collection of rain droplets (Self-collection of raindrops, abbreviated as SCR), automatic conversion of cloud rain (Autoconversion, abbreviated as AUTO), and collection of cloud droplets by rain droplets (Accretion, abbreviated as ACC). Therefore, the change rates of the first-mode cloud drop and the second-mode cloud drop and the rain drop moment are respectively as follows:
Wherein, when the cloud drops are self-collected (SCC), combining (3.15) formula, in the SCC process, three moment quantities of two modal cloud drops The rate of change can be written as:
First modality cloud drop moment change rate:
bringing (3.2) and (3.7) into (3.19), the rate of change of the moment of the first modality cloud can be expressed as:
rate of change of second modality cloud drip moment:
Bringing (3.2) and (3.7) into (3.21), the rate of change of the second mode cloud order moment can be expressed as:
In automatic cloud conversion (AUTO), the AUTO process is the conversion of generated cloud droplets greater than x m into raindrops from a collection process. Therefore, the calculation formula should be the same as the formula of the cloud self-collection process, except that the integral domain is different, i.e., the integral lower limit is x m. In the AUTO process, three moment of two modal cloud drops The rate of change can be written as follows:
First modality cloud drop moment change rate:
/>
Here, the Is an incomplete gamma function.
Rate of change of the moment of the second modality cloud droplets:
when raindrops collect cloud drops (ACC), the rate of change of the raindrop moment in the ACC process includes three items: the growth rate and the reduction rate of the raindrops in the process of collecting the raindrops are respectively the growth rate of the raindrops in the process of collecting the raindrops (the raindrops are also converted into the raindrops):
bringing (3.3), (3.7) and (3.8) into formula (3.25), the above formula can be written as:
Reduction rate of first modality cloud drip moment: in combination of (3.3), (3.7) and (3.8), the rate of reduction of the (ACC) cloud order moment in the process of collecting the first-modality cloud by the raindrops can be given by:
rate of decrease in second modality cloud order moment: in combination of (3.3), (3.7) and (3.8), the rate of reduction of the (ACC) cloud order moment in the process of collecting the second-mode cloud by the raindrops can be given by:
in the raindrop self-collection (SCR), the rate of change of the moment of the (SCR) order in the raindrop self-collection process can be written as:
The first term on the right in the expression (3.29) represents the rate of increase in the amount of moment of the raindrop in the raindrop self-collection process, and the second term on the right represents the rate of decrease in the amount of moment of the raindrop in the raindrop self-collection process.
Bringing (3.3) and (3.8) into (3.29), the rate of change of the rain drop step moment during the rain drop self-collection process can be written as:
In the specific embodiment, the weather forecast method based on the cloud micro physical process provided by the invention establishes an aerosol activation parameterized model by fitting a regression equation of a radius and an activation radius of dry aerosol; establishing a multi-mode cloud drip spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter; establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution; and weather simulation forecasting is carried out by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
Firstly, constructing a regression formula between the radius of dry aerosol and the wet radius of the dry aerosol when the environmental supersaturation reaches the critical supersaturation calculated by Kou La theory, accurately calculating the actual wet radius of the aerosol during activation, and further accurately giving out the initial cloud water content, the reflectivity factor and the activated cloud droplet concentration; then the activated cloud droplet particle spectrum is expressed by a gamma function, and the cloud droplet spectrum evolution is accurately described by constructing a normal differential equation set of a cloud droplet concentration and a spectrum shape parameter and a slope parameter in the gamma function; furthermore, to characterize the distribution of the multi-modal cloud drip spectrum produced by the first and second activations of the aerosol, it is proposed to use a plurality of gamma distribution functions to characterize the multi-modal cloud drip spectrum; further, a cloud drop self-collection, a cloud drop automatic conversion rate, a rain drop collecting cloud drop rate and a rain drop self-collection rate analysis solution in the warm rain forming process are obtained by solving a cloud drop random collision equation based on a multi-mode cloud drop spectrum. The accuracy of weather forecast is improved, especially the accuracy of weather forecast in disastrous weather is improved, and the technical problem of poor accuracy of weather forecast in the prior art is solved.
In order to verify the technical effects, the application adopts 14 groups of data in the table 1 to simulate, and the simulation results are compared with the results in the prior art to obtain the following conclusion:
From the simulation result, the method provided by the invention effectively solves the key problems of the prior proposal as mentioned above:
First, compared to the actual activation radius (14 sets of point distributions for examples 1-14 in fig. 1-3), the new scheme based on formulas (1.2) - (1.3) can reasonably model the activation radius of the aerosol, as shown by the solid black line in fig. 1-3; meanwhile, the new scheme is compared with a double-parameter scheme for fixing the spectral shape parameters and a Mo Ruisen scheme for calculating the spectral shape parameters based on an empirical formula, and a Lagrange grading scheme is introduced as a comparison standard. It should be pointed out that the classification scheme focuses on the microphysical process of various hydrogel particles, the particle size distribution of the classification scheme can be described by tens to hundreds of stages, the growth characteristics of the hydrogel particles in each stage can be calculated by solving a microphysical equation, and the evolution of irregular cloud drip spectrum distribution in the cloud can be more accurately simulated, but the classification scheme can be used as a comparison standard for testing the merits of the parameterization scheme because of the huge calculation amount which can not be used for weather service forecast. Fig. 4 shows the cloud spectrum evolution simulated by the new scheme, the two-parameter scheme, the Mo Ruisen scheme and the step scheme. The cloud spectrum evolution simulated by the stepping scheme shows that as the radius increase rate of the cloud drops is inversely proportional to the radius of the cloud drops, the increase rate of small cloud drops is larger than that of large cloud drops, and the cloud spectrum is gradually narrowed on the particle spectrum. In the simulation of the overall parameterization scheme, the cloud spectrum of Mo Ruisen and the cloud spectrum of the double-parameter scheme are falsely widened due to the fact that spectrum shape parameters cannot be accurately calculated. The newly established scheme simulation result is consistent with the grading scheme simulation result, and the evolution of the cloud drip spectrum can be accurately simulated.
Fig. 5 is a comparative experiment of the cloud spectrum evolution in the single mode cloud spectrum scheme and the new scheme and is compared with the results of the lagrangian shift scheme simulation with a simulation time of 900s. The new scheme can well simulate the multi-mode characteristics of the cloud drip spectrum, the simulated multi-mode cloud drip spectrum is consistent with the simulation result of the grading scheme, the cloud drip spectrum simulated by the single-mode cloud drip spectrum scheme is quite different from the simulation result of the grading scheme, the big cloud drip at the right end of the cloud drip spectrum, namely, the rain embryo, can not be simulated, even the big cloud drip at the right end of the particle spectrum is reduced in 190s-220s, mainly because the new activated cloud drip is required to follow the same spectrum distribution as the earliest activated big cloud drip based on the scheme of the single-mode gamma distribution function, and the new cloud drip is supposed to be distributed in a wide size range immediately. The scheme based on the gamma distribution function of the single-mode cloud drip spectrum can cause simulation errors of large cloud drips in the cloud drip spectrum, and the simulation results show that the method provided by the invention effectively solves the cloud simulation problem by adopting a plurality of gamma distribution functions.
FIG. 6 is a comparison of automatic conversion of cloud and rain at different initial cloud drop concentrations (30-2000 cm -3) and initial cloud water content (0.25-5 gm -3). It is generally believed that the automatic conversion of cloud and rain increases with increasing cloud water content and decreases with increasing number concentration, with negligible automatic conversion for small cloud droplets, as shown by the stepper scheme simulation results (fig. 6 b). Several parameterization schemes are currently in common use: the simulation results of KK00 (shown in fig. 6 c), XL09 (shown in fig. 6 d), LD04 (shown in fig. 6 e) and SB06 (shown in fig. 6 f) for the automatic conversion rate of cloud and the classification scheme are very different, and the simulation results of the new scheme are closest to the classification scheme (shown in fig. 6 a), because the automatic conversion rate of cloud and rain in the new scheme is based on the analytical solution of the quasi-random collision theory.
For ease of understanding, the following will explain the correlation results in comparison with the test:
FIG. 1 is a plot of sodium chloride (NaCl) dry aerosol radius versus Kou La critical radius, kou La critical radius incorporating hygroscopic parameters, actual activated wet radius, and activated wet radius calculated by fitting the equation for examples 1-14 when the ambient supersaturation reaches its critical supersaturation calculated by Kou La theory. Wherein the moisture absorption parameters in the moisture absorption correction scheme are set to 1.0 and 1.4, respectively.
Fig. 2 shows the relationship of the ammonium nitrate (NH 4NO3) dry aerosol radius to the Kou La critical radius, the Kou La critical radius incorporating the hygroscopic parameter, the actual activation wet radius and the activation wet radius calculated by the fitting equation when the ambient supersaturation reaches its critical supersaturation calculated by Kou La theory. Wherein the moisture absorption parameters were set to 0.5 and 0.7, respectively.
Fig. 3 shows the relationship of the ammonium sulfate ((NH 4)2SO4) dry aerosol radius to Kou La critical radius, kou La critical radius incorporating the hygroscopic parameter, actual activated wet radius and activated wet radius calculated by fitting formula when the ambient supersaturation reaches its critical supersaturation calculated by Kou La theory, wherein the hygroscopic parameter (kh) is set to 0.3 and 0.7, respectively.
Fig. 4 shows the cloud spectra at 10min simulated using the new, two-parameter, mo Ruisen and step schemes: a. the supersaturation degree is 0.03%; b. the supersaturation degree was 0.01%.
Figure 5 shows the simulated cloud spectrum evolution of the single mode cloud spectrum scheme and the new scheme and the simulated comparison with the simulation of the step scheme, simulation time 900s.
Fig. 6 shows calculated automatic cloud-to-rain conversion at different initial cloud drop concentrations and cloud water content: a. a new scheme; b. a gear scheme, an existing common parameterization scheme: KK00; xl09; e.ld04; f.SB06.
Fig. 8 shows an initial aerosol spectrum.
In addition to the above method, the present invention also provides a weather forecast device based on a cloud micro-physical process, as shown in fig. 9, the device includes:
The first modeling unit 901 is configured to establish an aerosol activation parameterized model by fitting a regression equation of a radius of the dry aerosol and an activation radius;
the second modeling unit 902 is configured to build a multi-mode cloud droplet spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter;
The third modeling unit 903 is configured to build a warm rain forming three-parameter analysis model by deriving a multi-mode cloud droplet self-collection rate, a cloud rain automatic conversion rate, a rain droplet self-collection rate, and a collected cloud droplet rate analysis solution;
and the result output unit 904 is used for performing weather simulation forecasting by using the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
According to the weather forecast device based on the cloud micro physical process, an aerosol activation parameterized model is established by fitting a regression equation of a radius and an activation radius of dry aerosol; establishing a multi-mode cloud drip spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter; establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution; and weather simulation forecasting is carried out by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
Firstly, constructing a regression formula between the radius of dry aerosol and the wet radius of the dry aerosol when the environmental supersaturation reaches the critical supersaturation calculated by Kou La theory, accurately calculating the actual wet radius of the aerosol during activation, and further accurately giving out the initial cloud water content, the reflectivity factor and the activated cloud droplet concentration; then the activated cloud droplet particle spectrum is expressed by a gamma function, and the cloud droplet spectrum evolution is accurately described by constructing a normal differential equation set of a cloud droplet concentration and a spectrum shape parameter and a slope parameter in the gamma function; furthermore, to characterize the distribution of the multi-modal cloud drip spectrum produced by the first and second activations of the aerosol, it is proposed to use a plurality of gamma distribution functions to characterize the multi-modal cloud drip spectrum; further, a cloud drop self-collection, a cloud drop automatic conversion rate, a rain drop collecting cloud drop rate and a rain drop self-collection rate analysis solution in the warm rain forming process are obtained by solving a cloud drop random collision equation based on a multi-mode cloud drop spectrum. The accuracy of weather forecast is improved, especially the accuracy of weather forecast in disastrous weather is improved, and the technical problem of poor accuracy of weather forecast in the prior art is solved.
In one embodiment, a computer device is provided, which may be a server, and the internal structure of which may be as shown in fig. 10. The computer device includes a processor, a memory, and a network interface connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and model predictions. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The model predictions of the computer device are used to store static information and dynamic information data. The network interface of the computer device is used for communicating with an external terminal through a network connection. Which computer program, when being executed by a processor, carries out the steps of the above-mentioned method embodiments.
It will be appreciated by those skilled in the art that the structure shown in FIG. 10 is merely a block diagram of some of the structures associated with the present inventive arrangements and is not limiting of the computer device to which the present inventive arrangements may be applied, and that a particular computer device may include more or fewer components than shown, or may combine some of the components, or have a different arrangement of components.
Corresponding to the above embodiments, the present invention further provides a computer storage medium, which contains one or more program instructions. Wherein the one or more program instructions are for performing the method as described above by a weight verification system.
The present invention also provides a computer program product comprising a computer program storable on a non-transitory computer readable storage medium, the computer program being capable of performing the above method when being executed by a processor.
In the embodiment of the invention, the processor may be an integrated circuit chip with signal processing capability. The processor may be a general purpose processor, a digital signal processor (DIGITAL SIGNAL processor, DSP for short), an application specific integrated circuit (Application Specific processor NTEGRATED CIRCUIT ASIC for short), a field programmable gate array (FieldProgrammable GATE ARRAY FPGA for short), or other programmable logic device, discrete gate or transistor logic device, discrete hardware components.
The disclosed methods, steps, and logic blocks in the embodiments of the present invention may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present invention may be embodied directly in the execution of a hardware decoding processor, or in the execution of a combination of hardware and software modules in a decoding processor. The software modules may be located in a random access memory, flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The processor reads the information in the storage medium and, in combination with its hardware, performs the steps of the above method.
The storage medium may be memory, for example, may be volatile memory or nonvolatile memory, or may include both volatile and nonvolatile memory.
The nonvolatile Memory may be a Read-Only Memory (ROM), a Programmable ROM (PROM), an Erasable PROM (EPROM), an electrically Erasable ROM (ELECTRICALLY EPROM, EEPROM), or a flash Memory.
The volatile memory may be a random access memory (Random Access Memory, RAM for short) which acts as an external cache. By way of example, and not limitation, many forms of RAM are available, such as static random access memory (STATIC RAM, SRAM), dynamic random access memory (DYNAMIC RAM, DRAM), synchronous Dynamic Random Access Memory (SDRAM), double data rate Synchronous dynamic random access memory (Double DATA RATESDRAM, ddr SDRAM), enhanced Synchronous dynamic random access memory (ENHANCED SDRAM, ESDRAM), synchronous link dynamic random access memory (SYNCHLINK DRAM, SLDRAM), and direct memory bus random access memory (DirectRambus RAM, DRRAM).
The storage media described in embodiments of the present invention are intended to comprise, without being limited to, these and any other suitable types of memory.
Those skilled in the art will appreciate that in one or more of the examples described above, the functions described in the present invention may be implemented in a combination of hardware and software. When the software is applied, the corresponding functions may be stored in a computer-readable medium or transmitted as one or more instructions or code on the computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a general purpose or special purpose computer.
The foregoing detailed description of the invention has been presented for purposes of illustration and description, and it should be understood that the foregoing is by way of illustration and description only, and is not intended to limit the scope of the invention.
Claims (7)
1. A weather forecast method based on a cloud micro-physical process, the method comprising:
Establishing an aerosol activation parameterized model by fitting a regression equation of the radius of the dry aerosol and the activation radius;
establishing a multi-mode cloud drip spectrum condensation three-parameter model by constructing a normal differential equation set of a number concentration, a spectrum shape and a slope parameter;
Establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution;
utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain to form a three-parameter analysis model for weather simulation prediction;
wherein, the regression equation of fitting dry aerosol radius and activation radius specifically includes:
Fitting regression equations of the radius and the activation radius of the dry aerosols of sodium chloride, ammonium nitrate and ammonium sulfate respectively based on the simulation result of the high-resolution Lagrangian step mode;
the system of ordinary differential equations of the number concentration, the spectrum shape and the slope parameters constructed by the cloud droplet concentration, the cloud water content and the reflectivity factors is as follows:
Wherein M 0c is cloud drop concentration, M 1c is cloud water content, M 2c is reflectivity, and H 0c＝1,H1c＝106,H2c＝1012(πρw/6)-2,ρw is water density;
the multi-mode cloud drop self-collection rate, the cloud and rain automatic conversion rate, the rain drop self-collection rate and the analysis solution of the cloud drop collection rate are as follows:
in the formula, SCC is short for a cloud drop self-collecting process, SCR is short for a rain drop self-collecting process, AUTO is short for a cloud rain automatic conversion process, and ACC is short for a rain drop collecting cloud drop process; Representing the order moment of the first modality cloud drip spectrum,/> Representing the order moment of the second modality cloud drip spectrum,/>The value of p is 0,1 and 2, and subscripts c1, c2 and r respectively represent first-mode cloud drops, second-mode cloud drops and rain drops ,xm＝5.23×10-7g,kc＝9.44×109cm3g-2s-1,kr＝5.78×103cm3g-1s-1.
2. The weather forecast method based on the cloud micro physical process of claim 1, wherein a regression equation of a radius of a dry aerosol fitted with a dry aerosol of sodium chloride and an activation radius is:
rwet1＝7.54rdry1 0.8318
wherein r dry1 is the radius of sodium chloride dry aerosol, in μm, r wet1 is the sodium chloride activation radius, in μm.
3. The weather forecast method based on the cloud micro-physical process of claim 1, wherein a regression equation of a dry aerosol radius and an activation radius of the fitting ammonium nitrate dry aerosol is:
rwet2＝6.58rdry2 0.835
Wherein r dry2 is the radius of the ammonium nitrate dry aerosol, the unit μm, and r wet2 is the ammonium nitrate activation radius, the unit μm.
4. The weather forecast method based on the cloud micro-physical process of claim 1, wherein the regression equation of the radius of the dry aerosol fitted with the dry aerosol of ammonium sulfate and the activation radius is:
rwet3＝5.83rdry3 0.8396
Wherein r dry3 is the radius of the ammonium sulfate dry aerosol, the unit μm, and r wet3 is the ammonium sulfate activation radius, the unit μm.
5. Weather forecast device based on cloud micro-physics process for implementing the method according to any of claims 1-4, characterized in that it comprises:
The first modeling unit is used for building an aerosol activation parameterized model by fitting a regression equation of the radius of the dry aerosol and the activation radius;
the second modeling unit is used for establishing a multi-mode cloud droplet spectrum condensation three-parameter model by establishing a normal differential equation set of a digital concentration, a spectrum shape and a slope parameter;
The third modeling unit is used for establishing a warm rain forming three-parameter analysis model by deducing a multi-mode cloud drop self-collection rate, a cloud rain automatic conversion rate, a rain drop self-collection rate and a cloud drop collection rate analysis solution;
and the result output unit is used for performing weather simulation prediction by utilizing the aerosol activation parameterized model, the multi-mode cloud drip spectrum condensation three-parameter model and the warm rain forming three-parameter analysis model.
6. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any one of claims 1 to 4 when the program is executed.
7. A non-transitory computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method according to any of claims 1 to 4.
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