Parameter inversion method based on slope solute transport process

Abstract

The invention provides a parameter inversion method based on a slope solute transport process, and the method comprises the steps: employing a one-dimensional Saint-Venant equation and a fractional order convection diffusion equation of pollutant migration, combining an actual slope flow condition, and increasing the constraint of a diffusion coefficient and mass exchange rate coefficient calibration process. The slope nutrient loss degree evaluation method has the advantages that the equation parameters of the migration model are added in parameter inversion to serve as physical constraints, the complexity and heterogeneity of the nutrient transportation process are fully considered, and therefore the fractional order, the diffusion coefficient and the mass exchange rate coefficient are calibrated, and the accuracy of slope nutrient loss degree evaluation is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of environmental protection, and particularly to a parameter inversion method based on the process of solute transport on a slope surface. Background Technique

[0002] Hillslope flow is the most important carrier of nutrient loss in plateau mountainous areas. Hillslope flow caused by intense rainfall will lead to the rapid loss of nutrients in the soil, reduce vegetation density, and cause obvious soil erosion and water body eutrophication. Due to the influence of rainfall, slope and slope length, solute characteristics, underlying surface, soil characteristics and vegetation conditions on the nutrient transport process, including non-uniform distribution, temporal variation, multi-source input and biological interaction, etc., it becomes complex. In the simulation of nitrogen transport process, it is often described by constructing an anomalous transport model.

[0003] Diffusion coefficient and mass exchange rate coefficient are the core parameters describing the diffusion process of nutrients with slope surface flow. Affected by the above influencing factors, they are non-constant parameters. Since the inversion of two parameters is required and they affect each other, the inversion difficulty is high. Existing parameter inversion methods such as least squares fitting often have the problem of multiple solutions in practical applications, and the numerical simulation method of computational fluid dynamics is difficult to solve the uncertainty of parameters and assumptions, resulting in deviation of simulation results. Summary of the Invention

[0004] To solve the current technical problems, the main purpose of the present invention is to provide a parameter inversion method based on the process of solute transport on a slope surface. By using the one-dimensional Saint-Venant equation and the fractional convection-diffusion equation of pollutant migration, combined with the actual slope surface flow conditions, the constraints on the calibration process of the diffusion coefficient and mass exchange rate coefficient are increased.

[0005] To achieve the above technical features, the object of the present invention is realized as follows: A parameter inversion method based on the process of solute transport on a slope surface, comprising the following steps: Step 1, acquisition of solute transport process data: Study the characteristics of the slope area and collect and obtain the solute transport process data of the slope area; Step 2, establishment of a one-dimensional slope surface solute transport model: Based on the process of solute transport on the slope surface, establish a one-dimensional slope surface solute transport model by combining the Saint-Venant equation and the fractional convection-diffusion equation of solute migration; Step 3, establishment of an objective function: Based on the one-dimensional slope surface solute transport model established in Step 2, establish an objective function to be optimized; Step 4, solution of the objective function: Solve the objective function constructed in step 3 using the corresponding algorithm, and finally obtain the diffusion coefficient and mass exchange rate to be determined; Step 5, calculate the nutrient loss of a single slope during rainfall: Use the solute transport process data obtained in step 1, and combine with the diffusion coefficient and mass exchange rate obtained in step 4, input them into the one-dimensional slope solute transport model in step 2, and solve to obtain the nutrient loss of the slope during rainfall; Step 6, calculate and give an early warning of the nutrient loss of the entire slope during rainfall.

[0006] Preferably, step 1 specifically includes: Collect data on rainfall, slope and slope length, solute characteristics, underlying surface, soil characteristics, and vegetation conditions in the study slope area, and collect historical solute transport process data of multiple cross-sections in the slope area or similar areas.

[0007] Preferably, the equations of the one-dimensional slope solute transport model established in step 2 are: -s; (1) ; (2) In the formula: S is the cross-sectional area of the flowing water, determined by the underlying surface and water depth h; Q is the cross-sectional flow rate; q is the flow rate of the inflow per unit length, referring to the rainfall; s is the infiltration flow rate, determined by the soil saturation; C is the concentration of the nutrient solute; C 1 is the initial concentration of the nutrient solute; is the mass exchange rate, limited by the solute characteristics, directly reflecting the retention state of the solute by the soil solute; u is the flow velocity; Q = S×h×u, K is the solute diffusion velocity, describing the movement ability of nutrients N and P in the water body; is the order of the time fractional order, and its value range is [0,1], where , K and are important equation parameters.

[0008] Preferably, the specific establishment process of the objective function in step 3 includes: Step 3.1, establish a neural network for calibrating the two parameters of the solute diffusion velocity and mass exchange rate under the constraint of the slope solute transport process according to the one-dimensional slope solute transport model in step 2. Equations (3), (4), (5), and (6) are used to calibrate the order of the time fractional order , diffusion coefficient K, and mass exchange rate of the neural network, and establish the corresponding objective function to be optimized, as shown in equation (4); -s; (3) ; (4) ; (5) - ; (6) Step 3.2, equation (4) is the residual of the one-dimensional slope solute transport model, is the diffusion coefficient K and is the mass exchange rate The corresponding physics-driven neural network model, the output of the network is an approximation of the true diffusion coefficient, is the true mass exchange rate The approximate value of = , the model parameters that need to be fitted are recorded as , the output of the network = (x,t; )and = (x,t; ) is the approximate value of the actual flow and nutrients, and the model parameters that need to be fitted are recorded as ; Step 3.3, equation (3) is the output of the neural network for the observed cross-section nutrient N or P element concentration Q * and C * The approximation error of Step 3.4, establish the objective function: ; (7)

[0009] Preferably, the specific process in step 4 is: The historical nutrient content flow data collected in step 1 are input into the objective function established in step 3.4, and the objective function is solved by the classic gradient descent method until the optimal neural network parameters are found, so that the output of the neural network satisfies the control equation as much as possible and is as close to the observed data as possible. After the optimization is completed, the optimal , then the diffusion coefficient is and , = , which is the diffusion coefficient K to be determined and the mass exchange rate .

[0010] Preferably, the specific process in step 5 is: The real-time rainfall monitoring and forecast data and solute transport process data of step 1 are used as input conditions, combined with the diffusion coefficient K, fractional order α and mass exchange rate β calibrated in step 4, and input into the one-dimensional slope solute transport model of step 2. The finite difference method is used to solve the change process of nutrient content in the slope area during rainfall. The product of the single-width flow rate and the concentration of the solute of the slope during the entire rainfall time is integrated, and the result is the nutrient loss of the slope during the rainfall period.

[0011] Preferably, the specific process in step 6 is: repeat steps 1 to 5, and the nutrient loss of multiple slopes during the rainfall period can be calculated in real time. The sum is the nutrient input of the collected rivers or lakes during the entire rainfall period, which is compared with the eutrophication warning value of lakes and rivers. If it exceeds the warning value, it will be reported to the relevant departments for their decision-making basis.

[0012] The present invention has the following beneficial effects: The advantage of the method of the present invention is that the equation parameters of the migration model are added as physical constraints in the parameter inversion, and the complexity and heterogeneity of the nutrient transport process are fully considered, so that the fractional order, diffusion coefficient and mass exchange rate coefficient are calibrated, thereby improving the accuracy of the assessment of the degree of nutrient loss on the slope. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0014] Figure 1 It is a specific method flow chart of the present invention.

[0015] Figure 2 It is a schematic diagram of a slope of the present invention. DETAILED DESCRIPTION

[0016] The embodiments of the present invention are further described below in conjunction with the accompanying drawings.

[0017] Embodiment 1: See also Figure 1-2 , a parameter inversion method based on the slope solute transport process, including the following steps: Step 1: Acquisition of solute transport process data: Collect and study rainfall, slope gradient and slope length, solute characteristics, underlying surface, soil characteristics and vegetation conditions in slope areas, and collect historical solute transport process data for multiple sections in slope areas or similar areas.

[0018] Step 2: Establishment of one-dimensional slope solute transport model: Based on the solute transport process on the slope, the Saint-Venant equation and the fractional-order convection-diffusion equation of solute migration are combined to establish a one-dimensional solute transport model on the slope. The equations of the one-dimensional slope solute transport model established in Step 2 are as follows: -s; (1) ; (2) Where: S is the cross-sectional area of the water flow, determined by the underlying surface and the water depth h; Q is the cross-sectional flow rate; q is the flow rate per unit length of the inflow, referring to the rainfall; s is the infiltration flow rate, determined by the soil saturation; C is the concentration of the nutrient solute; C 1 is the initial concentration of the nutrient solute; is the mass exchange rate, limited by the solute characteristics, directly reflecting the retention state of the solute by the soil solute; u is the flow velocity; Q = S×h×u, K is the solute diffusion velocity, describing the movement ability of nutrients N and P in the water body; is the time fractional order, and its value range is [0, 1], where , K and are important equation parameters.

[0019] Step 3, establishment of the objective function: Step 3.1, based on the one-dimensional slope solute transport model in Step 2, establish a neural network for calibrating the two parameters of the solute diffusion velocity and the mass exchange rate under the constraint of the slope solute transport process. Equations (3), (4), (5), and (6) are for calibrating the time fractional order , diffusion coefficient K, mass exchange rate of the neural network, and establish the corresponding objective function to be optimized, as shown in Equation (4); -s; (3) ; (4) ; (5) -[[]] ; (6) Step 3.2, Equation (4) is the residual of the one-dimensional slope solute transport model, and is the neural network model driven by physics corresponding to the diffusion coefficient K and the mass exchange rate . The output of the network is an approximation of the true diffusion coefficient, is an approximation of the true mass exchange rate , =[[]] . The model parameters to be fitted are denoted as . The output =[[]] (x,t; ) and =[[]] (x, t; ) is an approximation of the real flow rate and nutrients. The model parameters to be fitted are denoted as ; Step 3.3: Equation (3) represents the approximation error of the neural network output with respect to the observed cross-sectional nutrient N or P element concentration Q * and C * . Step 3.4: Establish the objective function: ; (7)

[0020] Step 4: Solve the objective function: Input the historical nutrient element content and flow rate data collected in Step 1 into the objective function established in Step 3.4, and use classical gradient descent methods to solve the objective function until the optimal neural network parameters are found, such that the output of the neural network can satisfy the governing equations as much as possible and approximate the observed data as much as possible. After optimization, find the optimal , then the calibrated diffusion coefficient is and , = , which are the diffusion coefficient K to be determined and the mass exchange rate .

[0021] Step 5: Calculate the nutrient loss during rainfall for a single slope: Use the real-time rainfall monitoring and forecasting data and solute transport process data from Step 1 as input conditions, and combine the calibrated diffusion coefficient K, fractional order α, and mass exchange rate β from Step 4 to input into the one-dimensional slope solute transport model in Step 2. Solve using the finite difference method to calculate the change process of nutrient content during rainfall in the slope area in real time. Integrate the product of the unit-width flow rate and solute concentration of the slope over the entire rainfall time, and the result is the nutrient loss during rainfall for this slope.

[0022] Step 6: Calculate the nutrient loss during rainfall for the entire slope and issue a warning.

[0023] Repeat Steps 1 to 5 to calculate the nutrient loss during rainfall for multiple slopes in real time. The sum is the nutrient input to the converging river or lake during the entire rainfall period. Compare it with the eutrophication warning value of the lake or river. If it exceeds, report it to the relevant department for their decision-making basis.

Claims

1. A parameter inversion method based on slope solute transport process, characterized in that: The following steps are involved: Step 1: Acquisition of solute transport process data: Study the characteristics of the slope area and collect data on the solute transport process in the slope area; Step 2: Establishment of one-dimensional slope solute transport model: Based on the solute transport process on the slope, the Saint-Venant equation and the fractional-order convection-diffusion equation of solute migration are combined to establish a one-dimensional solute transport model on the slope. Step 3, establishment of objective function: Based on the one-dimensional slope solute transport model established in step 2, the objective function to be optimized is established; Step 4, solving the objective function: The objective function constructed in step 3 is solved by using the corresponding algorithm, and finally the required diffusion coefficient and mass exchange rate are obtained; Step 5, calculation of nutrient loss from a single slope during rainfall: Using the solute transport process data obtained in step 1, combined with the diffusion coefficient and mass exchange rate obtained in step 4, the data are input into the one-dimensional slope solute transport model in step 2 to solve the loss of nutrients on the slope during rainfall; Step 6: Calculation and early warning of nutrient loss on the entire slope during rainfall.

2. A parameter inversion method based on slope solute transport process according to claim 1, characterized in that: Step 1 specifically includes: Collect and study rainfall, slope and slope length, solute characteristics, underlying surface, soil characteristics and vegetation conditions in slope areas, and collect historical solute transport process data for multiple sections in slope areas or similar areas.

3. A parameter inversion method based on slope solute transport process according to claim 2, characterized in that: The equations of the one-dimensional slope solute transport model established in step 2 are: -s；（1） ；（2） Where: S is the cross-sectional area of ​​the water flow, which is determined by the underlying surface and water depth h; Q is the cross-sectional flow rate; q is the inflow per unit length, which refers to rainfall; s is the infiltration flow, which is determined by the saturation of the soil; C is the concentration of nutrient solutes; C1 is the initial concentration of nutrient solutes; is the mass exchange rate, which is limited by the solute characteristics and directly reflects the retention state of the solute by the soil solute; u is the flow rate; Q = S × h × u, K is the solute diffusion rate, which describes the movement capacity of nutrients N and P in the water body; is the time fractional order, and its value range is [0,1], where , K and are important equation parameters, x is the spatial position, and t is the time.

4. A parameter inversion method based on slope solute transport process according to claim 3, characterized in that: The specific process of establishing the objective function in step 3 includes: Step 3.1, based on the one-dimensional slope solute transport model in step 2, a neural network for dual-parameter calibration of solute diffusion velocity and mass exchange rate under the constraints of slope solute transport process is established. Equations (3), (4), (5), and (6) are the fractional order of the calibration time. , diffusion coefficient K, mass exchange rate The neural network is used to establish the corresponding objective function to be optimized, see equation (4); -s；（3） ；（4） ；（5） - ；（6） Step 3.2, equation (4) is the residual of the one-dimensional slope solute transport model, is the diffusion coefficient K and is the mass exchange rate The corresponding physics-driven neural network model, the output of the network is an approximation of the true diffusion coefficient, is the true mass exchange rate The approximate value of = , the model parameters that need to be fitted are recorded as , the output of the network = (x,t; )and = (x,t; ) is the approximate value of the actual flow and nutrients, and the model parameters that need to be fitted are recorded as ; Step 3.3, equation (3) is the output of the neural network for the observed cross-section nutrient N or P element concentration Q * and C * The approximation error of Step 3.4, establish the objective function: ；（7）。 5. A parameter inversion method based on slope solute transport process according to claim 4, characterized in that: The specific process in step 4 is: The historical nutrient content flow data collected in step 1 are input into the objective function established in step 3.4, and the objective function is solved by the classic gradient descent method until the optimal neural network parameters are found, so that the output of the neural network satisfies the control equation as much as possible and is as close to the observed data as possible. After the optimization is completed, the optimal , then the diffusion coefficient is and , = , which is the diffusion coefficient K to be determined and the mass exchange rate .

6. A parameter inversion method based on slope solute transport process according to claim 5, characterized in that: The specific process in step 5 is: using the real-time rainfall monitoring forecast data and solute transport process data of step 1 as input conditions, combined with the diffusion coefficient K, fractional order α and mass exchange rate β calibrated in step 4, input into the one-dimensional slope solute transport model of step 2, and solve it using the finite difference method, so as to calculate the change process of nutrient content in the slope area during rainfall in real time. Integrate the product of the single-width flow rate of the slope during the entire rainfall time and the concentration of the solute, and the result is the nutrient loss of the slope during the rainfall period.

7. A parameter inversion method based on slope solute transport process according to claim 6, characterized in that: The specific process in step 6 is: repeat steps 1 to 5 to calculate in real time the amount of nutrient loss from multiple slopes during the rainfall period. The sum is the nutrient input of the collected rivers or lakes during the entire rainfall period. Compare it with the eutrophication warning value of lakes and rivers. If it exceeds the warning value, report it to the relevant departments for their decision-making basis.

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