Method for simulating runoff process in dry season

Abstract

The invention discloses a dry season runoff process simulation method, and relates to the field of hydrological modeling. The method comprises the following steps: determining an edge distribution model of monthly runoff and average runoff in the dry season based on monthly runoff process sample data in the dry season; based on the marginal distribution model, adopting a D-vine Copula method to carry out high-dimensional joint distribution simulation of the runoff process in the dry season, and determining a high-dimensional joint distribution model; obtaining a given dry season average runoff or design frequency, and converting the given dry season average runoff or design frequency into a dry season monthly runoff process joint distribution frequency by adopting a Kendall function; and based on the dry-season monthly runoff process joint distribution frequency and the high-dimensional joint distribution model, randomly simulating and reversely deducing the dry-season monthly runoff process. Compared with the prior art, the method can accurately simulate the nonlinear and asymmetric dependency relationship of the runoff process in the dry season.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological modeling, and more specifically, to a method for simulating a runoff process during a dry season. Background Art

[0002] According to the changes in water conditions such as river water level and flow rate in a year, the river water conditions can be divided into flood season, normal water season and dry season. The runoff process refers to the change process of runoff in a certain river section over a certain period of time (such as dry season) based on a certain time scale (such as month). For example, the monthly runoff process in the dry season is the product of the combined action of natural geographical factors such as precipitation, temperature, and underlying surface conditions. River runoff is crucial to ensuring the supply of water resources in downstream areas. The water supply security in downstream areas should not only focus on the runoff volume of upstream water, but also on the runoff process of upstream water, especially the runoff process in the dry season. Under the influence of extreme climate change and intense human activities, the runoff process in the dry season has become more complicated, and the management of water resources in the basin faces more severe challenges.

[0003] In the prior art, two types of functions, Elliptical copulas and Archimedean copulas, are often used to simulate runoff. Among them, Elliptical copulas are usually used to describe symmetrically distributed variables and are suitable for variable sequences with clear statistical characteristics, but their disadvantage is that their descriptive ability is limited for runoff processes with nonlinear dependencies. Archimedean copulas have obvious advantages in modeling asymmetric two-variable joint distributions due to their flexibility and adaptability; although Archimedean Copulas are more flexible in statistical simulation of two-variable joint distributions, they cannot independently construct high-dimensional joint distribution simulations and lack structured tools, which limits their high-dimensional joint distribution simulations of runoff processes during dry seasons. Summary of the invention

[0004] In order to overcome the limitations of the above-mentioned prior art, the present invention provides a method for simulating a runoff process in a dry season.

[0005] In order to solve the above technical problems, the technical solution of the present invention is as follows: In a first aspect, a method for simulating a dry season runoff process comprises: Based on the sample data of monthly runoff process in dry season, the marginal distribution model of monthly runoff and average runoff in dry season is determined; Based on the marginal distribution model, the D-vine Copula method is used to carry out high-dimensional joint distribution simulation of the dry season runoff process and determine the high-dimensional joint distribution model; Get the average runoff or design frequency in a given dry season, and convert it into the joint distribution frequency of the monthly runoff process in the dry season using the Kendall function; Based on the joint distribution frequency of the dry season monthly runoff process and the high-dimensional joint distribution model, the dry season monthly runoff process is inferred by random simulation.

[0006] In a second aspect, an electronic device includes: A memory for storing computer executable instructions or computer programs; The processor is used to implement the method described in the first aspect when executing the computer executable instructions or computer program stored in the memory.

[0007] In a third aspect, a computer-readable storage medium stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, at least one program, a code set or an instruction set is loaded and executed by a processor to implement the method described in the first aspect.

[0008] In a fourth aspect, a computer program product comprises a computer program or computer executable instructions, wherein when the computer program or computer executable instructions are executed by a processor, the method of the first aspect is implemented.

[0009] Compared with the prior art, the technical solution of the present invention has the following beneficial effects: The present invention can accurately simulate the nonlinear and asymmetric dependence of the runoff process in the dry season through the D-vine copula high-dimensional joint distribution and Kendall function conversion, and can effectively realize the design of the runoff process in the dry season, providing technical support for the formulation of refined water resources regulation strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 Schematic diagram of the flow chart of the method for simulating the runoff process during the dry season in Example 1 of the present application.

[0011] Figure 2 Schematic diagram of the structure and parameters of the high-dimensional joint distribution model established in Example 2 of the present application. DETAILED DESCRIPTION

[0012] The terms "including" and "having" and any variations thereof in the specification and claims of the present application and the above-mentioned drawings are intended to cover non-exclusive inclusion, so that a process, method, system, product or device comprising a series of units is not necessarily limited to those units, but may include other units not explicitly listed or inherent to these processes, methods, products or devices. The term "determine" broadly covers a variety of actions, and may include obtaining, calculating, computing, processing, deriving, investigating, searching (e.g., searching in a table, database or other data structure), ascertaining, and similar actions, and may also include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and similar actions, and may also include generating, creating, establishing and similar actions, as well as parsing, selecting, selecting and similar actions, etc. The relevant definitions of other terms will be given in the following description.

[0013] It should be noted that when an element is considered to be "connected" to another element, it can be directly connected to the other element, or connected to the other element through an intermediate element. In addition, the "connection" in the following embodiments should be understood as "electrical connection", "communication connection", etc. if there is transmission of electrical signals or data between the connected objects.

[0014] The accompanying drawings are only used for illustrative purposes and are not to be construed as limiting the present application; In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product; It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0015] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0016] Example 1 This embodiment provides a method for simulating a runoff process during a dry season, referring to FIG1 , comprising: Based on the sample data of monthly runoff process in dry season, the marginal distribution model of monthly runoff and average runoff in dry season is determined; Based on the marginal distribution model, the D-vine Copula method is used to carry out high-dimensional joint distribution simulation of the dry season runoff process and determine the high-dimensional joint distribution model; Get the average runoff or design frequency in a given dry season, and convert it into the joint distribution frequency of the monthly runoff process in the dry season using the Kendall function; Based on the joint distribution frequency of the dry season monthly runoff process and the high-dimensional joint distribution model, the dry season monthly runoff process is inferred by random simulation.

[0017] In this embodiment, the D-vine Copula method is used to simulate the high-dimensional asymmetric joint distribution of the dry season runoff process, and the Kendall function is used to convert the joint distribution frequency of the dry season monthly runoff process. It can not only accurately simulate the nonlinear and asymmetric dependence of the dry season runoff process, but also effectively realize the design of the dry season runoff process, providing technical support for the formulation of refined water resources regulation strategies.

[0018] In some preferred embodiments, the marginal distribution model for determining the monthly runoff and average runoff during the dry season includes: The sample data of monthly runoff process in dry season is defined as ), is the number of dry season months, is the number of years, and the average runoff in the dry season is ,have:

[0019]

[0020] In the formula, and Respectively Dry season of the year Cumulative probability of monthly runoff and average runoff during the dry season; and Respectively Dry season of the year The statistical distribution of monthly runoff and average runoff in the dry season, P-III distribution was selected to carry out univariate distribution simulation of monthly runoff and average runoff in the dry season, which is also the marginal distribution model of the subsequent high-dimensional joint distribution model (D-vine copula model).

[0021] In some optional embodiments, determining the high-dimensional joint distribution model includes: According to Sklar theorem, a high-dimensional joint distribution model of dry season runoff process is established. for:

[0022] In the formula, Indicates the dry season Marginal distribution model of monthly runoff; A density function representing the high-dimensional joint distribution model; is the number of dry season months; The high-dimensional joint distribution model adopts the structural hierarchy of D-vine Copula, calculates the correlation coefficient between monthly runoff as the weighted distance, sorts according to the sum of distances, and determines the first level in turn. The node order of the high-dimensional joint distribution model is obtained by recursion step by step. The node relationship forms a joint distribution structure composed of binary Copula functions.

[0023] Furthermore, the density function expression of the high-dimensional joint distribution model is:

[0024] In the formula, represents the bivariate density function, represents the conditional distribution function.

[0025] Furthermore, the binary Copula distribution between nodes can be optimized using Elliptical and / or Archimedean Copula function families.

[0026] In some optional embodiments, the Kendall function The expression is:

[0027] In the formula, is a preset frequency level value, and , through the Kendall transformation function Establish the mapping relationship between the joint distribution frequency of monthly runoff in the dry season and the average runoff frequency in the dry season; represents the joint distribution frequency of the dry season monthly runoff process; is the indicator function; The sample length simulated for the dry season runoff process; Then, for a given dry season average flow Or design frequency ,have:

[0028] Those skilled in the art should understand that Can be regarded as the joint distribution frequency Quantile in the sample; Under the hydrological scenario, Represents the quantile of the joint distribution of runoff for a certain return period (e.g., 10 years, 50 years).

[0029] Furthermore, for a given dry season average flow or design frequency, the dry season monthly runoff process can be simulated and inferred, including: Given the average flow rate during the dry season Or design frequency , according to formula (6) we can get ; According to the obtained high-dimensional joint distribution model, random simulation generatesN Frequency of marginal distribution of monthly runoff in dry season ,and N Be large enough (such as ), from which we can obtain L Group , whose joint distribution frequency is close to q ,Right now:

[0030] In the formula, To simulate and generate a set of marginal distribution frequencies of monthly runoff in the dry season in the sample The corresponding joint distribution frequency; The error is a relative minimum, such as N =10 -2 q .

[0031] Then according to formula (1), we can find the inverse function: get L The runoff process in the dry season is .

[0032] In some specific implementation processes, the monthly runoff distribution type can be selected or the runoff process can be determined based on the maximum weight function according to the water resources regulation strategy.

[0033] Example 2 This embodiment takes a certain river basin as an example, whose dry season is from October each year to March of the following year. Based on the method provided in Example 1, the steps are as follows: S1. Collect long-term series data of monthly runoff process in the dry season at a station in the basin, and obtain the runoff of each month in the dry season based on P-III simulation. and average runoff The distribution parameters are shown in Table 1.

[0034] Table 1 Parameters of univariate P-III distribution of dry season runoff series

[0035] S2. Calculate the correlation coefficient between monthly runoff, as shown in Table 2.

[0036] Table 2 Correlation coefficients between monthly runoffs during the dry season

[0037] S3. Sort by the sum of correlation coefficients to get the first level of the D-vine copula model The node order is 4-3-5-2-1-6, and the other levels are obtained step by step The node relationship between nodes is simulated by using the two-variable copula function to obtain the high-dimensional joint distribution model and parameters between nodes. , as shown in Figure 2.

[0038] S4, for a given dry season average runoff ( =2783 m3 / s, p = 0.05), the monthly runoff process in the dry season based on the concave distribution is shown in Table 3.

[0039] Table 3 A monthly runoff process for a given dry season average runoff

[0040] It can be understood that the options in the above-mentioned embodiment 1 are also applicable to this embodiment, so they will not be described again here.

[0041] Example 3 This embodiment provides a computer-readable storage medium, on which is stored at least one instruction, at least one program, code set or instruction set, and the at least one instruction, at least one program, code set or instruction set is loaded and executed by a processor, so that the processor executes part or all of the steps of the method provided in Example 1 or Example 2 of the present application.

[0042] It is understood that the storage medium may be transient or non-transient. Exemplarily, the storage medium includes, but is not limited to, a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and other media that can store program codes.

[0043] Exemplarily, the processor may be a central processing unit (CPU), a microprocessor (MPU), a digital signal processor (DSP), or a field programmable gate array (FPGA).

[0044] Exemplarily, the read-only memory includes but is not limited to MASK ROM, PROM, EPROM, EEPROM, Flash, etc.

[0045] Exemplarily, the random access memory includes but is not limited to DRAM, SRAM, SDRAM, DDR SDRAM, etc.

[0046] In some examples, a computer program product is provided, which can be implemented in hardware, software or a combination thereof. As a non-limiting example, the computer program product can be embodied as the storage medium, or as a software product, such as an SDK (Software Development Kit).

[0047] As a non-limiting example, a computer program product is provided, the computer program product includes a computer program or a computer executable instruction, the computer program or the computer executable instruction is stored in a computer-readable storage medium. A processor of an electronic device reads the computer program or the computer executable instruction from the computer-readable storage medium, and the processor executes the computer executable instruction, so that the electronic device performs some or all steps of the method described in the embodiment of the present application.

[0048] In some examples, a computer program is provided, comprising a computer-readable code, and when the computer-readable code is run in a computer device, a processor in the computer device executes a part or all of the steps in the method.

[0049] In some specific implementation processes, the above computer readable code is implemented based on R language or Python.

[0050] This embodiment also proposes an electronic device, including a memory and a processor, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and when the processor executes the at least one instruction, at least one program, a code set or an instruction set, it implements part or all of the steps of the method described in Example 1 or Example 2.

[0051] In some examples, a hardware entity of the electronic device is provided, including: a processor, a memory and a communication interface; wherein the processor generally controls the overall operation of the electronic device; the communication interface is used to enable the electronic device to communicate with other terminals or servers through a network; the memory is configured to store instructions and applications executable by the processor, and can also cache data to be processed or processed by the processor and various modules in the electronic device (including but not limited to image data, audio data, voice communication data and video communication data), which can be implemented by flash memory (FLASH), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM) or random access memory (RAM).

[0052] The processor may include one or more processing elements. Thus, the processor may include one or more integrated circuits (ICs) configured to perform the functions of the processor. In addition, each integrated circuit may include circuits (e.g., a first circuit, a second circuit, and other circuits, etc.) configured to perform the functions of the processor.

[0053] Furthermore, data may be transmitted between the processor, the communication interface and the memory via a bus, which may include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together.

[0054] It can be understood that the options in the above-mentioned embodiment 1 or embodiment 2 are also applicable to this embodiment, so they are not described again here.

[0055] The same or similar reference numerals correspond to the same or similar components; The terms used to describe the positional relationship in the drawings are only used for illustrative purposes and should not be construed as limiting the present application; It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application may be combined with each other.

[0056] In different specific implementations, the method or system described in the present application can be implemented in software, hardware or a combination thereof. In addition, the order of the steps of the method can be changed, and various elements can be added, reordered, combined, omitted, modified, etc.

[0057] Obviously, the above-mentioned embodiments of the present application are merely examples for clearly illustrating the present application, and are not intended to limit the implementation methods of the present application, and are not intended to limit the present application. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. Each discrete structure / function module or unit can be integrated together to form an independent part, or each module can exist separately, or two or more modules can be integrated to form an independent part, and the structure and function of the discrete components can be implemented as a combined structure or component. It is not necessary and impossible to enumerate all the implementation methods here. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the claims of the present application.

Claims

1. A method for simulating runoff process during dry season, characterized in that: include: Based on the sample data of monthly runoff process in dry season, the marginal distribution model of monthly runoff and average runoff in dry season is determined; Based on the marginal distribution model, the D-vine Copula method is used to carry out high-dimensional joint distribution simulation of the dry season runoff process and determine the high-dimensional joint distribution model; Get the average runoff or design frequency in a given dry season, and convert it into the joint distribution frequency of the monthly runoff process in the dry season using the Kendall function; Based on the joint distribution frequency of the dry season monthly runoff process and the high-dimensional joint distribution model, the dry season monthly runoff process is inferred by random simulation.

2. A method for simulating dry season runoff according to claim 1, characterized in that: The marginal distribution model for determining the monthly runoff and average runoff during the dry season includes: The sample data of monthly runoff process in dry season is defined as ), is the number of dry season months, is the number of years, and the average runoff in the dry season is ,have: In the formula, and Respectively Dry season of the year Cumulative probability of monthly runoff and average runoff during the dry season; and Respectively Dry season of the year The statistical distribution of monthly runoff and average runoff in the dry season uses P-III distribution to simulate the univariate distribution of monthly runoff and average runoff in the dry season as the marginal distribution model.

3. A method for simulating dry season runoff according to claim 2, characterized in that: Determining the high-dimensional joint distribution model includes: According to Sklar theorem, a high-dimensional joint distribution model of dry season runoff process is established. for: In the formula, Indicates the dry season Marginal distribution model of monthly runoff; A density function representing the high-dimensional joint distribution model; is the number of dry season months; The high-dimensional joint distribution model adopts the structural hierarchy of D-vine Copula, calculates the correlation coefficient between monthly runoff as the weighted distance, sorts according to the sum of distances, and determines the first level in turn. The node order of the high-dimensional joint distribution model is obtained by recursion step by step. The node relationship forms a joint distribution structure composed of binary Copula distribution functions.

4. A method for simulating dry season runoff according to claim 3, characterized in that: The density function expression of the high-dimensional joint distribution model is: In the formula, represents the bivariate density function, represents the conditional distribution function.

5. A method for simulating dry season runoff according to claim 4, characterized in that: The binary Copula distribution function between nodes adopts the Elliptical and / or Archimedean Copula function family.

6. A method for simulating dry season runoff according to claims 2 to 5, characterized in that: The Kendall function The expression is: In the formula, is a preset frequency level value, and , through the Kendall transformation function Establish the mapping relationship between the joint distribution frequency of monthly runoff in the dry season and the average runoff frequency in the dry season; represents the joint distribution frequency of the dry season monthly runoff process; is the indicator function; The sample length simulated for the dry season runoff process; Then, for a given dry season average flow Or design frequency ,have: 。 7. A method for simulating dry season runoff according to claim 6, characterized in that: For a given dry season average flow or design frequency, the stochastic simulation reverses the dry season monthly runoff process, including: According to the high-dimensional joint distribution model, random simulation generates Frequency of marginal distribution of monthly runoff in dry season , from which we obtain Group , whose joint distribution frequency is close to ,Right now: In the formula, To simulate and generate a set of marginal distribution frequencies of monthly runoff in the dry season in the sample The corresponding joint distribution frequency; Represents the error, which is a relative minimum value; According to formula (1), the inverse function is get The runoff process in the dry season is .

8. An electronic device, characterized in that: include: A memory for storing computer executable instructions or computer programs; A processor, used to implement the method according to any one of claims 1 to 7 when executing computer executable instructions or computer programs stored in the memory.

9. A computer-readable storage medium, characterized in that: The storage medium stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, at least one program, a code set or an instruction set is loaded and executed by a processor to implement the method as described in any one of claims 1-7.

10. A computer program product comprising a computer program or computer executable instructions, characterized in that: When the computer program or computer executable instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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