Method and device for describing complex meteorological phenomena based on reflectivity products

Abstract

The embodiments of the present application provide a method, device, equipment and computer-readable storage medium for describing complex meteorological phenomena based on reflectivity products. The method includes obtaining weather radar reflectivity factor data; generating reflectivity factor change vector data based on the weather radar reflectivity factor data; generating a surface dot matrix of a reflective target structure based on the reflectivity factor change vector data; vertically projecting the surface dot matrix to generate a radar combined reflectivity product embedded in the target space structure; analyzing the reflectivity product to complete the description of the current meteorological phenomenon. In this way, the analysis precision and accuracy of the meteorological activity process are improved, which can be applied to artificial meteorological forecasts and related meteorological research, and improves the description and early warning capabilities of complex meteorological phenomena.

Description

Technical Field

[0001] Embodiments of the present application relate to the field of meteorological data processing and analysis, and in particular, to methods, devices, equipment, and computer-readable storage media for describing complex meteorological phenomena based on reflectivity products. Background Art

[0002] Meteorological radar data is an important data basis for weather forecasting and meteorological research. Common weather radar data products include radar combination mosaic, combined reflectivity, echo top height, etc. Among them, the combined reflectivity product is formed by performing Cartesian projection on radar multi-elevation scanning data to generate multi-layer reflectivity factor data and then combining them. The above products play an important role in weather forecasting and the study of meteorological activity processes.

[0003] At present, the algorithm for generating combined reflectance products mainly converts the same Cartesian projection point<x,y> The reflectivity factors of multiple levels on the image are compared, and the largest value is taken as the final reflectivity factor. Although this algorithm has high computational efficiency and can more comprehensively reflect the radar characteristics during meteorological activities, its disadvantage is that it ignores the internal structural characteristics of the scanned target and the spatial distribution and changes of the reflectivity factor, which is not sufficient for accurate forecasting and warning of extreme weather. The internal structural characteristics of radar scanned targets are of great significance for near-term weather forecasts and extreme weather warnings (such as thunderstorms, hail, heavy rains, etc.). In addition, the existing algorithms do not make full use of the spatial information in the radar scanning data, but simply compare the maximum values, failing to reflect the three-dimensional structural characteristics of the target.

[0004] In order to make up for the shortcomings of existing algorithms, it is urgent to build a method that can accurately describe complex meteorological phenomena. Summary of the invention

[0005] According to the embodiment of the present application, a weather warning solution based on reflectivity products is provided, which can not only reflect the size of the reflectivity factor of the projection point, but also reflect the spatial structure information of the scanned target. By generating a reflectivity product containing the target spatial structure information, the analysis precision and accuracy of the meteorological activity process is improved.

[0006] In a first aspect of the present application, a method for describing complex meteorological phenomena based on reflectivity products is provided. The method comprises:

[0007] Obtain weather radar reflectivity factor data;

[0008] Based on the weather radar reflectivity factor data, generating reflectivity factor change vector data;

[0009] Based on the reflectivity factor change vector data, generating a surface dot matrix of a reflective target structure;

[0010] vertically projecting the surface dot matrix to generate a radar composite reflectivity product embedded in the target spatial structure;

[0011] Analyze the reflectivity products to complete the description of current meteorological phenomena.

[0012] Further, generating reflectivity factor change vector data based on the weather radar reflectivity factor data includes:

[0013] Based on the weather radar reflectivity factor data, construct a four-dimensional data set including the spatial coordinates and values ​​of the reflectivity factor;

[0014] Based on the four-dimensional data group, reflectivity factor change vector data is generated.

[0015] Further, generating a surface dot matrix of a reflective target structure based on the reflectivity factor change vector data includes:

[0016] Based on a preset vector modulus threshold, a structure surface point set is constructed;

[0017] Traversing the reflectivity factor change vector data, and calculating the modulus value of each vector data;

[0018] The touch value that meets the first preset condition is stored in the structure surface point array set;

[0019] Each vector data stored in the structure surface point array set is subjected to standardization processing to obtain target data meeting the second preset condition;

[0020] Based on the target data, a surface array of reflective target structures is generated.

[0021] Furthermore, the step of performing standardization processing on each vector data stored in the structure surface point array set to obtain target data meeting the second preset condition includes:

[0022] Traversing the target vector data in the structure surface point array set to obtain a neighborhood data set including reflectivity factor change data of the neighborhood of the target vector data;

[0023] Calculate the normalized vector of each reflectivity factor change data in the neighborhood data set;

[0024] Multiplying the standardized vector of each reflectivity factor change data with the target vector data respectively to obtain a target value set;

[0025] The target value set is analyzed to obtain target data that meets the second preset condition.

[0026] Furthermore, it also includes:

[0027] The structure surface point set is initially an empty set.

[0028] In a second aspect of the present application, a device for describing complex meteorological phenomena based on reflectivity products is provided. The device comprises:

[0029] An acquisition module is used to obtain weather radar reflectivity factor data;

[0030] A first generating module, used for generating reflectivity factor change vector data based on the weather radar reflectivity factor data;

[0031] A second generating module, for generating a surface dot matrix of a reflective target structure based on the reflectivity factor change vector data;

[0032] A projection module, used for vertically projecting the surface dot matrix to generate a radar combined reflectivity product embedded in the target spatial structure;

[0033] The description module is used to analyze the reflectance products and complete the description of the current meteorological phenomena.

[0034] In a third aspect of the present application, an electronic device is provided, which includes a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the program, the method described above is implemented.

[0035] In a fourth aspect of the present application, a computer-readable storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the method according to the first aspect of the present application is implemented.

[0036] The method for describing complex meteorological phenomena based on reflectivity products provided in the embodiment of the present application obtains meteorological radar reflectivity factor data; generates reflectivity factor change vector data based on the meteorological radar reflectivity factor data; generates a surface dot matrix of a reflective target structure based on the reflectivity factor change vector data; vertically projects the surface dot matrix to generate a radar combined reflectivity product embedded in the target space structure; analyzes the reflectivity product to complete the description of the current meteorological phenomenon, thereby improving the precision and accuracy of the analysis of meteorological activity processes, and can be applied to artificial meteorological forecasts and related meteorological research, improving the description and warning capabilities of complex meteorological phenomena.

[0037] It should be understood that the contents described in the Summary of the Invention are not intended to limit the key or important features of the embodiments of the present application, nor are they intended to limit the scope of the present application. Other features of the present application will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The above and other features, advantages and aspects of the embodiments of the present application will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, wherein:

[0039] Figure 1 A flowchart of a method for describing complex meteorological phenomena of a reflectivity product according to an embodiment of the present application;

[0040] Figure 2 A block diagram of a device for describing complex meteorological phenomena of a reflectivity product according to an embodiment of the present application;

[0041] Figure 3 It is a schematic diagram of the structure of a terminal device or a server suitable for implementing the embodiments of the present application. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solution and advantages of the embodiments disclosed in the present invention clearer, the technical solution in the embodiments disclosed in the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments disclosed in the present invention. Obviously, the described embodiments are part of the embodiments disclosed in the present invention, rather than all the embodiments. Based on the embodiments disclosed in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection disclosed in the present invention.

[0043] In addition, the term "and / or" in this article is only a description of the association relationship between the associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0044] Figure 1 A flow chart of a method for describing complex meteorological phenomena based on reflectivity products according to an embodiment of the present invention is shown. The method comprises:

[0045] S110, obtaining weather radar reflectivity factor data.

[0046] In this embodiment, the description method (eg, server) for the weather warning method based on reflectivity product can obtain weather radar reflectivity factor data through a wired or wireless connection.

[0047] Furthermore, the above-mentioned execution entity may obtain the weather radar reflectivity factor data sent by an electronic device (such as a mobile phone, tablet computer or other terminal device) that is in communication with it, or the weather radar reflectivity factor data pre-stored locally.

[0048] S120, generating reflectivity factor change vector data based on the weather radar reflectivity factor data.

[0049] In some embodiments, based on the weather radar reflectivity factor data, a four-dimensional data set (x, y, z, v) including the spatial coordinates and values ​​of the reflectivity factor is constructed, wherein (x, y, z) is the spatial coordinate and v is the corresponding reflectivity factor value.

[0050] Further, based on the four-dimensional data group, reflectivity factor change vector data is generated.

[0051] Specifically, in the three-dimensional coordinate range The inner loop traverses the three-dimensional reflectivity factor data;

[0052] For each point (x, y, z), traverse and if the point satisfies the boundary condition x= Or x= , y= Or y= , z = or z= , then set the reflectivity factor change vector of the point to (0,0,0); if the above boundary conditions are not met, calculate the reflectivity factor change near the point:

[0053] Get neighborhood reflectivity factor data , , , according to the above neighborhood data, set the reflectivity factor change vector of the current point:

[0054] ;

[0055] Among them: v1, v2, v3 are the values ​​of the reflectivity factor data adjacent to the spatial coordinates of the current reflectivity factor data.

[0056] S130, generating a surface dot matrix of a reflective target structure based on the reflectivity factor change vector data.

[0057] In some embodiments, a vector modulus threshold z is set to screen the structure surface points and generate the structure surface point array set I. The threshold z can be set according to the actual application scenario, for example, determined by experiments, determined by using an adaptive threshold, etc.

[0058] Traverse the reflectivity factor change vector data, calculate the modulus value of each vector data, and store the modulus value that meets the first preset condition into the structure surface point array set I:

[0059] For each reflectivity factor change vector data , calculate its modulus , if the modulus If it is greater than the threshold Z, the point is preset as a structural surface point and placed in the structural surface point set I.

[0060] Each vector data stored in the structure surface point array set is subjected to standardization processing to obtain target data that meets the second preset condition, and a surface point array of the reflective target structure is generated based on the target data:

[0061] Refine the structure surface point set, for each surface point , and proceed as follows:

[0062] Normalize a vector:

[0063] ;

[0064] in, , , ;

[0065] Choose an appropriate neighborhood size based on the scale and complexity of the target structure. Take the neighborhood reflectivity factor change data (Fixed radius neighborhood, the neighborhood size can also be dynamically adjusted according to data density), satisfying:

[0066] , , ;

[0067] Traversing neighborhood reflectivity factor change data :

[0068] Calculating vectors :

[0069] ;

[0070] Normalize a vector:

[0071] ;

[0072] calculate and The dot product of , and its absolute value is T:

[0073] ;

[0074] Furthermore, the eight reflectivity factor data with the smallest T value in the neighborhood are taken to make the following judgment: there is one or more neighborhood data belonging to set I, and there is at least one data normalized vector with The standardized vector product of is greater than 0; if the above conditions are met, the data point Recorded as structural surface points.

[0075] S140, vertically projecting the surface dot matrix to generate a radar combined reflectivity product embedded in the target space structure.

[0076] In some embodiments, a two-dimensional plane (x, y) is defined, and satisfies , , initialize the value of any point in the plane to (0,0).

[0077] Project structure surface points onto a 2D plane:

[0078] For each structural surface point (x, y, z), project it to the corresponding position on the two-dimensional plane (x, y):

[0079] ;

[0080] By accumulating 1, the projection values ​​of different points at the same location can be accumulated, highlighting the areas with frequent reflectivity changes on the two-dimensional plane to reflect the comprehensive reflectivity intensity of the location. The process of accumulating 1 actually forms a density map or heat map on the two-dimensional plane. The density map can show the reflectivity changes and density of different areas, providing intuitive reference data for meteorological analysis and forecasting.

[0081] After the projection of all target structure surface points is completed, the radar combined reflectivity data product (x, y) embedded in the target spatial structure is obtained.

[0082] S150, analyze the reflectance product and complete the description of the current meteorological phenomenon.

[0083] In some embodiments, the description of the current meteorological phenomenon is completed by analyzing the reflectivity product obtained in step S140.

[0084] Furthermore, based on the description of current meteorological phenomena, meteorological warning, meteorological analysis and related meteorological research can be carried out.

[0085] According to the embodiments disclosed in the present invention, the following technical effects are achieved:

[0086] Improved the analysis accuracy of meteorological activity processes:

[0087] By generating reflectivity factor change vector data, the change of radar reflectivity factor in spatial coordinates (x, y, z) can be recorded in detail. The vector data provides detailed information on the internal structure of the target, making the analysis of the target more precise and accurate. The surface dot matrix of the target structure is generated according to the reflectivity factor change vector data, which can accurately depict the surface morphology of the target. The surface dot matrix can reveal the spatial structural characteristics inside the target, supplementing the traditional method that only records the information of the maximum reflectivity factor value, thereby improving the analysis accuracy.

[0088] Improved accuracy of nowcast weather forecasts:

[0089] Existing methods ignore the spatial distribution and variation of reflectivity factors, while the present invention can reflect the internal structural characteristics of the target, which is particularly important for near-term weather forecasting. Because the internal structure of the weather system is crucial to predicting its evolution and development; the reflectivity products generated by the present invention can describe complex meteorological phenomena in more detail, such as thunderstorms, hail, and rainstorms, which usually have complex internal structures. By providing more detailed structural information, the present invention can more accurately predict and describe the above phenomena.

[0090] Enhanced extreme weather warning capabilities:

[0091] By analyzing the reflectivity factor change vector data, areas where the reflectivity factor changes dramatically can be identified. Such areas are often potential locations for extreme weather (such as severe convection, heavy rain, etc.). By identifying these areas, early warnings can be issued to improve the timeliness and accuracy of extreme weather warnings. The simple maximum value comparison in traditional methods cannot reflect the three-dimensional structural characteristics of the target, while the present invention discloses that by constructing a target structure surface dot matrix and utilizing the three-dimensional structural characteristics of the target, the occurrence and development of extreme weather can be better predicted, thereby improving early warning capabilities.

[0092] Enriched the types and applications of meteorological data:

[0093] The new type of combined reflectivity product generated by the present invention contains target spatial structure information, which is a useful supplement to existing meteorological data products. It can provide more comprehensive and detailed meteorological data and provide more information support for meteorological forecasting and research. The application of the new reflectivity product is not limited to artificial meteorological forecasting, but can also be used for related meteorological research. By providing more detailed target structure information, it can support more in-depth meteorological science research and promote the development of meteorological science.

[0094] Improved computing efficiency and reliability:

[0095] The present invention discloses that in the process of generating reflectivity factor change vector data and constructing a target structure surface dot matrix, efficient algorithm steps are designed, such as calculation of standardized vectors and traversal of neighborhood data, etc. The above steps improve calculation efficiency while ensuring accuracy; by setting the threshold of the reflectivity factor change vector and the standardized processing of the neighborhood data, the influence of noise on the result can be effectively reduced, and the reliability of the reflectivity product can be improved.

[0096] In summary, the method for describing meteorological phenomena provided by the present invention greatly improves the ability to describe and warn of complex meteorological phenomena, and can be widely used in artificial meteorological forecasting and related meteorological research.

[0097] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily required by the present application.

[0098] The above is an introduction to the method embodiment. The following is a further explanation of the scheme described in this application through an apparatus embodiment.

[0099] Figure 2 FIG. 1 is a block diagram of a device for describing complex meteorological phenomena based on reflectivity products according to an embodiment of the present application, Figure 2 Shown include:

[0100] An acquisition module 210 is used to acquire weather radar reflectivity factor data;

[0101] A first generating module 220, configured to generate reflectivity factor change vector data based on the weather radar reflectivity factor data;

[0102] A second generating module 230, for generating a surface dot matrix of a reflective target structure based on the reflectivity factor change vector data;

[0103] A projection module 240 is used to perform vertical projection on the surface dot matrix to generate a radar combined reflectivity product embedded in the target spatial structure;

[0104] The description module 250 is used to analyze the reflectance product and complete the description of the current meteorological phenomenon.

[0105] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the described module can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0106] Figure 3 A schematic diagram of the structure of a terminal device or server suitable for implementing an embodiment of the present application is shown.

[0107] like Figure 3 As shown, the terminal device or server includes a central processing unit (CPU) 301, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 302 or the program loaded from the storage part 308 into the random access memory (RAM) 303. In RAM 303, various programs and data required for the operation of the terminal device or server are also stored. CPU 301, ROM 302 and RAM 303 are connected to each other through a bus 304. An input / output (I / O) interface 305 is also connected to the bus 304.

[0108] The following components are connected to the I / O interface 305: an input section 306 including a keyboard, a mouse, etc.; an output section 307 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 308 including a hard disk, etc.; and a communication section 309 including a network interface card such as a LAN card, a modem, etc. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the I / O interface 305 as needed. A removable medium 311, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 310 as needed, so that a computer program read therefrom is installed into the storage section 308 as needed.

[0109] In particular, according to an embodiment of the present application, the above method flow steps can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a machine-readable medium, and the computer program includes a program code for executing the method shown in the flow chart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 309, and / or installed from the removable medium 311. When the computer program is executed by the central processing unit (CPU) 301, the above-mentioned functions defined in the system of the present application are executed.

[0110] It should be noted that the computer-readable medium shown in the present application may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries a computer-readable program code. This propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer-readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0111] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each box in the flow chart or block diagram can represent a module, a program segment or a part of the code, and the aforementioned module, program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0112] The units or modules involved in the embodiments described in the present application may be implemented by software or hardware. The units or modules described may also be arranged in a processor. The names of these units or modules do not, in some cases, constitute limitations on the units or modules themselves.

[0113] As another aspect, the present application further provides a computer-readable storage medium, which may be included in the electronic device described in the above embodiment; or may exist independently without being assembled into the electronic device. The above computer-readable storage medium stores one or more programs, and when the above programs are used by one or more processors to execute the method described in the present application.

[0114] The above description is only a preferred embodiment of the present application and an explanation of the technical principles used. Those skilled in the art should understand that the scope of application involved in the present application is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the aforementioned application concept. For example, the above features are replaced with (but not limited to) technical features with similar functions applied in the present application.

Claims

1. A method for describing complex meteorological phenomena based on reflectivity products, characterized in that: include: Obtain weather radar reflectivity factor data; Based on the weather radar reflectivity factor data, generating reflectivity factor change vector data; Based on the reflectivity factor change vector data, a surface dot matrix of a reflective target structure is generated, including: Based on a preset vector modulus threshold, a structure surface point set is constructed; Traversing the reflectivity factor change vector data, and calculating the modulus value of each vector data; Storing the module value that meets the first preset condition into the structure surface point array set; Each vector data stored in the structure surface point array set is subjected to standardization processing to obtain target data meeting the second preset condition; Based on the target data, generating a surface dot matrix of a reflective target structure; vertically projecting the surface dot matrix to generate a radar composite reflectivity product embedded in the target spatial structure; Analyze the reflectivity products to complete the description of current meteorological phenomena.

2. The method according to claim 1, characterized in that The generating reflectivity factor change vector data based on the weather radar reflectivity factor data comprises: Based on the weather radar reflectivity factor data, construct a four-dimensional data set including the spatial coordinates and values ​​of the reflectivity factor; Based on the four-dimensional data group, reflectivity factor change vector data is generated.

3. The method according to claim 2, characterized in that The step of performing standardization on each vector data stored in the structure surface point array set to obtain target data meeting the second preset condition comprises: Traversing the target vector data in the structure surface point array set to obtain a neighborhood data set including reflectivity factor change data of the neighborhood of the target vector data; Calculate the normalized vector of each reflectivity factor change data in the neighborhood data set; Multiplying the standardized vector of each reflectivity factor change data with the target vector data respectively to obtain a target value set; The target value set is analyzed to obtain target data that meets the second preset condition.

4. The method according to claim 3, characterized in that Also includes: The structure surface point set is initially an empty set.

5. A device for describing complex meteorological phenomena based on reflectivity products, characterized in that: include: An acquisition module is used to obtain weather radar reflectivity factor data; A first generating module, used for generating reflectivity factor change vector data based on the weather radar reflectivity factor data; The second generating module is used to generate a surface dot matrix of a reflective target structure based on the reflectivity factor change vector data, including: Based on a preset vector modulus threshold, a structure surface point set is constructed; Traversing the reflectivity factor change vector data, and calculating the modulus value of each vector data; Storing the module value that meets the first preset condition into the structure surface point array set; Each vector data stored in the structure surface point array set is subjected to standardization processing to obtain target data meeting the second preset condition; Based on the target data, generating a surface dot matrix of a reflective target structure; A projection module, used for vertically projecting the surface dot matrix to generate a radar combined reflectivity product embedded in the target spatial structure; The description module is used to analyze the reflectance products and complete the description of the current meteorological phenomena.

6. The device according to claim 5, characterized in that The generating reflectivity factor change vector data based on the weather radar reflectivity factor data comprises: Based on the weather radar reflectivity factor data, construct a four-dimensional data set including the spatial coordinates and values ​​of the reflectivity factor; Based on the four-dimensional data group, reflectivity factor change vector data is generated.

7. An electronic device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 4 is implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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