Theoretical analysis method and device for simulating transition distribution of multi-sized microcystis colonies

Abstract

To solve the technical problem of the difficulty in accurately describing transition distribution process of multi-sized Microcystis colonies.SOLUTION: The present disclosure provides a theoretical analysis method and device for simulating transition distribution of multi-sized Microcystis colonies. The method comprises: classifying all Microcystis colonies into multiple groups based on size; constructing an initial concentration control equation for each group and simplifying it into a target concentration control equation; setting initial and boundary conditions for a concentration; converting these into a dimensionless form; and further analytically calculating a dimensionless concentration control equation based on target quantity moments and central moments, additional conditions, initial conditions, and boundary conditions for each group, to obtain an analytical expression for a spatial concentration distribution of all Microcystis colonies. Consequently, it is possible to precisely describe a transition distribution process of multi-sized Microcystis colonies.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to the field of aquatic ecological environment technology, and in particular to a theoretical analysis method and apparatus for simulating the succession distribution of multi-sized Microcystis colonies. [Background technology]

[0002] Microcystis can be divided into unicellular and colonial forms. In natural environments, Microcystis often exists in colonial form, and they vary in size. The spatial distribution of Microcystis determines the dynamics of water bloom occurrence and disappearance. In eutrophic water bodies, Microcystis typically reaches high biomass, making Microcystis succession in water bodies a key process in the occurrence of water blooms. Currently, research methods for the succession and distribution of multi-sized Microcystis colonies include field observations, laboratory experiments, and numerical simulations. However, the lack of theoretical analysis methods makes it difficult to accurately describe the succession and distribution process of multi-sized Microcystis colonies, making it difficult to provide reliable support for water bloom prediction and forecasting. Summary of the Invention [Problem to be solved by the invention]

[0003] In order to solve or at least partially solve the above technical problems, the present disclosure provides a theoretical analysis method and apparatus for simulating the transition distribution of multi-sized Microcystis colonies, which differs from the theoretical analysis method for the transition distribution of single-sized Microcystis colonies. The present disclosure reflects the effects of different environmental gradients on the transition characteristics and transport features of Microcystis colony patches, and can accurately describe the transition distribution process of multi-sized Microcystis colonies, providing reliable support for the prediction and forecasting of water blooms. [Means for solving the problem]

[0004] An embodiment of the present disclosure provides a theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies, the method comprising: Dividing all the Microcystis colonies into a plurality of groups of Microcystis colonies according to size, and obtaining the percentage of the number of Microcystis colonies in each group relative to the total number of all the Microcystis colonies; constructing an initial concentration control equation for each group of Microcystis colonies, and performing a simplification process on the initial concentration control equation based on the two-dimensional wind flow velocity pattern to obtain a target concentration control equation for each group of Microcystis colonies; Determining the initial concentration condition of the Microcystis colony of each group based on the quantity percentage and the total quantity of the Microcystis colony of each group, and obtaining the concentration boundary condition of the Microcystis colony of each group; Transforming the target concentration control equation, the initial concentration condition, and the boundary concentration condition based on the introduction of dimensionless parameters to obtain a dimensionless concentration control equation, initial concentration condition, and boundary concentration condition for each group of Microcystis colonies; A step of processing the non-dimensional concentration control equation of each group of Microcystis colonies based on the target quantity order concentration moment analysis formula, the target quantity center concentration moment analysis formula, the preset concentration distribution additional condition, the non-dimensional concentration initial condition, and the non-dimensional concentration boundary condition to obtain the target quantity order concentration moment and the target quantity center concentration moment of each group of Microcystis colonies; and calculating based on the target quantity class concentration moment and the target quantity center concentration moment of the Microcystis colonies of each group to obtain an analytical formula for the spatial concentration distribution of all the Microcystis colonies.

[0005] Optionally, construct an initial concentration control equation for each group of Microcystis colonies as follows: JPEG2025178168000002.jpg24170 where C iis the concentration of the i-th group of Microcystis colonies, where i is a positive integer, t is time, μ is the vector flow velocity, and μ b i is the vector transition rate of the i-th group of Microcystis colonies, λ is the diffusion coefficient of the water flow, and ∇ is the gradient operator. The initial concentration control equation is simplified based on the two-dimensional wind velocity pattern to obtain the target concentration control equation for each group of Microcystis colonies as follows: JPEG2025178168000003.jpg28170where μ is the longitudinal flow velocity and w b i is the succession rate of the i-th group of Microcystis colonies, and λ b ixx is the diffusion coefficient along the x direction of the i-th group of Microcystis colonies, and λ b izz is the diffusion coefficient along the z direction of the i-th group of Microcystis colonies.

[0006] Selectably, set an initial time, and the microcystis colony patches are concentrated at x=0 and z=0. Based on the percentage of the microcystis colonies in each group and the total number, determine the initial concentration conditions of the microcystis colonies in each group as follows: JPEG2025178168000004.jpg25170 where N i is the percentage of the number of Microcystis colonies in the i-th group, Q is the total number of Microcystis colonies, and δ is the Dirac function. At x = ±∞, z = 0, z = H (H is the water depth), the concentration boundary conditions for the Microcystis colonies of each group are as follows: JPEG2025178168000005.jpg50170Used to indicate that the flux of Microcystis colonies at the free surface and bottom is zero.

[0007] Selectively, the dimensionless parameters to be introduced are: JPEG2025178168000006.jpg53170 Based on the introduction of dimensionless parameters, the target concentration control equation, the concentration initial condition and the concentration boundary condition are transformed to obtain the dimensionless concentration control equation, dimensionless concentration initial condition and dimensionless concentration boundary condition of each group of Microcystis colony, which are respectively as follows: JPEG2025178168000007.jpg94170i Reflects the relative strength of vertical succession and total vertical spread of Microcystis colonies of the order group.

[0008] Optionally, the target quantity order concentration moment analysis formula for each group of Microcystis colonies is: JPEG2025178168000008.jpg24170, The target quantity center concentration moment analysis formula for each group of Microcystis colonies is: JPEG2025178168000009.jpg83170The obtained second-order central density moment, third-order central density moment, and fourth-order central density moment are, respectively: JPEG2025178168000010.jpg36170.

[0009] The selectable, preset concentration distribution addition conditions are: JPEG2025178168000011.jpg21170, Processing a dimensionless concentration control equation for each group of Microcystis colonies based on the target number order concentration moment analysis formula for each group of Microcystis colonies, the preset concentration distribution additional condition, the dimensionless concentration initial condition, and the dimensionless concentration boundary condition; JPEG2025178168000012.jpg109170 If p>0, the p of the i-th group of Microcystis colonies is JPEG2025178168000013.jpg77170

[0010] Optionally, the step of calculating based on the target quantity class concentration moment and the target quantity center concentration moment of the Microcystis colony of each group to obtain a spatial concentration distribution analysis formula for all Microcystis colonies includes: According to the target number order concentration moment of each group of Microcystis colonies, Chatwin asymptotic expansion formula is applied to obtain the following analytical formula for the spatial concentration distribution of all Microcystis colonies: JPEG2025178168000014.jpg70170Here, the polynomial coefficient a n Determine.

[0011]

[0013] An embodiment of the present disclosure further provides a theoretical analysis device for simulating the transition distribution of multi-sized Microcystis colonies, the device comprising: A grouping and acquisition module for dividing all the microcystis colonies into a plurality of groups of microcystis colonies according to their size and acquiring the percentage of the number of the microcystis colonies in each group relative to the total number of all the microcystis colonies; a construction and simplification module for constructing an initial concentration control equation for each group of Microcystis colonies, and performing a simplification process on the initial concentration control equation based on a two-dimensional wind velocity pattern to obtain a target concentration control equation for each group of Microcystis colonies; A determination and acquisition module for determining an initial concentration condition of the Microcystis colony of each group based on the quantity percentage of the Microcystis colony of each group and the total quantity, and acquiring a concentration boundary condition of the Microcystis colony of each group; a conversion module for converting the target concentration control equation, the initial concentration condition, and the boundary concentration condition based on the introduction of a dimensionless parameter to obtain a dimensionless concentration control equation, an initial concentration condition, and a boundary concentration condition for each group of Microcystis colonies; a processing module for processing the non-dimensional concentration control equations of the Microcystis colonies of each group based on the target quantity order concentration moment analysis formula, the target quantity center concentration moment analysis formula, the preset concentration distribution additional conditions, the non-dimensional concentration initial conditions, and the non-dimensional concentration boundary conditions of the Microcystis colonies of each group to obtain the target quantity order concentration moment and the target quantity center concentration moment of the Microcystis colonies of each group; and a calculation module for calculating based on the target quantity class concentration moment and the target quantity center concentration moment of the Microcystis colony of each group to obtain an analytical formula for the spatial concentration distribution of all the Microcystis colonies.

[0012] An embodiment of the present disclosure provides an electronic device, the electronic device including a processor and a memory for storing instructions executable by the processor, the processor being adapted to read the executable instructions from the memory and execute the instructions to implement a theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies provided in an embodiment of the present disclosure.

[0013] An embodiment of the present disclosure further provides a computer-readable storage medium having stored thereon a computer program for executing the theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies provided in the embodiment of the present disclosure. [Effects of the Invention]

[0014] The technical solutions provided in the embodiments of the present disclosure have the following advantages over the prior art: The theoretical analysis method for simulating the transient distribution of multi-sized Microcystis colonies provided in the embodiments of the present disclosure divides all Microcystis colonies into multiple groups of Microcystis colonies according to size, obtains the quantitative percentage of Microcystis colonies in each group relative to the total number of all Microcystis colonies, constructs an initial concentration control equation for Microcystis colonies in each group, performs a simplification process on the initial concentration control equation based on the two-dimensional wind flow velocity pattern to obtain a target concentration control equation for Microcystis colonies in each group, determines the initial concentration conditions for Microcystis colonies in each group based on the quantitative percentage and total number of Microcystis colonies in each group, obtains the concentration boundary conditions for Microcystis colonies in each group, and calculates the dimensionless parameters Based on the introduction of the formula, the target concentration control equation, the concentration initial condition and the concentration boundary condition are transformed to obtain the dimensionless concentration control equation, the dimensionless concentration initial condition and the dimensionless concentration boundary condition for each group of Microcystis colonies. Based on the target quantity order concentration moment analysis formula, the target quantity center concentration moment analysis formula, the preset concentration distribution additional condition, the dimensionless concentration initial condition and the dimensionless concentration boundary condition for each group of Microcystis colonies, the dimensionless concentration control equation for each group of Microcystis colonies is processed to obtain the target quantity order concentration moment and the target quantity center concentration moment for each group of Microcystis colonies. Based on the target quantity order concentration moment and the target quantity center concentration moment for each group of Microcystis colonies, calculations are performed to obtain the spatial concentration distribution analysis formula for all Microcystis colonies.The present disclosure solves the technical problem that, due to the lack of theoretical analytical methods for the transitional distribution of multi-sized Microcystis colonies, it is not possible to accurately describe the transitional distribution process of multi-sized Microcystis colonies, making it difficult to provide reliable support for the prediction and forecasting of water blooms. Unlike theoretical analytical methods for the transitional distribution of single-sized Microcystis colonies, the embodiments of the present disclosure reflect the effects of different environmental gradients on the transitional and transport characteristics of Microcystis colony patches, making it possible to accurately describe the transitional distribution process of multi-sized Microcystis colonies, thereby providing reliable support for the prediction and forecasting of water blooms. [Brief explanation of the drawings]

[0015] The above and other features, advantages, and aspects of each embodiment of the present disclosure will become more apparent with reference to the following specific embodiments in conjunction with the drawings. Throughout the drawings, the same or similar reference numerals represent the same or similar elements. Please note that the drawings are schematic and the dimensions of the actual objects and elements are not necessarily drawn to scale.

[0016] [Figure 1] FIG. 1 is an illustrative diagram showing the flow of a theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies provided in an embodiment of the present disclosure. [Figure 2] FIG. 1 is a schematic diagram illustrating the transition of different sized Microcystis colonies in aeolian currents provided in an embodiment of the present disclosure. [Figure 3] FIG. 1 is a schematic diagram of the spatial concentration distribution of Microcystis colonies provided in the examples of the present disclosure. [Figure 4] FIG. 1 is a schematic diagram of the spatial concentration distribution of another Microcystis colony provided in an embodiment of the present disclosure. [Figure 5] FIG. 1 is a schematic diagram showing the spatial concentration distribution of Microcystis colonies provided in the examples of the present disclosure. [Figure 6] FIG. 10 is a schematic diagram of the spatial concentration distribution of additional Microcystis colonies provided in examples of the present disclosure. [Figure 7]FIG. 1 is a schematic diagram of the structure of a theoretical analysis device for simulating the transition distribution of multi-sized Microcystis colonies provided in an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0017] Hereinafter, embodiments of the present disclosure will be described in more detail with reference to the drawings. Although some embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be realized in various forms and should not be construed as being limited to the embodiments described herein, but rather, these embodiments are provided for a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure only serve as examples and do not limit the protection scope of the present disclosure.

[0018] It should be understood that the steps recited in the method embodiments of the present disclosure may be performed in different orders and / or in parallel, and that method embodiments may include additional steps and / or omit performing steps as shown. The scope of the present disclosure is not limited in this respect.

[0019] As used herein, the term "comprises" and variations thereof mean an open inclusion, i.e., "including, but not limited to." The term "based on" means "based at least in part on." The term "in one embodiment" refers to "at least one embodiment," the term "in another embodiment" refers to "at least one other embodiment," and the term "in some embodiments" refers to "at least some embodiments." Relevant definitions of other terms are provided below.

[0020] It should be noted that the concepts of "first," "second," etc. mentioned in this disclosure are used only to distinguish between different devices, modules, or units, and are not intended to limit the order or interdependence of functions performed by these devices, modules, or units.

[0021] It should be noted that the modifications "one" and "multiple" referred to in this disclosure are exemplary only and not limiting, and the reader will understand that they should be understood as "one or more" unless the context clearly indicates otherwise.

[0022] The names of messages or information exchanged between devices in the embodiments of the present disclosure are for illustrative purposes only and are not used to limit the scope of these messages or information.

[0023] Conventional methods have a technical problem in that they cannot fully reflect the existence state of Microcystis colonies of a single size in a natural environment. However, the theoretical analysis method for simulating the transition distribution of Microcystis colonies of multiple sizes provided in the embodiments of the present disclosure can solve the above-mentioned problem. By taking into account the different sizes of Microcystis colonies, a concentration control equation for Microcystis colonies of multiple sizes can be constructed and analytically solved, which can accurately reflect the transition distribution state of Microcystis colonies of multiple sizes and improve the accuracy of water bloom prediction and forecasting.

[0024] 1 is a schematic diagram of the flow of a theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies provided in an embodiment of the present disclosure, which can be realized by software and / or hardware and generally can be integrated into electronic devices. As shown in FIG. 1, the method includes steps 101 to 106.

[0025] In step 101, all the Microcystis colonies are divided into a plurality of groups of Microcystis colonies according to their size, and the percentage of the number of Microcystis colonies in each group relative to the total number of all the Microcystis colonies is obtained.

[0026] Specifically, the transport process of Microcystis colonies in water bodies is very complex, involving convective entrainment and turbulent diffusion in the water body, longitudinal transition and self-diffusion of Microcystis colonies, and interactions between Microcystis colonies and the water body. In the embodiments of the present disclosure, the convective diffusion effect of the water body and the transition characteristics of Microcystis colonies themselves are mainly considered, while the effects of changes in density of Microcystis colonies, interactions between Microcystis colonies, and the hydrodynamic transition characteristics of Microcystis colonies themselves are ignored.

[0027] In the embodiments of the present disclosure, each Microcystis colony has a variety of different shapes in actual application scenarios, and pretreatment can simplify the various differently shaped Microcystis colonies into a circular shape. Furthermore, all Microcystis colonies can be understood to include Microcystis colonies of different sizes, where size can be understood as the size of an equivalent diameter, and Microcystis colonies of different sizes can be understood as circles with different equivalent diameters, and the circles contain multiple Microcystis.

[0028] In an embodiment of the present disclosure, all Microcystis colonies can be divided into multiple groups of Microcystis colonies according to size, for example, by setting different size ranges such as 15 to 20 micrometers, 20 to 25 micrometers, etc., and dividing the Microcystis colonies belonging to different size ranges into multiple groups, with each group containing Microcystis colonies of the same or similar size.

[0029] Furthermore, the number of each type of Microcystis contained in each group of Microcystis colonies is counted to obtain the total number of all Microcystis colonies, and the percentage of the number of Microcystis colonies in each group relative to the total number of all Microcystis colonies can then be calculated. Subsequently, multiple groups of Microcystis colonies are processed simultaneously, allowing for a rapid and effective theoretical analysis of the transition distribution of multi-sized Microcystis colonies.

[0030] Specifically, in natural environments, there are generally Microcystis colonies of different sizes. All Microcystis colonies are divided into n groups according to size, where the equivalent diameter is D i The ratio of the i-th group of Microcystis colonies to the total colonies is N i The concentration of multi-sized Microcystis colonies, C, can be calculated using the following formula (1): JPEG2025178168000015.jpg29151 where C i is the concentration of the i-th group of Microcystis colonies.

[0031] As an example, consider the transition process of Microcystis colony patches in an aeolian stream in a Cartesian coordinate system, where x is parallel to the water flow direction, the z axis points vertically upward, and the origin is set at the bottom. Figure 2 shows a schematic diagram of the transition of Microcystis colonies of different sizes in an aeolian stream.

[0032] For example, as shown in Figure 2, all Microcystis colonies contain three types of Microcystis colonies with different sizes, so they can be divided into three groups, and subsequent treatments can be performed on the Microcystis colonies of the three groups simultaneously.

[0033] In step 102, an initial concentration control equation for each group of Microcystis colonies is constructed, and a simplification process is performed on the initial concentration control equation based on the two-dimensional wind flow velocity pattern to obtain a target concentration control equation for each group of Microcystis colonies.

[0034] In some examples, the initial concentration control equation for each group of Microcystis colonies is constructed, as shown in Equation (2). JPEG2025178168000016.jpg29157

[0035] JPEG2025178168000017.jpg42170Based on the two-dimensional wind flow velocity pattern, a simplification process was performed on the initial concentration control equation to obtain the target concentration control equation for Microcystis colonies in each group, as shown in equation (3). JPEG2025178168000018.jpg23170

[0036] JPEG2025178168000019.jpg45170

[0037] In step 103, the initial concentration conditions of the Microcystis colonies of each group are determined based on the quantity percentage and total quantity of the Microcystis colonies of each group, and the concentration boundary conditions of the Microcystis colonies of each group are obtained.

[0038] In some embodiments, an initial time is set, and the Microcystis colony patches are concentrated at x = 0 and z = 0. Based on the percentage and total number of Microcystis colonies in each group, the initial concentration conditions of the Microcystis colonies in each group are determined, as shown in Equation (4). JPEG2025178168000020.jpg19170

[0039] JPEG2025178168000021.jpg54170

[0040] JPEG2025178168000022.jpg33164Here, equation (6) is used to express that the flux of Microcystis colonies at the free surface and bottom is zero.

[0041] In step 104, based on the introduction of dimensionless parameters, the target concentration control equation, the concentration initial condition and the concentration boundary condition are transformed to obtain the dimensionless concentration control equation, the dimensionless concentration initial condition and the dimensionless concentration boundary condition for each group of Microcystis colonies.

[0042] In some embodiments, the dimensionless parameter introduced is: JPEG2025178168000023.jpg15170

[0043] JPEG2025178168000024.jpg35170

[0044] Based on the introduction of dimensionless parameters, the target concentration control equation, concentration initial condition, and concentration boundary condition were transformed to obtain the dimensionless concentration control equation, dimensionless concentration initial condition, and dimensionless concentration boundary condition for each group of Microcystis colony, which are respectively as follows: JPEG2025178168000025.jpg87170

[0045] That is, by substituting the dimensionless parameters into equations (3), (4), (5), and (6), we obtain equations (7), (8), (9), and (10).

[0046] JPEG2025178168000026.jpg54170

[0047] In step 105, the non-dimensional concentration control equation for each group of Microcystis colonies is processed based on the target quantity class concentration moment analysis formula, target quantity center concentration moment analysis formula, preset concentration distribution additional conditions, non-dimensional concentration initial conditions, and non-dimensional concentration boundary conditions for each group of Microcystis colonies to obtain the target quantity class concentration moment and target quantity center concentration moment for each group of Microcystis colonies.

[0048] In the embodiment of the present disclosure, the target quantity can be set as needed, for example, 4 floors.

[0049] In some embodiments, the Aris concentration moment method is deployed to analyze the overall transition characteristics of Microcystis colonies in wind currents, and the p-th order concentration moment and p-th order central concentration moment of the i-th group of Microcystis colonies are defined. The target number order concentration moment analysis formula for each group of Microcystis colonies is as follows: JPEG2025178168000027.jpg29170

[0050] The target quantity central concentration moment analysis formula for each group of Microcystis colony is as follows: JPEG2025178168000028.jpg48170

[0051] JPEG2025178168000029.jpg44170Represents the position of the center of gravity of the Microcystis colony patch.

[0052] For example, the obtained second-order central concentration moment, third-order central concentration moment, and fourth-order central concentration moment are respectively: JPEG2025178168000030.jpg36170.

[0053] In some embodiments, the preset concentration distribution addition conditions are as follows: JPEG2025178168000031.jpg28170

[0054] Based on the target quantity order concentration moment analysis formula of each group of Microcystis colony, the preset concentration distribution additional condition, the dimensionless concentration initial condition, and the dimensionless concentration boundary condition, the dimensionless concentration control equation of each group of Microcystis colony is processed; JPEG2025178168000032.jpg181170

[0055] In step 106, the spatial concentration distribution analysis formula of all Microcystis colonies is obtained by calculation based on the target quantity class concentration moment and the target quantity center concentration moment of each group of Microcystis colonies.

[0056] In some embodiments, the step of calculating the spatial concentration distribution analysis formula of all Microcystis colonies based on the target quantity class concentration moment and the target quantity center concentration moment of each group of Microcystis colonies includes: According to the target number order concentration moment of each group of Microcystis colonies, Chatwin asymptotic expansion formula is applied to obtain the spatial concentration distribution analytical formula of all Microcystis colonies as follows: JPEG2025178168000033.jpg63170Here, the polynomial coefficient a n Determine.

[0057] It should be understood that the target quantity can be set as needed. In this disclosure, the fourth order is taken as an example, and based on the previously calculated concentration moments from the zeroth order to the fourth order, Chatwin asymptotic expansion formula, i.e., Edgeworth expansion formula, is applied to obtain an analytical formula for the spatial concentration distribution of Microcystis colonies in the aeolian flow, so that the polynomial coefficients are: JPEG2025178168000034.jpg19170.

[0058] Therefore, by taking the first four coefficients and using them as an approximate solution, we can ensure computational efficiency while still ensuring computational efficiency.

[0059] This disclosure is based on a concentration distribution model for multi-sized Microcystis colonies, taking into account the transition characteristics of the Microcystis colonies themselves, and establishes a two-dimensional model of the transport of multi-sized Microcystis colonies in the aeolian current environment of shallow lakes. Analytical solutions for concentration moments of order 0 to 4 are obtained using the Aris concentration moment method to obtain the overall transition characteristics of Microcystis colonies, and concentration moments of different orders can reflect different characteristics of Microcystis colony transition. Based on the analytical solutions for concentration moments of order 0 to 4, combined with Chatwin's asymptotic expansion formula, two-dimensional concentration distribution of Microcystis colonies is obtained. A theoretical analysis of the transition distribution of multiple groups of Microcystis colonies of different sizes is simultaneously calculated, thereby obtaining a theoretical analysis of the transition distribution of all Microcystis colonies of different sizes. This allows for rapid and accurate simulation of the transition distribution process of multi-sized Microcystis colonies, providing reliable support for the prediction and forecasting of water blooms.

[0060] To summarize the above, the theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies provided in the embodiments of the present disclosure divides all Microcystis colonies into multiple groups of Microcystis colonies according to size, obtains the quantitative percentage of each group of Microcystis colonies relative to the total number of all Microcystis colonies, constructs an initial concentration control equation for each group of Microcystis colonies, performs a simplification process on the initial concentration control equation based on the two-dimensional wind flow velocity pattern to obtain a target concentration control equation for each group of Microcystis colonies, determines the initial concentration conditions for each group of Microcystis colonies based on the quantitative percentage and total number of Microcystis colonies in each group, obtains the concentration boundary conditions for each group of Microcystis colonies, and calculates the non-dimensional pattern. Based on the introduction of parameters, the target concentration control equation, concentration initial conditions and concentration boundary conditions are converted to obtain the dimensionless concentration control equation, dimensionless concentration initial conditions and dimensionless concentration boundary conditions for each group of Microcystis colonies. Based on the target quantity order concentration moment analysis formula, target quantity center concentration moment analysis formula, preset concentration distribution additional conditions, dimensionless concentration initial conditions and dimensionless concentration boundary conditions for each group of Microcystis colonies, the dimensionless concentration control equation for each group of Microcystis colonies is processed to obtain the target quantity order concentration moment and target quantity center concentration moment for each group of Microcystis colonies. Based on the target quantity order concentration moment and target quantity center concentration moment for each group of Microcystis colonies, calculations are performed to obtain the spatial concentration distribution analysis formula for all Microcystis colonies. The present disclosure solves the technical problem that, due to the lack of theoretical analytical methods for the transitional distribution of multi-sized Microcystis colonies, it is not possible to accurately describe the transitional distribution process of multi-sized Microcystis colonies, making it difficult to provide reliable support for the prediction and forecasting of water blooms. Unlike theoretical analytical methods for the transitional distribution of single-sized Microcystis colonies, the embodiments of the present disclosure reflect the effects of different environmental gradients on the transitional and transport characteristics of Microcystis colony patches, making it possible to accurately describe the transitional distribution process of multi-sized Microcystis colonies, thereby providing reliable support for the prediction and forecasting of water blooms.

[0061] As an example, we used a transport model of multi-sized Microcystis colonies to study the spatial concentration distribution of Microcystis colony patches under different environmental gradient conditions and further interpret the differences in Microcystis colony concentration distribution under different environmental gradient conditions. Tables 1-3 show the proportions and ascent rates of Microcystis colonies of different sizes under three environmental gradient conditions.

[0062] Table 1 Proportion and ascent rate of Microcystis colonies of different sizes in environmental gradient 1 JPEG2025178168000035.jpg75170

[0063] Table 2 Proportion and ascent rate of Microcystis colonies of different sizes in environmental gradient 2 JPEG2025178168000036.jpg77170

[0064] Table 3 Proportion and ascent rate of Microcystis colonies of different sizes across environmental gradient 3 JPEG2025178168000037.jpg65170

[0065] From this, it can be seen that the concentration distribution of Microcystis colonies differs under different environmental gradient conditions. Specifically, as shown in Figures 3 to 6, the spatial concentration distribution of Microcystis colonies under different environmental gradient conditions and at different times (τ = 0.1, 0.5, 1.0, 5.0) is shown. Figure 3 shows the change in Ω with ξ and ζ, and Pe x = 1.0, τ = 0.1. In Figure 3, (a) is the environmental gradient 1 in Table 1, (b) is the environmental gradient 2 in Table 2, and (c) is the environmental gradient 3 in Table 3. Figure 4 shows the change of Ω with ξ and ζ, and Pe x = 1.0, τ = 0.5. In Figure 4, (a) is the environmental gradient 1 in Table 1, (b) is the environmental gradient 2 in Table 2, and (c) is the environmental gradient 3 in Table 3. Figure 5 shows the change of Ω with ξ and ζ, and Pe x= 1.0, τ = 1.0. In Figure 5, (a) is the environmental gradient 1 in Table 1, (b) is the environmental gradient 2 in Table 2, and (c) is the environmental gradient 3 in Table 3. Figure 6 shows the change of Ω with ξ and ζ, and Pe x = 1.0, τ = 5.0, and in Figure 6, (a) is environmental gradient 1 in Table 1, (b) is environmental gradient 2 in Table 2, and (c) is environmental gradient 3 in Table 3.

[0066] 7 is a schematic diagram of the structure of a theoretical analysis device for simulating the transition distribution of multi-sized Microcystis colonies provided in an embodiment of the present disclosure, which can be realized by software and / or hardware and generally can be integrated into electronic devices. As shown in FIG. 7, the device: A grouping and acquisition module 701 for dividing all the microcystis colonies into a plurality of groups of microcystis colonies according to their size and acquiring the percentage of the number of the microcystis colonies in each group relative to the total number of all the microcystis colonies; a construction and simplification module 702 for constructing an initial concentration control equation for each group of Microcystis colonies, and performing a simplification process on the initial concentration control equation based on a two-dimensional wind flow velocity pattern to obtain a target concentration control equation for each group of Microcystis colonies; A determination and acquisition module 703 for determining the initial concentration condition of the Microcystis colony of each group based on the quantity percentage of the Microcystis colony of each group and the total quantity, and obtaining the concentration boundary condition of the Microcystis colony of each group; a conversion module 704 for converting the target concentration control equation, the initial concentration condition, and the boundary concentration condition based on the introduction of dimensionless parameters to obtain a dimensionless concentration control equation, the initial concentration condition, and the boundary concentration condition for each group of Microcystis colonies; a processing module 705 for processing the non-dimensional concentration control equations of the Microcystis colonies of each group based on the target quantity order concentration moment analysis formula, the target quantity center concentration moment analysis formula, the preset concentration distribution additional conditions, the non-dimensional concentration initial conditions, and the non-dimensional concentration boundary conditions of the Microcystis colonies of each group to obtain the target quantity order concentration moment and the target quantity center concentration moment of the Microcystis colonies of each group; and a calculation module 706 for calculating based on the target number class concentration moment and the target number center concentration moment of the Microcystis colony of each group to obtain an analytical formula for the spatial concentration distribution of all the Microcystis colonies.

[0067] The theoretical analysis device for simulating the transition distribution of multi-sized Microcystis colonies provided in the embodiments of the present disclosure can execute the theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies provided in any embodiment of the present disclosure, has corresponding functional modules for executing the method, and has beneficial effects associated with the method.

[0068] An embodiment of the present disclosure provides a computer program product including a computer program / instruction that, when executed by a processor, performs the theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies provided in any embodiment of the present disclosure.

[0069] According to one or more embodiments of the present disclosure, the present disclosure provides an electronic device, a processor; a memory for storing instructions executable by the processor; The processor is used to read the executable instructions from the memory and execute the instructions to implement the theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies described in any one of the claims provided in the present disclosure.

[0070] According to one or more embodiments of the present disclosure, the present disclosure provides a computer-readable storage medium having stored thereon a computer program for executing a theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies described in any one of the claims provided herein.

[0071] The above description merely describes preferred embodiments and applied technical principles of the present disclosure. Those skilled in the art will understand that the scope of the present disclosure is not limited to the technical solution formed by a specific combination of the above technical features, but should include other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosed concept, such as, for example, a technical solution formed by replacing the above features with technical features having similar functions disclosed in the present disclosure (but not limited to these).

[0072] Also, although operations are depicted in a particular order, it should not be understood that these operations must be performed in the particular order or sequence shown. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although the above description includes several specific implementation details, these should not be construed as limiting the scope of the present disclosure. Some features that are described in the context of separate embodiments may also be implemented in a single embodiment in a combined manner. Conversely, various features that are described in the context of a single embodiment may be implemented in multiple embodiments individually or in any suitable subcombination.

[0073] Although the present subject matter has been described using language specific to structural features and / or methodological acts, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are merely example forms of implementing the claims.

Claims

1. Dividing all the Microcystis colonies into a plurality of groups of Microcystis colonies according to size, and obtaining the percentage of the number of Microcystis colonies in each group relative to the total number of all the Microcystis colonies; constructing an initial concentration control equation for each group of Microcystis colonies, and performing a simplification process on the initial concentration control equation based on a two-dimensional wind flow velocity pattern to obtain a target concentration control equation for each group of Microcystis colonies; Determining the initial concentration condition of the Microcystis colony of each group based on the quantity percentage and the total quantity of the Microcystis colony of each group, and obtaining the concentration boundary condition of the Microcystis colony of each group; Transforming the target concentration control equation, the initial concentration condition, and the boundary concentration condition based on the introduction of dimensionless parameters to obtain a dimensionless concentration control equation, initial concentration condition, and boundary concentration condition for each group of Microcystis colonies; A step of processing the non-dimensional concentration control equation of each group of Microcystis colonies based on the target quantity order concentration moment analysis formula, the target quantity center concentration moment analysis formula, the preset concentration distribution additional condition, the non-dimensional concentration initial condition, and the non-dimensional concentration boundary condition to obtain the target quantity order concentration moment and the target quantity center concentration moment of each group of Microcystis colonies; and calculating the spatial concentration distribution analysis formula of all Microcystis colonies based on the target quantity class concentration moment and the target quantity center concentration moment of the Microcystis colonies of each group, A theoretical analysis method for simulating the succession distribution of multi-sized Microcystis colonies, characterized by:

2. The following initial concentration control equation for each group of Microcystis colonies was constructed: Here, C ｉ is the concentration of the i-th group of Microcystis colonies, where i is a positive integer, t is time, μ is the vector flow velocity, and μ b i is the vector transition rate of the i-th group of Microcystis colonies, λ is the diffusion coefficient of the water flow, and ∇ is the gradient operator. The initial concentration control equation is simplified based on the two-dimensional wind velocity pattern to obtain the target concentration control equation for each group of Microcystis colonies as follows: where μ is the longitudinal velocity and w b i is the succession rate of the i-th group of Microcystis colonies themselves, and λ b ixx is the diffusion coefficient of the i-th group of Microcystis colonies along the x direction, and λ b izz is the diffusion coefficient along the z direction of the i-th group of Microcystis colonies, A theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies according to claim 1.

3. An initial time is set, and the microcystis colony patches are concentrated at x = 0 and z = 0. Based on the percentage and total quantity of the microcystis colonies in each group, the initial concentration conditions of the microcystis colonies in each group are determined as follows: Here, N ｉ is the percentage of the number of Microcystis colonies in the i-th group, Q is the total number of Microcystis colonies, and δ is the Dirac function. At x = ±∞, z = 0, z = H (H is the water depth), the concentration boundary conditions for the Microcystis colonies of each group are as follows: Used to represent zero flux of Microcystis colonies at the free surface and bottom, A theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies according to claim 1.

4. The dimensionless parameters to be introduced are: and Based on the introduction of dimensionless parameters, the target concentration control equation, the concentration initial condition and the concentration boundary condition are transformed to obtain the dimensionless concentration control equation, the dimensionless concentration initial condition and the dimensionless concentration boundary condition of each group of Microcystis colony, which are respectively as follows: reflecting the relative strength of vertical succession and total vertical spread of the i-th group of Microcystis colonies. A theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies according to claim 1.

5. The target quantity concentration moment analysis formula for each group of Microcystis colonies is: and The target quantity center concentration moment analysis formula for each group of Microcystis colonies is: and where: That is, A theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies according to claim 1.

6. The preset concentration distribution addition conditions are: and Processing a dimensionless concentration control equation for each group of Microcystis colonies based on the target number order concentration moment analysis formula for each group of Microcystis colonies, the preset concentration distribution additional condition, the dimensionless concentration initial condition, and the dimensionless concentration boundary condition; If p=0, If p>0, The theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies according to claim 5.

7. The step of calculating the spatial concentration distribution analysis formula of all Microcystis colonies based on the target quantity class concentration moment and the target quantity center concentration moment of each group of Microcystis colonies is as follows: According to the target number order concentration moment of each group of Microcystis colonies, Chatwin asymptotic expansion formula is applied to obtain the following spatial concentration distribution analytical formula for all Microcystis colonies: Here, the polynomial coefficient a ｎ Determine The theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies according to claim 6.

8. A grouping and acquisition module for dividing all Microcystis colonies into a plurality of groups of Microcystis colonies according to size and acquiring the percentage of the number of Microcystis colonies in each group relative to the total number of all Microcystis colonies; a construction and simplification module for constructing an initial concentration control equation for each group of Microcystis colonies, and performing a simplification process on the initial concentration control equation based on a two-dimensional wind flow velocity pattern to obtain a target concentration control equation for each group of Microcystis colonies; A determination and acquisition module for determining the initial concentration condition of the Microcystis colony of each group based on the quantity percentage and the total quantity of the Microcystis colony of each group, and obtaining the concentration boundary condition of the Microcystis colony of each group; a conversion module for converting the target concentration control equation, the initial concentration condition, and the boundary concentration condition based on the introduction of a dimensionless parameter to obtain a dimensionless concentration control equation, an initial concentration condition, and a boundary concentration condition for each group of Microcystis colonies; a processing module for processing the non-dimensional concentration control equations of the Microcystis colonies of each group based on the target quantity order concentration moment analysis formula, the target quantity center concentration moment analysis formula, the preset concentration distribution additional conditions, the non-dimensional concentration initial conditions, and the non-dimensional concentration boundary conditions of the Microcystis colonies of each group to obtain the target quantity order concentration moment and the target quantity center concentration moment of the Microcystis colonies of each group; A calculation module for calculating based on the target quantity class concentration moment and the target quantity center concentration moment of the Microcystis colony of each group to obtain a spatial concentration distribution analysis formula for all Microcystis colonies; A theoretical analysis device for simulating the transition distribution of multi-sized Microcystis colonies, characterized by:

9. a processor; a memory for storing instructions executable by the processor; The processor is adapted to read the executable instructions from the memory and execute the instructions to implement the theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies according to any one of claims 1 to 7. An electronic device characterized by:

10. A computer-readable storage medium storing a computer program for executing a theoretical analysis method for simulating the transition distribution of multi-sized Microcystis colonies described in any one of claims 1 to 7.

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