A prediction method based on the dynamic process of offshore coral reef ecosystem

Abstract

The present invention relates to the technical field of offshore coral reef ecosystems, and in particular to a prediction method based on the dynamic process of offshore coral reef ecosystems. Compared with traditional monitoring methods, the method based on a mathematical model of the present invention improves the computational cost of solving the mathematical model, has higher spatiotemporal resolution and prediction ability for coral reef ecosystems, can quickly identify ecological phase shifts and intervene, and is helpful to prevent the degradation of coral reef ecosystems.

Description

Technical Field

[0001] The invention relates to the technical field of offshore coral reef ecosystems, and in particular to a prediction method based on the dynamic process of offshore coral reef ecosystems. Background Art

[0002] Coral reefs are one of the most valuable marine ecosystems in the world because of their unique biodiversity and ecology. In recent years, due to threats such as global climate change, ocean acidification, marine pollution, overfishing and coastal development, coral reefs are facing a serious crisis and their size is rapidly decreasing worldwide.

[0003] Rapid identification and intervention of ecological phase shifts are favorable measures to prevent the degradation of coral reef ecosystems. Coral reef ecosystems are widely affected by temporal and spatial effects (Dizon and Yap, 2006). Traditional monitoring methods usually rely on field surveys and sampling, which are limited by factors such as sea area coverage, survey frequency and sampling accuracy, resulting in data limitations and uncertainties; traditional monitoring methods often require a lot of time, manpower and financial investment, and it is difficult to cover a large area of ​​sea, resulting in high costs and low efficiency; traditional monitoring methods mainly reflect the current status and it is difficult to accurately predict the future trend of coral reef ecosystem changes, especially in the face of complex environmental factors such as climate change.

[0004] Ecosystem models provide potentially powerful tools for coral reef ecosystem managers, simplifying ecosystem structure and processes, and are particularly suitable for operations that are difficult to test in the field. They also help understand the degradation and development mechanisms of coral reefs from the perspective of ecosystem integrity. Coral reef ecosystems have complex dynamic processes, including coral growth, algal competition, fish grazing, etc., so it is necessary to develop models that can accurately reflect these processes. The development of ecosystem models is limited by the limitations of mathematical modeling and programming skills, and requires professionals with interdisciplinary backgrounds to develop and optimize them. Coral reef ecosystems are affected by a variety of external environmental factors, such as climate change, marine pollution, etc., so ecosystem models need to have a certain degree of adaptability and predictability to cope with changes under different scenarios.

[0005] Therefore, establishing a scientific and complete coral reef ecosystem evolution model and developing a numerical solver that is widely applicable and user-friendly will help to understand the degradation mechanism of coral reef ecosystems and predict the development process of coral reef communities, which is particularly important for the dynamic regulation of coral reef ecosystems in the context of global change.

[0006] At present, many researchers have discussed the equilibrium point and stability of Mumby's model. Some scholars have also improved the model by adding other community influencing factors in the coral reef ecosystem or adding time lag terms on the basis of the original model, and discussed the equilibrium point, local asymptotic stability conditions, boundedness, etc. of the improved model. However, the environmental influencing factors of the coral ecosystem have not been used to improve the model, nor have the existing coral reef ecosystem models been used to predict and solve the future development of the coral reef ecosystem and build a convenient user-friendly interface numerical solver. Therefore, while optimizing the coral reef evolution model, it is urgent to solve the solution prediction and problems of the model to improve the usability of the coral reef evolution model, so that more researchers and even people without professional backgrounds can use it directly, so that potential problems and risks of coral reefs can be discovered and solved in a timely manner, and appropriate intervention measures can be taken to protect and manage the coral reef ecosystem. Summary of the invention

[0007] The purpose of the invention is to propose a prediction method based on the dynamic process of offshore coral reef ecosystem to solve the problem of solving the coral reef ecosystem evolution model and the limitation of programming skills, and to provide a convenient, visual and user-friendly numerical solver to improve the usability of two-dimensional to four-dimensional and sea surface temperature response models and predict the future dynamic evolution of coral reefs.

[0008] In order to solve the problems existing in the prior art, the present invention adopts the following technical solutions:

[0009] A simulation prediction method based on the dynamic process of offshore coral reef ecosystem includes the following steps:

[0010] S1. Obtain data related to seawater temperature and coral reef growth rate in the area to be tested;

[0011] S2. constructing an SST response model based on a two-dimensional to four-dimensional coral reef ecosystem model and data related to seawater temperature and coral reef growth rate in the test area;

[0012] S3, performing numerical solution based on the SST response model to obtain a solution result;

[0013] S4. Obtain measured data of two-dimensional to four-dimensional coral reef ecosystems and obtain the initial parameters of each coral reef system model to predict the future dynamic evolution of coral reefs.

[0014] As an improvement of the technical solution of the simulation prediction method based on the dynamic process of the offshore coral reef ecosystem of the present invention, the following steps are also included:

[0015] In S5, disturbance data is obtained, and a disturbance model is obtained using the SST response model and the disturbance data;

[0016] S6. Based on the SST response model, the disturbance model is used in combination to observe the coral recovery time and the re-stabilization time.

[0017] As an improvement of the technical solution of the simulation prediction method based on the dynamic process of the offshore coral reef ecosystem of the present invention, the disturbance data includes the disturbance starting time step, the disturbance duration step, the coral decline target, accuracy, and the recovery and re-stabilization time results.

[0018] As an improvement of the technical solution of the simulation prediction method based on the dynamic process of the offshore coral reef ecosystem of the present invention, the SST response model is as follows:

[0019]

[0020] Among them, L max is the maximum growth rate, α is the parameter of the growth rate sensitivity to temperature, T is the ambient temperature, T opt is the optimum temperature, where α ranges from 0 to 1, and the larger it is, the narrower the temperature range for coral growth.

[0021] As an improvement of the technical solution of the simulation prediction method based on the dynamic process of offshore coral reef ecosystem of the present invention, the SST response model includes a sea surface temperature-coral growth rate model and a time variation data model;

[0022] The sea surface temperature-coral growth rate model is expressed by the following formula:

[0023]

[0024] L is the growth rate, L max is the maximum growth rate, α is the parameter of the growth rate sensitivity to temperature, T is the ambient temperature, T opt is the optimum temperature, where α ranges from 0 to 1, and the larger it is, the narrower the temperature range for coral growth;

[0025] The time-varying data model is represented by the following expression:

[0026] SST=a sin(bt+c)+d cos(et+f)+gt^h (3)

[0027] Where SST is sea temperature, t is time, and ah is the fitting parameter;

[0028] The SST response model is obtained by combining the sea surface temperature-coral growth rate model and the time variation data model.

[0029] As an improvement of the technical solution of the simulation prediction method based on the dynamic process of the offshore coral reef ecosystem of the present invention, in S3, the coral reef ecosystem model is numerically solved by using an explicit solution method and an implicit solution method respectively.

[0030] As an improvement of the technical solution of the simulation prediction method based on the dynamic process of the offshore coral reef ecosystem of the present invention, the explicit solution method is the fourth-order Runge-Kutta method, and the implicit solution method is the implicit solution Newmark method.

[0031] As an improvement of the technical solution of the simulation and prediction method based on the dynamic process of the offshore coral reef ecosystem of the present invention, the simulation and prediction method based on the dynamic process of the offshore coral reef ecosystem uses a user operation interface of the coral reef ecosystem model constructed by MATLAB App Designer, and the user operation interface can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model.

[0032] Beneficial effects of the present invention:

[0033] 1. The present invention provides a more accurate and comprehensive model, taking into account more ecological factors, such as parrotfish, sea urchins, herbivorous fish, etc., as well as the impact of external environmental factors such as sea surface temperature on coral growth;

[0034] 2. The present invention adopts an efficient and accurate numerical solution method to ensure the reliable solution of the model and provide reliable data support for further research;

[0035] 3. In the present invention, the application of the model is made more convenient and intuitive, not only for professional researchers but also for ordinary users, so as to timely discover and solve the problems and risks of coral reef ecosystems;

[0036] 4. Compared with traditional monitoring methods, the model-based method of the present invention improves the computational cost of solving the model, has higher spatiotemporal resolution and prediction capabilities for coral reef ecosystems, can quickly identify ecological phase shifts and intervene, and helps prevent the degradation of coral reef ecosystems.

[0037] 5. In the present invention, the existing two-dimensional to four-dimensional coral reef ecosystem model is used, combined with the data related to the seawater temperature and coral reef growth rate of the measured area, to construct the SST response model, and the fourth-order Runge-Kutta method and Newmark method are used to solve the model, combined with the measured data of the Nansha coral reef ecosystem, to optimize the model and obtain the initial parameters of each coral reef system model. The user interface of the coral reef ecosystem model constructed with MATLAB App Designer can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the process of the present invention;

[0039] Figure 2 It is the software interface diagram of the present invention;

[0040] Figure 3 A software interface diagram of a two-dimensional coral reef ecosystem functional area in the present invention;

[0041] Figure 4 A software interface diagram of an example of running the coral reef ecological model in the present invention;

[0042] Figure 5 is the vector field diagram in the present invention;

[0043] Figure 6 This is a software interface diagram of the forced disturbance model function area in the present invention;

[0044] Figure 7 A software interface diagram of the functional areas of the three-dimensional coral reef ecosystem in the present invention;

[0045] Figure 8 A software interface diagram of the functional areas of the three-dimensional coral reef ecosystem in the present invention;

[0046] Fig. 9 It is a software interface diagram of the functional area of ​​the four-dimensional coral reef ecosystem in the present invention;

[0047] Fig.10 This is a software interface diagram for simulating prediction results in the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical scheme and beneficial effects of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0049] like Figure 1 As shown, a simulation prediction method based on the dynamic process of offshore coral reef ecosystem includes the following steps:

[0050] S1. Obtain data related to seawater temperature and coral reef growth rate in the area to be tested;

[0051] S2. Construct an SST response model based on two-dimensional to four-dimensional coral reef ecosystem models and data related to seawater temperature and coral reef growth rate in the test area;

[0052] S3, perform numerical solution based on the SST response model to obtain the solution result;

[0053] S4. Obtain measured data of coral reef ecosystems and obtain the initial parameters of each coral reef system model to predict the future dynamic evolution of coral reefs.

[0054] In the present invention, the existing mathematical model of coral reef ecosystem from two dimensions to four dimensions is used, and the data related to seawater temperature and coral reef growth rate in the measured area are obtained to construct the SST response model, and the model is solved by the fourth-order Runge-Kutta method and the Newmark method, and the model is optimized by combining the measured data of the Nansha coral reef ecosystem to obtain the initial parameters of each coral reef system model. The user interface of the coral reef ecosystem model constructed with MATLAB App Designer can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model.

[0055] In detail, the two-dimensional to four-dimensional coral reef ecosystem model in the present invention adopts Mumby

[0056] The mathematical model of the coral reef ecosystem simplifies the coral reef ecosystem into corals, macroalgae and fungi and algae, and proposes the following assumptions:

[0057] 1) Macroalgae will grow and cover macroalgae eaten by fish and naturally dead corals; 2) The growth of corals is restricted by fungi and algae; 3) Macroalgae will cover corals; 4) Macroalgae will occupy the ecological niche of dead corals by asexual reproduction on algae beds. The evolution of the above ecosystem can be represented by the following nonlinear ordinary differential equation:

[0058]

[0059] Among them, a represents the coverage rate of large algae on corals; g represents the biting rate of large algae by parrotfish; b is the asexual reproduction rate of large algae on the algae bed; r represents the growth rate of corals on the algae bed; and d represents the natural mortality rate of corals.

[0060] Since the system is covered by corals (C), macroalgae (M) and algae beds (T), a specific area is covered, so T+M+C is always a constant (set to 1), then T = 1-MC, and the equation can be simplified to:

[0061]

[0062] Furthermore, based on the Mumby model, the following improvements were made by considering the predation of parrotfish: 1) The Logistic growth function was used to express the change of parrotfish population density; 2) The grazing intensity changed with the change of parrotfish population density, and g(P) = P was used to replace the original parrotfish biting rate g on large algae, which clarified the impact of parrotfish population density changes on grazing intensity; 3) K(C) was used to indicate that the environmental carrying capacity was affected by the number of corals. The model is as follows:

[0063]

[0064] Where s represents the growth rate of parrotfish, f represents the human fishing rate of parrotfish, and K(C) is a dimensionless term to consider two effects of coral number on parrotfish: 1) Assuming K(C) = C, it means that external interference has destroyed the structure of coral reefs, parrotfish lack sufficient shelter, and habitat has become the main factor limiting the growth of parrotfish population density; 2) Assuming K(C) = 1-zC, it means that external interference has only reduced the number of corals and has not destroyed the structure of coral reefs. Food has become the main factor limiting the growth of parrotfish populations, and z is the linear relationship between coral coverage area and carrying capacity.

[0065] Furthermore, based on the above model, the functional function is used to describe the biomass transfer between different trophic levels, and the model is developed as follows:

[0066]

[0067] Among them, γ is the asexual reproduction rate of large algae on the algae bed, b1 is the predation rate of parrotfish on large algae, b2 is the predation rate of parrotfish on small algae, e1 is the conversion rate of parrotfish preying on large algae, e2 is the conversion rate of parrotfish preying on small algae, and f is the loss rate of parrotfish. This model only considers the situation where the coral reef structure is not destroyed, so the maximum environmental carrying capacity of parrotfish is not affected by other factors, and K(C)=1.

[0068] Coral reef ecosystems improve the resilience of corals by introducing natural herbivores to prey on algae. Sea urchins prey on large algae, which is beneficial to the growth of corals. Zhang Miaoling (2021) established a model based on the dynamic relationship between corals, seaweed, sea urchins, and herbivorous fish to study the stability of the system's equilibrium point.

[0069] The 3D models of corals, seaweed and sea urchins are as follows:

[0070]

[0071] The four-dimensional models of corals, seaweed, sea urchins and herbivorous fish are as follows:

[0072]

[0073] β represents the growth rate of seaweed; α represents the growth rate of coral in the presence of seaweed; g represents the predation rate of sea urchins on seaweed; d1 represents the natural mortality rate of seaweed; r represents the growth rate of coral on algae lawns; d2 represents the natural mortality rate of corals; ε represents the energy conversion rate; d3 represents the natural mortality rate of sea urchins; d4 represents the natural mortality rate of fish; θ represents the fishing coefficient; δ1 represents the biting rate of herbivorous fish on seaweed; δ2 represents the biting rate of herbivorous fish on corals; η1 and η2 represent the energy conversion rate.

[0074] Moreover, corals have extremely high requirements for their growth environment, and extreme environments can have a negative impact on their growth. Currently, the rise in SST associated with increased anthropogenic greenhouse gas emissions has been identified as the main threat to the persistence of coral reefs. SST affects the physiological processes of corals, the efficiency of photosynthesis, and the relationship between corals and symbiotic algae. There is an optimal temperature range for coral growth, and both low and high temperatures will significantly inhibit it.

[0075] Based on this, a sea surface temperature-coral growth rate model is constructed, considering that there is an optimum temperature for coral growth, and the growth rate corresponding to the optimum growth temperature is the maximum value; as the sea surface temperature deviates from the optimum temperature, the growth rate will decrease, and exponential decay is used to describe the decrease in growth rate as the temperature deviates from the optimum temperature; a parameter of growth rate sensitivity to temperature is added to control the coral growth temperature range, and a larger α value means that the growth rate is more sensitive to temperature changes:

[0076]

[0077] L is the growth rate, L max is the maximum growth rate, α is the parameter of the growth rate sensitivity to temperature, T is the ambient temperature, T opt is the optimum temperature, where α ranges from 0 to 1, and the larger it is, the narrower the temperature range for coral growth.

[0078] In order to reflect the change of SST over time, the average SST data of the past years and the SST data of the Nansha Islands in the SSP245 scenario from 2015 to 2100 in the CMIP6 climate model are used. The SST unit is ℃ and the spatial resolution is 1°×1°. The SST change data over time are fitted. Considering the fluctuation and rising characteristics of the data, a fitting equation is constructed that uses trend terms to describe the overall change of the data and adds periodic terms to describe the fluctuation:

[0079] SST=a sin(bt+c)+d cos(et+f)+gt^h (8)

[0080] Where SST is sea temperature, t is time, and ah is the fitting parameter.

[0081] The updated coral reef ecosystem model incorporating the effects of SST on coral growth rates is as follows:

[0082]

[0083] Then, two different solution methods, explicit and implicit, are used to numerically solve the coral reef ecosystem model. As a specific embodiment of the present invention, the explicit solution method uses the fourth-order Runge-Kutta method, which is a commonly used numerical integration method for solving ordinary differential equations. It is one of the most commonly used integration methods in numerical analysis because it strikes a good balance between accuracy and computational efficiency. It estimates the solution by gradually approximating the value of the function at a series of discrete time points. The following is the basic principle of the fourth-order Runge-Kutta method:

[0084] y′(t n )=f(t n ,y n )

[0085] y(t0)=f(t0,y0)

[0086] t0 is the initial time, y0 is the initial state, f(t n ,y n ) is a function of time and state.

[0087] The fourth-order Runge-Kutta solution algorithm is:

[0088]

[0089] The key to the fourth-order Runge-Kutta method is to use multiple estimated slopes to calculate the solution for the next time step, thereby improving the accuracy of the numerical solution. Based on the known initial conditions and the derivative function of the differential equation, multiple intermediate steps are used to estimate the value of the unknown function at different time steps, thereby constructing a numerical solution over the entire time range. Four intermediate quantities are calculated first, and finally the weighted average is used to calculate the value for the next time step.

[0090] The implicit solution Newmark method is a numerical integration method for solving dynamic problems. The motion of a dynamic system can be described by a differential equation of the following form (Li Hongjing et al., 2011):

[0091]

[0092] Where M is the mass matrix, ü represents the acceleration, C is the damping matrix, represents velocity, K is the stiffness matrix, u represents displacement, and F(t) represents external load or force.

[0093] First, the time continuous domain is discretized into a time step of Δt, and the state of the system is solved at each time step. Under the premise of knowing the value of the previous moment, the value of the next moment is obtained:

[0094]

[0095] γ and β are control parameters. As a specific embodiment of the present invention, γ = 0.5, or Since different values ​​will affect the numerical stability and accuracy of the algorithm. Finally, update the external load or force F according to the physical characteristics of the system and the requirements of the problem. n+1 The model of the present invention is a simple first-order nonlinear ordinary differential equation system, all corresponding velocities and accelerations are 0, and only the displacement needs to be updated.

[0096] In some embodiments of the present invention, the following steps are also included:

[0097] In S5, disturbance data is obtained, and a disturbance model is obtained using the SST response model and the disturbance data. In S6, based on the SST response model and in combination with the disturbance model, the coral recovery time and the re-stabilization time are observed.

[0098] Furthermore, the disturbance data includes the disturbance start time step, disturbance duration step, coral decline target, accuracy, and recovery and re-stabilization time results.

[0099] In some embodiments of the invention, the SST response model is as follows:

[0100]

[0101] Among them, L max is the maximum growth rate, α is the parameter of the growth rate sensitivity to temperature, T is the ambient temperature, T opt is the optimum temperature, where α ranges from 0 to 1, and the larger it is, the narrower the temperature range for coral growth.

[0102] Furthermore, the SST response model includes a sea surface temperature-coral growth rate model and a temporal variation data model;

[0103] The sea surface temperature-coral growth rate model is expressed by the following formula:

[0104]

[0105] L is the growth rate, L max is the maximum growth rate, α is the parameter of the growth rate sensitivity to temperature, T is the ambient temperature, T opt is the optimum temperature, where α ranges from 0 to 1, and the larger it is, the narrower the temperature range for coral growth;

[0106] The time-varying data model is represented by the following notation:

[0107] SST=a sin(bt+c)+d cos(et+f)+gt^h (3)

[0108] Where SST is sea temperature, t is time, and ah is the fitting parameter;

[0109] The SST response model was obtained by combining the sea surface temperature-coral growth rate model with the temporal variation data model.

[0110] In some embodiments of the present invention, an explicit solution method and an implicit solution method are respectively used to numerically solve the coral reef ecosystem model.

[0111] As a specific embodiment of the present invention, the explicit solution method is the fourth-order Runge-Kutta method, and the implicit solution method is the implicit solution Newmark method.

[0112] In some embodiments of the present invention, a user interface of a coral reef ecosystem model is constructed using MATLAB App Designer based on a simulation and prediction method for dynamic processes of offshore coral reef ecosystems. The user interface can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model.

[0113] When the present invention is used, the Mumby three-dimensional numerical model is used as the original model, combined with the optimized model of other subsequent researchers as the basis, the model is solved by using the fourth-order Runge-Kutta method and the Newmark method, and the model is optimized in combination with the measured data of the Nansha coral reef ecosystem to obtain the initial parameters of each coral reef system model. The user operation interface of the coral reef ecosystem model constructed with MATLAB AppDesigner can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model.

[0114] The user operation interface of the coral reef ecosystem model of the present invention includes at least five modules: 1. Measured data mapping, which can be used to draw measured data maps for comparison with prediction maps and observe the changes of corals and macroalgae in the coral reef ecosystem in the past; 2. Two-dimensional coral reef ecosystem model, which mainly predicts based on input parameters, waits for the final coverage of corals and macroalgae, and verifies the stability of the system and the final point, and a forced disturbance model, which performs a forced disturbance on the coral reef ecosystem to observe the recovery and stability after the disturbance; 3. Three-dimensional coral reef ecosystem model: dynamic prediction model and disturbance model of coral, macroalgae and parrotfish, coral, macroalgae and sea urchin; 4. Dynamic prediction model and disturbance model of coral, macroalgae, sea urchin and herbivorous fish; 5. Sea surface temperature response model.

[0115] It should be noted that, by inputting parameters in the corresponding operation interface, corresponding data are obtained through the user operation interface of the coral reef ecosystem model constructed by MATLAB AppDesigner.

[0116] Example 1

[0117] like Figure 4 As shown, the original model is a two-dimensional coral reef ecological model, which mainly obtains the change of coral and macroalgae coverage in the coral reef ecosystem over time based on the Mumby model, and the final numerical solution and verification system and final stability;

[0118] In this embodiment, if Figure 4 As shown, an SST response model is constructed based on a two-dimensional coral reef ecological model, and then a numerical solution is performed based on the SST response model to obtain the solution results. Then, the initial parameters of each coral reef system model are obtained through the measured data of two-dimensional to four-dimensional coral reef ecosystems to predict the future dynamic evolution of coral reefs.

[0119] In detail, in an embodiment of the present invention, by inputting parameters, the effect of obtaining data related to the seawater temperature and coral reef growth rate of the measured area is achieved, and the data includes coral growth rate, natural mortality rate of coral, coverage rate of large algae on coral, grazing rate of parrotfish on large algae, asexual reproduction rate of large algae on algae beds and initial coral and large algae coverage, and the start and end times of the parameter settings are preset.

[0120] As a preferred data of this embodiment, the time step (default is 0.01) and the error tolerance (default is 0.001) are set, and finally the update frequency of the real-time drawing is set (default is 600 time steps).

[0121] Then, a numerical solution is performed based on the SST response model, and the coral reef ecosystem of this embodiment is solved by explicit solution method and implicit solution method respectively to obtain the initial parameters of the coral reef ecosystem in order to predict the dynamic evolution of coral reefs in the future.

[0122] Among them, due to the user interface of the coral reef ecosystem model built in MATLAB App Designer, the user interface can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model. After entering the relevant data in the user interface of the coral reef ecosystem model built by MATLAB App Designer and performing explicit solution and implicit solution respectively, the corresponding coral and large algae change over time graph, that is, the value corresponding to the final time point, will be displayed in the user interface, and after the implicit operation is completed, the time required for the system to stabilize will also be displayed. Clicking the verification button will obtain the eigenvalues ​​corresponding to the system Jacobian matrix and the stable state of the final point (such as Figure 5 shown).

[0123] In addition, since in the nonlinear ordinary differential equations, the vector field diagram is a graphical representation method used to visualize the behavior of the solution of the system in the phase space. Phase space is a multidimensional space in which each dimension corresponds to a variable in the system of equations, and the vector at each point represents the derivative or rate of change at that point. The vector field diagram represents these vectors in the form of arrows, thereby depicting the direction of evolution of the system at different points. By clicking the vector field diagram button in the user interface of the coral reef ecosystem model built by MATLAB App Designer, the vector field diagram of this system will be obtained (such as Figure 6 shown).

[0124] Furthermore, by obtaining disturbance data, the disturbance model is obtained using the SST response model and the disturbance data; based on the SST response model, the disturbance model is combined to observe the coral recovery time and the time for re-stabilization.

[0125] Among them, the disturbance data include the disturbance start time step, disturbance duration step, coral decline target, accuracy, and recovery and re-stabilization time results.

[0126] In detail, the perturbation model generally runs on the basis of implicit Newmark. Under the action of the perturbation model, the SST response model constructed in this embodiment can forcibly perturb the coral coverage at a specific time to observe the coral recovery time and re-stabilization time, the change in the coverage of coral fish and large algae after the disturbance, etc. The system obtains the perturbation data through the input of parameters, which mainly includes the perturbation start time step, perturbation duration step, coral decline target, accuracy, and recovery and re-stabilization time results. The recovery and re-stabilization time occurs after the perturbation ends. The appearance of NaN may be due to insufficient overall range or the initial accuracy of 1e-5 used in the code may be too harsh, or oscillation occurs.

[0127] Example 2

[0128] like Figure 8 As shown, the original model is a three-dimensional coral reef ecological model, which mainly obtains the change of coral and macroalgae coverage in the coral reef ecosystem over time based on the Mumby model, and the final numerical solution and verification system and final stability;

[0129] In this embodiment, if Figure 8 As shown, an SST response model is constructed based on a two-dimensional coral reef ecological model, and then a numerical solution is performed based on the SST response model to obtain the solution results. Then, the initial parameters of each coral reef system model are obtained through the measured data of the two-dimensional coral reef ecosystem to predict the future dynamic evolution of coral reefs.

[0130] In detail, in an embodiment of the present invention, by inputting parameters, the effect of obtaining data related to the seawater temperature and coral reef growth rate of the measured area is achieved, and the data include coral growth rate, natural mortality rate of coral, coverage of large algae on coral, grazing rate of parrotfish on large algae, asexual reproduction rate of large algae on algae beds, inherent growth rate of parrotfish, mortality rate of parrotfish due to fishing or competition, and linear strength relationship between coral coverage and carrying capacity.

[0131] In addition, the measured data of the three-dimensional coral reef ecosystem can be obtained by inputting the parameters of parrotfish and algae predation. The parameters mainly include the predation rate of parrotfish on large algae, the conversion rate of parrotfish predation on large algae, the predation rate of parrotfish on small algae, the conversion rate of parrotfish predation on small algae, and the start and end time of the parameter settings can be preset.

[0132] Then, a numerical solution is performed based on the SST response model, and the coral reef ecosystem of this embodiment is solved by explicit solution method and implicit solution method respectively to obtain the initial parameters of the coral reef ecosystem in order to predict the dynamic evolution of coral reefs in the future.

[0133] Among them, due to the user interface of the coral reef ecosystem model built in MATLAB App Designer, the user interface can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model. After entering the relevant data in the user interface of the coral reef ecosystem model built by MATLAB App Designer and performing explicit solution and implicit solution respectively, the corresponding coral and large algae change over time graph, that is, the value corresponding to the final time point, will be displayed in the user interface, and after the implicit operation is completed, the time required for the system to stabilize will also be displayed. Clicking the verification button will obtain the eigenvalues ​​corresponding to the system Jacobian matrix and the stable state of the final point (such as Fig. 9 shown).

[0134] Furthermore, by obtaining disturbance data, the disturbance model is obtained using the SST response model and the disturbance data; based on the SST response model, the disturbance model is combined to observe the coral recovery time and the time for re-stabilization.

[0135] Among them, the disturbance data include the disturbance start time step, disturbance duration step, coral decline target, accuracy, and recovery and re-stabilization time results.

[0136] In detail, the perturbation model generally runs on the basis of implicit Newmark. Under the action of the perturbation model, the SST response model constructed in this embodiment can forcibly perturb the coral coverage at a specific time to observe the coral recovery time and re-stabilization time, the change in the coverage of coral fish and large algae after the disturbance, etc. The system obtains the perturbation data through the input of parameters, which mainly includes the perturbation start time step, perturbation duration step, coral decline target, accuracy, and recovery and re-stabilization time results. The recovery and re-stabilization time occurs after the perturbation ends. The appearance of NaN may be due to insufficient overall range or the initial accuracy of 1e-5 used in the code may be too harsh, or oscillation occurs.

[0137] Example 3

[0138] like Fig.10 As shown, the original model is a four-dimensional coral reef ecological model, which mainly obtains the changes in the coverage of corals and macroalgae in the coral reef ecosystem over time based on the Mumby model, and the final numerical solution and verification system and final stability;

[0139] In this embodiment, if Fig.10 As shown, an SST response model is constructed based on a two-dimensional coral reef ecological model, and then a numerical solution is performed based on the SST response model to obtain the solution results. Then, the initial parameters of each coral reef system model are obtained through the measured data of the two-dimensional coral reef ecosystem to predict the future dynamic evolution of coral reefs.

[0140] In detail, in an embodiment of the present invention, by inputting parameters, the effect of obtaining data related to the seawater temperature and the coral reef growth rate of the measured area is achieved, and the data include the growth rate of corals, the natural mortality rate of corals, the coverage rate of large algae on corals, the asexual reproduction rate of large seaweed on algae beds, the nibbling rate of corals by herbivorous fish, the predation rate of large algae by sea urchins, the nibbling rate of seaweed by herbivorous fish, the natural mortality rate of large algae, the energy transfer rate of sea urchins, the capture coefficient of sea urchins, the natural mortality rate of sea urchins, the energy transfer rate of herbivorous fish to seaweed, the energy transfer rate of herbivorous fish to corals, and the natural mortality rate of herbivorous fish.

[0141] In addition, the measured data of the three-dimensional coral reef ecosystem can be obtained by inputting the parameters of parrotfish and algae predation. The parameters mainly include the predation rate of parrotfish on large algae, the conversion rate of parrotfish predation on large algae, the predation rate of parrotfish on small algae, the conversion rate of parrotfish predation on small algae, and the start and end time of the parameter settings can be preset.

[0142] Then, a numerical solution is performed based on the SST response model, and the coral reef ecosystem of this embodiment is solved by explicit solution method and implicit solution method respectively to obtain the initial parameters of the coral reef ecosystem in order to predict the dynamic evolution of coral reefs in the future.

[0143] Among them, due to the user interface of the coral reef ecosystem model built in MATLAB App Designer, the user interface can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model. After entering the relevant data in the user interface of the coral reef ecosystem model built by MATLAB App Designer and performing explicit solution and implicit solution respectively, the corresponding coral and large algae change over time graph, that is, the value corresponding to the final time point, will be displayed in the user interface, and after the implicit operation is completed, the time required for the system to stabilize will also be displayed. Clicking the verification button will obtain the eigenvalues ​​corresponding to the system Jacobian matrix and the stable state of the final point (such as Fig.10 shown).

[0144] Furthermore, by obtaining disturbance data, the disturbance model is obtained using the SST response model and the disturbance data; based on the SST response model, the disturbance model is combined to observe the coral recovery time and the time for re-stabilization.

[0145] Among them, the disturbance data include the disturbance start time step, disturbance duration step, coral decline target, accuracy, and recovery and re-stabilization time results.

[0146] In detail, the perturbation model generally runs on the basis of implicit Newmark. Under the action of the perturbation model, the SST response model constructed in this embodiment can forcibly perturb the coral coverage at a specific time to observe the coral recovery time and re-stabilization time, the change in the coverage of coral fish and large algae after the disturbance, etc. The system obtains the perturbation data through the input of parameters, which mainly includes the perturbation start time step, perturbation duration step, coral decline target, accuracy, and recovery and re-stabilization time results. The recovery and re-stabilization time occurs after the perturbation ends. The appearance of NaN may be due to insufficient overall range or the initial accuracy of 1e-5 used in the code may be too harsh, or oscillation occurs.

[0147] Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without making any creative work shall fall within the scope of protection of the present invention.

Claims

1. A simulation prediction method based on the dynamic process of offshore coral reef ecosystem, characterized in that: The following steps are included: S1. Obtain data related to seawater temperature and coral reef growth rate in the area to be tested; S2. constructing an SST response model based on a two-dimensional to four-dimensional coral reef ecosystem model and data related to seawater temperature and coral reef growth rate in the test area; S3, performing numerical solution based on the SST response model to obtain a solution result; S4. Obtain measured data of two-dimensional to four-dimensional coral reef ecosystems and obtain the initial parameters of each coral reef system model to predict the future dynamic evolution of coral reefs; The SST response model is as follows: Among them, L max is the maximum growth rate, α is the parameter of the growth rate sensitivity to temperature, T is the ambient temperature, T opt is the optimum temperature, where α ranges from 0 to 1, and the larger it is, the narrower the temperature range for coral growth; Where M is the coverage of macroalgae, C is the coverage of corals, g is the biting rate of parrotfish on macroalgae, b is the asexual reproduction rate of macroalgae on the algae bed, t is time, c, e, f, j and h are the fitting parameters of the temperature equation respectively; The SST response model includes a sea surface temperature-coral growth rate model and a time variation data model; The sea surface temperature-coral growth rate model is expressed by the following formula: L is the growth rate, L max is the maximum growth rate, α is the parameter of the growth rate sensitivity to temperature, T is the ambient temperature, T opt is the optimum temperature, where α ranges from 0 to 1, and the larger it is, the narrower the temperature range for coral growth; The time-varying data model is represented by the following expression: SST=asin(bt+c)+dcos(et+f)+gt∧h (3) Where SST is sea temperature, t is time, and ah is the fitting parameter; The SST response model is obtained by combining the sea surface temperature-coral growth rate model and the time variation data model.

2. The simulation prediction method based on the dynamic process of offshore coral reef ecosystem according to claim 1, characterized in that: The following steps are also included: In S5, disturbance data is obtained, and a disturbance model is obtained using the SST response model and the disturbance data; S6. Based on the SST response model, the disturbance model is used in combination to observe the coral recovery time and the re-stabilization time.

3. The simulation prediction method based on the dynamic process of offshore coral reef ecosystem according to claim 2 is characterized in that: The disturbance data includes the disturbance start time step, disturbance duration step, coral decline target, accuracy, and recovery and re-stabilization time results.

4. The simulation prediction method based on the dynamic process of offshore coral reef ecosystem according to claim 1 is characterized in that: In S3, the coral reef ecosystem model is numerically solved using explicit and implicit solution methods.

5. The simulation prediction method based on the dynamic process of offshore coral reef ecosystem according to claim 4 is characterized in that: The explicit solution method is the fourth-order Runge-Kutta method, and the implicit solution method is the implicit solution Newmark method.

6. The simulation prediction method based on the dynamic process of offshore coral reef ecosystem according to claim 1 is characterized in that: The simulation prediction method based on the dynamic process of the offshore coral reef ecosystem is a user operation interface of the coral reef ecosystem model constructed with MATLAB App Designer, and the user operation interface can improve the high-performance numerical calculation and visualization capabilities of the coral reef ecosystem model.

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