CN117272866A - Variable grid simulation method and equipment for mass concentration of particle size segmented sand dust - Google Patents
Variable grid simulation method and equipment for mass concentration of particle size segmented sand dust Download PDFInfo
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- 239000004576 sand Substances 0.000 title claims abstract description 71
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Abstract
The embodiment of the specification discloses a variable grid simulation method and equipment for mass concentration of sand dust with segmented particle size. By determining the distribution form of sand and dust; determining a particle size segmentation method of sand; determining the volume fraction of the sand and dust emission of each particle size section according to the distribution form and the particle size segmentation method; and determining grid division in the atmosphere variable grid prediction model, and calculating the mass concentration of sand and dust in each grid in the atmosphere variable grid prediction model according to the volume fraction, so that accurate regional encryption sand and dust simulation is realized in the global scope, and more accurate basic conditions are provided for subsequent weather and atmospheric environment simulation.
Description
Technical Field
The specification relates to the field of atmospheric numerical simulation, in particular to a variable grid simulation method and equipment for mass concentration of sand and dust with segmented particle size.
Background
In numerical simulations of weather and atmospheric environmental changes, the properties of sand and dust in aerosols, in particular the mass concentration distribution, are significant for the influence of atmospheric processes. While the current simulation of sand and dust over the global area is still rough, there is still a great uncertainty in the numerical simulation of sand and dust and its effects on the area scale.
Based on this, a more accurate simulation scheme of the sand mass concentration based on particle size segmentation is needed, which can realize region encryption.
Disclosure of Invention
The embodiment of the specification provides a simulation method and equipment for mass concentration of sand and dust based on particle size segmentation in a global variable grid atmosphere frame, which are used for solving the following technical problems: there is a need for a more accurate simulation scheme for regional encryption based on mass concentration of particle size segmented sand.
To solve the above technical problems, one or more embodiments of the present specification are implemented as follows:
in a first aspect, embodiments of the present disclosure provide a method for simulating a variable grid of mass concentration of particulate size segmented dust, applied to an atmospheric variable grid prediction model, the method comprising:
determining the distribution of dustWherein N is total Is the total concentration, d n Is the numerical median diameter, sigma n Is the standard deviation;
particle size segmentation method for determining sandWherein N is the number of segments, i is more than or equal to 1 and less than or equal to N, and D U For the upper limit of diameter, D L Is the lower limit of the diameter, d is the diameter of sand and dust, d U (i) For the upper diameter limit in the ith segment, d L (i) Is the lower limit of the diameter in the ith segment;
determining the volume fraction of the discharged sand per segment according to the distribution form and the particle size segmentation method;
and determining grid division in the atmosphere variable grid prediction model, and calculating the mass concentration of sand and dust in each grid in the atmosphere variable grid prediction model according to the volume fraction.
In a second aspect, one or more embodiments of the present description provide an electronic device comprising:
at least one processor; the method comprises the steps of,
a memory communicatively coupled to the at least one processor; wherein,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of the first aspect.
The above-mentioned at least one technical solution adopted by one or more embodiments of the present disclosure can achieve the following beneficial effects: by determining the distribution form of sand and dust; determining a particle size segmentation method of sand; determining a volume fraction of the dust emissions for each segment according to the particle size segmentation method and distribution form; and determining grid division in the atmosphere variable grid prediction model, and calculating the mass concentration of sand and dust in each grid in the atmosphere variable grid prediction model according to the volume fraction, so that accurate regional encryption sand and dust simulation is realized in the global scope, the mass concentration in each region can be calculated, and more accurate basic conditions are provided for subsequent weather and atmospheric environment simulation.
Drawings
In order to more clearly illustrate the embodiments of the present description or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some of the embodiments described in the present description, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a method for simulating a variable grid of mass concentration of sand particles with a segmented particle size according to an embodiment of the present disclosure.
FIG. 2 is a schematic illustration of the distribution of dust emission volume fractions among 10 segments provided by embodiments of the present description;
FIG. 3 is a schematic diagram of a plurality of different grids provided in an embodiment of the present application;
FIG. 4a is a schematic representation of actual observed surface mass concentrations provided herein;
FIG. 4b is a schematic representation of calculated surface mass concentrations provided herein;
FIG. 4c is a plot of simulated computation versus observed scatter provided herein;
fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present disclosure.
Detailed Description
The embodiment of the specification provides a variable grid simulation method and equipment for mass concentration of particle size segmented sand dust.
In order to make the technical solutions in the present specification better understood by those skilled in the art, the technical solutions in the embodiments of the present specification will be clearly and completely described below with reference to the drawings in the embodiments of the present specification, and it is obvious that the described embodiments are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, shall fall within the scope of the present application.
Referring to fig. 1, fig. 1 is a schematic flow chart of a method for simulating a grid-changing process of mass concentration of sand and dust with a segmented particle size according to an embodiment of the present disclosure.
The process in fig. 1 is applied to the atmospheric variable grid prediction model, and may include the following steps:
s1, determining the distribution form of sand and dust.
The distribution pattern here refers to the distribution pattern of the diameter of the dust. To date, few studies have attempted to model and study sand and its effects with a global variable resolution model that is not static balanced. The iAMAS model developed in this study is based on the dynamic framework of the atmospheric variable mesh prediction model. The icamas is a global variable resolution atmosphere model, and the atmosphere solver in the icamas integrates non-static equilibrium equations, so that it is suitable for weather and climate simulation. MPAS-A uses an unstructured centroid Voronoi grid (grid or tessellation) as the basis for horizontal discretization in se:Sup>A fluid solver. It has proven to provide reliable weather fields such as wind and precipitation required to simulate sand.
First, in an atmospheric variable grid prediction model, corresponding surface features may be acquired or given, which are used to calculate the dust emission flux. Specifically, the dust discharge flux Dsrc (kg·m -2 ·s -1 ) The calculation mode of (2) is as follows:
wherein C is an empirical proportionality constant set to 1.0X10 -9 kg·s2·sm-5, and is highly adjustable, for having the same dimensions on the left and right sides of the equation. S is a source function defining the portion of the washout laminate available for wind erosion, the spatial resolution of the original S being 1 DEG x 1 deg. It is interpolated to different horizontal resolutions using a "bilinear" interpolation method, as needed.
sp is the mass fraction of sand particles of each size during discharge. The total dust discharge flux is the sum of the dust discharge fluxes of each size, and in this application, therefore, the sp value for the size of 0.2 to 2 μm is 0.1, the values of the sizes of 2 to 3.6 μm, 3.6 to 6 μm,6 to 12 μm 12 to 20 μm, and 20 to 40 μm are set to 1/5.
u10m is the wind speed at 10m, and uts is the threshold wind speed. If u10m is smaller than uts, no dust emission occurs. The threshold wind speed uts is a function of the density and size of the dust particles, the air density and the surface humidity, calculated as follows:
w is the relative humidity of the soil, by dividing the soil humidity by the saturation of the soil humiditySum value to calculate, and u ts0 Is the threshold speed of the dry soil.
By determining the dust emission flux, i.e. the total concentration N total . And then reassigned according to the lognormal size distribution. For example, one specific distribution is as follows:
wherein N is total Is the total concentration, d n Is the numerical median diameter, sigma n Is the standard deviation.
Equation (3) can be written as N (lnd)/Ntotal N (lndn, lnσn), where N (μ, σ) is a normal distribution function.
S2, determining the particle size sectional form of the sand.
The particle size fraction here refers to the fraction calculation of the diameter of the dust during the calculation. In this application, diameter is used to denote the size distribution of dust particles. Specifically, N segments (or referred to as size bins) may be used to simulate the size distribution of the dust. The number of given particle size segments and the upper limit and the lower limit of the diameter of sand, the particle size segmentation form of the sand is as follows:
n is the number of segments, i is more than or equal to 1 and less than or equal to N, and D U For the upper limit of diameter, D L Is the lower limit of the diameter, d is the diameter of sand and dust, d U (i) For the upper diameter limit in the ith segment, d L (i) Is the lower limit of the diameter in the ith segment.
For example, the lower limit of the diameter may be generally taken to be 0.04 μm, the upper limit of the diameter may be taken to be 10 μm, and N may be taken to be 8. And, in order to increase the computing power for coarse dust particles, the upper limit of the diameter in the model is further extended to 40 μm, i.e. the N-value is 10, and two segments are added, 10 μm to 20 μm and 20 μm to 40 μm. An exemplary segmented form of dust was obtained as shown in table 1.
Table 1: sectional form of sand and dust with ten particle size sections
Where bin represents the segment number, volume fraction is the Volume fraction, lower bound of diameter is the lower diameter limit in the segment, and Upper bound of diameter is the upper diameter limit in the segment.
S3, determining the volume fraction of the discharged sand and dust of each segment according to the segment form and the distribution form.
The lower and upper limits of the given diameters in each segment and the log-normal distribution, the volume fraction of discharged dust per segment can be calculated as:
where v is the dust volume fraction per bin, dL and dU are the lower and upper limits, respectively, of the calculated segment diameter, erf (x) is the "error function" encountered in integrating the normal distribution,
the volume fraction of each particle size fraction is listed in table 1, previously described. Note that, according to the above two lognormal distributions, the sum of the dust volume fractions of each particle size segment is close to 1 for 10 particle size segments, and less than 1 for other size ranges (98% for 9 particle size segments and 80% for 8 particle size segments). The volume size distribution of the discharged dust is shown in fig. 2. Fig. 2 is a schematic diagram of the distribution of the volume fraction of discharged dust in 10 segments provided in the examples of the present specification.
S4, determining grid division in the atmosphere variable grid prediction model, and calculating the mass concentration of sand and dust in each grid in the atmosphere variable grid prediction model according to the volume fraction.
Specifically, when meshing is performed, it may be determined that a global variable resolution or a uniform resolution is adopted in the atmospheric variable mesh prediction model, and horizontal and vertical meshing is determined according to the global variable resolution or the uniform resolution.
For example, a 55 vertical layer may be provided in the model, with the model top set at 30km. Meanwhile, two quasi-uniform resolution grids and three variable resolution grids are adopted horizontally. As shown in fig. 3, fig. 3 is a schematic diagram of a grid provided in an embodiment of the present application. The quasi-uniform grid has substantially the same grid spacing globally, while the variable resolution grid has finer grid spacing in the encryption area. There is a transition region between the fine and coarse resolution grids.
In fig. 3, (a) a global uniform resolution grid of 120km (U120 km); (b) A global variable resolution grid (V16 km EA) with V16-128km, and an encryption area is an east Asia sand source area; (c) A global variable resolution grid of V16-128km, the encryption area being a North African sand source area (V16 km NA); (d, e) is the spatial distribution of grid dimensions for V16km EA and V16km NA. (f) a global uniform resolution grid of 60km (U60 km); (g) V4-60km global variable resolution grid, the encryption area is east Asia sand source area (V4 km); (h) is the spatial distribution of the V4km grid dimensions.
The first variable resolution grid is characterized by a circular fine high resolution area (hereinafter referred to as V16km EA) centered on east asia and having a grid pitch of 16km, and covers the main sand source area of east asia and the mountain area around the tibetan plateau where the topography is complex (part c in fig. 3). The area is also largely affected by asian monsoon. The resolution outside the encryption area is about 120km.
The second variable resolution configuration has a grid similar to the first, but the circular fine high resolution area is centered on north africa (hereinafter V16km NA). The encryption area covers the global maximum sand source area. The terrain in this region is less complex than east asia. Both configurations may help to investigate the impact of refinement on sand modeling of areas with different terrain complexity.
Another globally variable resolution grid has a circular fine area with a resolution of 4 km. The details of the five grids provided herein are provided in table 2.
Table 2, details of five grids.
Wherein Center of Refinement is the center coordinates of the encryption area, and Diameter of Refinement is the diameter of the encryption area.
Meteorological initial conditions may be obtained from the corresponding data set. The dataset may be analyzed, for example, from the middle weather forecast center in europe (ERA temporary dataset), with a spatial resolution of about 80 km and a temporal resolution of 6 hours. The initial meteorological conditions and terrain are interpolated from the same dataset into each grid.
And obtaining meteorological initial conditions by giving grid information and obtaining the meteorological initial conditions, and further obtaining the mass concentration of sand and dust in each grid based on the calculation of the volume fraction value in each particle size section.
By determining the distribution form of sand and dust; determining the sectional form of sand; determining a volume fraction of discharged sand per segment from the segment form and the distribution form; and determining grid division in the atmosphere variable grid prediction model, and calculating the mass concentration of sand and dust in each grid in the atmosphere variable grid prediction model according to the volume fraction, so that accurate sand and dust simulation is realized in a global area range, the mass concentration in each area can be calculated, and more accurate basic conditions are provided for subsequent meteorological simulation.
In addition, in calculating the mass concentration of sand in each grid in the atmospheric variable grid prediction model based on the volume fraction, other factors need to be considered, including, for example, sand transport, dry and gravity settling, moisture dehumidification process, and the like
For sand transport, up to 30 aerosol-related variables that can be fully predicted, such as the mass and quantity of sand aerosols, are included in the atmospheric variable grid prediction model. The transmission scheme of the dust aerosol follows the same rules as the moisture scalar scheme in MPAS-se:Sup>A. The scheme adopts se:Sup>A third-order Runge-Kuttse:Sup>A method on an irregular Voronoi (hexagonal) grid of MPAS-A to solve se:Sup>A completely compressible non-hydrostatic motion equation. For the conservation variable, the predictive equation for the integration is projected in a conservation form. These equations are discretized in a finite volume formula, so the model accurately guarantees conservation of mass. Turbulent transport of dust particles within the Planetary Boundary Layer (PBL) is parameterized based on the exchange coefficients of PBL protocol diagnostics.
And for dry sedimentation and gravity sedimentation factors, adjusting the mass concentration of the dust particles in each section in each vertical grid according to the dry sedimentation and gravity sedimentation factors.
First, in this application, the dry deposition is parameterized. The formula of the dry deposition rate is as follows
In this function, ra is aerodynamic drag Rs is surface drag. The aerodynamic resistance Ra is as follows:
where k is von-karman constant (about 0.41), u is friction speed, and ψc is a correction for non-adiabatic effects on the atmosphere.
u is the friction speed. Diffusion efficiency term->Sc is schmitt number, calculated from sc=v/D, v is the kinematic viscosity of air, and D is the molecular diffusivity, using Stokes-Einstein equation: />kB is the boltzmann constant and T is the temperature.
zr is the roughness length, st is the stokes number, dc is the diameter of the obstacle in the study, and the value is 0.002. The gravity settling velocity was calculated as follows:
μ is the dynamic viscosity of air, d is the particle diameter, and Cc is the Cunningham correction factor following the method in Pruppacher and Klett (1978): cc=1.0+ (1.257+0.4e-1.1 d/2. Lambda.) (2λ/d), λ being the mean free path of air. Gravity settling not only removes sand particles from the vertical layer at the bottom of the mold, but also brings the particles from the vertical layer in the atmosphere to the vertical layer below.
Based on the foregoing, at each vertical level, the adjustment of the mass concentration of sand particles within each segment due to dry and gravity settling was calculated as follows:
qdust (k) is the particle concentration at the kth layer and at the t-th time step, qdust' (k) is the particle concentration at the kth layer at the (t+Δt) th time step, Δz (k) is the height of the kth layer, and Δt is the time step of the model, v g Is the gravity sedimentation velocity, v d Is the dry settling rate.
In one embodiment, the wet clean-up process also needs to be considered by a grid change, specifically including: acquiring cloud activation and wet removal parameters from the atmospheric variable grid prediction model; the following wet clean adjustments are made to the mass concentration of sand in each grid according to cloud activation and wet clean parameters:
wherein q represents the concentration; r represents rain, i is for Yun Bing, s is for snow, w is for cloud water, and g is for aragonite, the subscript represents the different process: au is used for automatic conversion, fz is used for freezing, cw is used for cloud water collection.
In particular, aerosol activation (or droplet nucleation) is based on a maximum supersaturation determined from the gaussian spectrum of rising gas flow velocity. Aerosol can affect the number of droplets, which can also change aerosol concentration through water processes and wet clean-up. In the cloud, aerosol particles are activated into the cloud water phase in each particle size segment, for example, bin number one denoted by durtcw 01.
The dust particles are also known as ice nuclei. The number of ice nuclei (Ni) in the mixed phase cloud from sand can be calculated as follows:
where a=5.94×10-5, b=3.33, c=0.0264, d=0.0033, t0=273.15k, n is the number concentration of sand particles in each size bin with an effective diameter greater than 0.5 μm. T is the temperature in K. It should be noted that Ni is an integer without size distribution.
Wet removal of dust particles including in-cloud (rain and dew) and under-cloud removal, durtcw is removed at the same loss rate in each particle size segment as shown in the following equation:
Dust cw ＝Dust cw * (1-dt qlsink), dt is the analog time step qlsink is the cloud water loss rate (wet clean parameter):
the wet clean rate was calculated as follows:
ψ(a)∫ 0 ∞ ∈E(e，p)A x [v t (r)-v g (p)]N(r)dr。
wherein r and p represent the radius (in cm) of the raindrops and particles, respectively; e and E are the retention and collision efficiencies of the hydrographic respectively; e is collection efficiency; vt and vg are the terminal velocity of the raindrops and the gravity settling velocity of the particles, respectively; n is the number density of raindrops; and ax=pi (r+p) 2 is the effective cross-sectional area.
To simplify the calculation, the gravitational settling of the particles was neglected, i.e. e=1, the radius of the rainfall ranging from 0.005 cm to 0.25 cm. The final formula for the wet removal rate is as follows:
through the wet cleaning process, the mass concentration of sand and dust in each grid can be calculated more accurately based on the water vapor condition in the atmosphere.
Furthermore, to verify the accuracy of the present application, the applicant also conducted corresponding five sets of experiments in the five grids previously described. And comparing the calculated result with the surface quality concentration obtained by actual observation. As shown in fig. 4a, 4b and 4c, fig. 4a is a schematic diagram of actual observed surface quality concentration provided herein, fig. 4b is a schematic diagram of calculated surface quality concentration provided herein, and fig. 4c is a plot of simulated calculation versus observed scatter provided herein. The Y-axis values are from the model mesh nearest to the observation point. The solid black lines are 1:1 lines, while the dashed black lines correspond to 10:1 and 1:10 lines. Different types of markers represent different sources of observed data: cross = miami university website; triangle = website of Mahowald et al. The color of the indicia is based on the geographic area delineated in panel fig. 4 a.
Based on observations, the concentration of surface dust is high in several major dust sources and in their vicinity (e.g., north and south africa, middle east, southwest united states, etc.) (fig. 4 a). In addition, the mass concentration of earth dust in the northern hemisphere is greater than that in the southern hemisphere. However, since the dust is primarily from the source region, the surface dust concentration is lower in remote areas (e.g., antarctic). Furthermore, the simulated dust concentration was evaluated by observation of all 47 sites. The simulated average dust concentration of 21.52. Mu. g m-3 was slightly greater than the observed value of 14.31. Mu. g m-3 (FIG. 4 b). In general, the simulation may reproduce the spatial distribution characteristics of the observed dust-course concentrations.
As shown in fig. 4c, in 9 areas, the difference between the observation and the simulation of almost all observation points is within an order of magnitude, and the simulation result is accurate. Overall, the comparison shows that the modeling results for the dust region are higher than the observations, while the modeling results for the remote region are lower than the observations. This may indicate that the removal process in the model has some positive bias, which may result in a reduction of sand particles delivered to remote areas.
In a second aspect, based on the same concept, one or more embodiments of the present disclosure further provide an apparatus corresponding to the above method, as shown in fig. 5.
As shown in fig. 5, fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present disclosure, where the device includes:
at least one processor; the method comprises the steps of,
a memory communicatively coupled to the at least one processor; wherein,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of the first aspect.
Based on the same idea, the embodiments of the present specification further provide a non-volatile computer storage medium corresponding to the above method, where computer executable instructions are stored, which when the computer reads the computer executable instructions in the storage medium, cause one or more processors to perform the method according to the first aspect.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for apparatus, devices, non-volatile computer storage medium embodiments, the description is relatively simple, as it is substantially similar to method embodiments, with reference to the section of the method embodiments being relevant.
The foregoing describes specific embodiments of the present disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
The foregoing is merely one or more embodiments of the present description and is not intended to limit the present description. Various modifications and alterations to one or more embodiments of this description will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, or the like, which is within the spirit and principles of one or more embodiments of the present description, is intended to be included within the scope of the claims of the present description.
Claims (7)
1. A variable grid simulation method for mass concentration of particle size segmented sand dust is applied to an atmospheric variable grid prediction model, and comprises the following steps:
determining the distribution of dustWherein N is total Is the total concentration of sand and dust, d n Is the median diameter, sigma, of the number concentration distribution n Is the standard deviation;
particle size segmentation method for determining sand and dust:wherein N is the sectional number of sand and dust, i is more than or equal to 1 and less than or equal to N, and D U At the upper limit of the total diameter, D L At the lower limit of the total diameter, d is the diameter of sand and dust, d U (i) Is the upper limit of the diameter in the ith particle size section, d L (i) Is the lower limit of the diameter in the ith particle size section;
determining the volume fraction of the sand and dust emission of each particle size section according to the sand and dust distribution form and the particle size segmentation method;
and determining grid division in the atmosphere variable grid prediction model, and calculating the mass concentration of sand and dust in each grid in the atmosphere variable grid prediction model according to the volume fraction.
2. The method of claim 1, wherein determining a meshing in the atmospheric variable meshing prediction model comprises:
and determining that global variable resolution or uniform resolution is adopted in the atmospheric variable grid prediction model, and determining horizontal and vertical grid division according to the global variable resolution or the uniform resolution.
3. The method of claim 1, wherein calculating a mass concentration of sand in each grid in the atmospheric variable grid prediction model from the volume fraction comprises:
determining grid division in the vertical direction in the atmosphere variation grid prediction model;
determining dry sedimentation and gravity sedimentation factors on each vertical grid;
and adjusting the mass concentration of the dust aerosol in each particle size section in each vertical grid according to the dry sedimentation and gravity sedimentation factors.
4. A method as claimed in claim 3, wherein adjusting the mass concentration of dust aerosol in each particle size section in each vertical grid according to the dry sedimentation and gravity sedimentation factors comprises:
the mass concentration of dust aerosol in each segment in each vertical grid was calculated as follows:
mass concentration of dust aerosol in each segment in each vertical grid:
wherein q dust(k) Is the particle concentration, q, at the kth layer and at the t time step ′ dust(k) Is the particle concentration of the kth layer at the (t+Δt) th time step, Δz (k) is the height of the kth layer, Δt is the time step of the model, v g Is the gravity sedimentation velocity, v d Is the dry settling rate.
5. The method of claim 1, wherein calculating a mass concentration of sand in each grid in the atmospheric variable grid prediction model from the volume fraction comprises:
acquiring dry sedimentation rate and wet removal parameters from the atmospheric variable grid prediction model;
dehumidifying and adjusting the mass concentration of sand and dust in each grid according to cloud activation and wet cleaning parameters, wherein the wet cleaning parameters
Wherein q represents the concentration; r represents rain, i is for Yun Bing, s is for snow, w is for cloud water, and g is for aragonite, the subscript represents the different process: au is used for automatic conversion, fz is used for freezing and cw is used for cloud water collection, qc represents the total concentration of cloud water.
6. The method of claim 1, wherein the lower diameter limit is 0.04 μm and the upper diameter limit is 40 μm.
7. An electronic device, comprising:
at least one processor; the method comprises the steps of,
a memory communicatively coupled to the at least one processor; wherein,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1 to 5.
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