A Schmidt stability calculation method and system based on mathematical model

Abstract

The invention discloses a Schmidt stability calculation method and system based on a mathematical model, which divides a research area into n calculation grid units; sets the initial conditions, boundary conditions and parameters of a hydrodynamic model, and uses the hydrodynamic model to calculate the hydrodynamic data of all grid units; sets the initial conditions, boundary conditions and parameters of a temperature model, and uses the temperature model to calculate the temperature data of all grid units according to the hydrodynamic data and the set initial conditions, boundary conditions and parameters of the temperature model; divides a target lake or reservoir into m layers vertically; obtains the distribution of the water temperature of the lake or reservoir in different spaces and times according to the hydrodynamic data and the temperature data; and calculates the Schmidt stability of the lake or reservoir in different calculation grids and at different times. Advantages: improves the calculation accuracy of lake and reservoir sub-regions, and lays a foundation for studying other water environment phenomena in reservoirs and managing water ecological problems.

Description

Technical Field

[0001] The invention relates to a Schmidt stability calculation method and system based on a mathematical model, belonging to the technical field of water environment simulation and prediction. Background Art

[0002] Water temperature is an important water quality factor for lakes or reservoirs. On the one hand, it affects the physical and chemical properties of the water body, and then affects other water quality indicators through physical and chemical processes; on the other hand, it also has an important impact on the ecological environment of the reservoir and the downstream river section. When the reservoir is deep, the vertical water temperature in front of the dam will be stratified, and there will be seasonal differences in surface and deep water temperatures. Therefore, accurately simulating the reservoir water temperature and analyzing the water temperature stratification law are the basis for analyzing and studying other water environment phenomena in the reservoir and managing water ecological problems.

[0003] Schmidt stability is a calculation method widely used to analyze the stability of temperature stratification. However, the calculation of the traditional Schmidt stability of the whole lake (reservoir) relies on data collected from fixed-point field monitoring experiments. The focus is usually on the water temperature in front of the dam, which has its limitations in time and space and cannot scientifically and reasonably calculate the stability of temperature stratification of the whole lake (reservoir). Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a Schmidt stability calculation method and system based on a mathematical model to make up for the shortage of time and space for field monitoring and to calculate the temperature stratification stability of the whole lake (reservoir) more scientifically and reasonably.

[0005] In order to solve the above technical problems, the present invention provides a Schmidt stability calculation method based on a mathematical model, comprising:

[0006] Determine the study area based on the geographical location and longitude and latitude coordinates of the target lake or reservoir, and divide the study area into n computational grid units;

[0007] Based on the hydrological data of the target lake or reservoir, the initial conditions, boundary conditions and parameters of the hydrodynamic model are set, and the hydrodynamic data of all grid cells are calculated using the hydrodynamic model;

[0008] Based on the meteorological data of the target lake or reservoir, the initial conditions, boundary conditions and temperature parameters of the temperature model are set, and the temperature data of all grid cells are calculated using the temperature model according to the hydrodynamic data and the set initial conditions, boundary conditions and temperature parameters of the temperature model;

[0009] Based on the actual water depth of the target lake or reservoir, the target lake or reservoir is divided into m layers vertically;

[0010] The distribution of the water temperature of the lake or reservoir in different spaces and times can be obtained based on the hydrodynamic data and temperature data;

[0011] The Schmidt stability of the lake or reservoir in different computational grids and at different times is calculated based on the distribution of the water temperature of the lake or reservoir in different spaces and times.

[0012] Furthermore, the initial conditions of the hydrodynamic module include underwater topography, initial water depth and initial water surface elevation; the boundary conditions of the hydrodynamic module include the flow into the lake or reservoir and the flow out of the lake or reservoir or the water level; and the hydrodynamic parameters include the roughness coefficient of the lake or reservoir bed.

[0013] Furthermore, the initial conditions of the temperature module include initial water temperature; the boundary conditions of the temperature module include meteorological boundary, wind boundary and water temperature boundary; and the temperature parameters include light attenuation coefficient and bottom bed temperature diffusion coefficient.

[0014] Furthermore, the coordinate system is a SIG coordinate system or a SGZ coordinate system.

[0015] Furthermore, it also includes:

[0016] The hydrodynamic parameters and temperature parameters of the lake or reservoir are calibrated and verified so that the absolute error between the model calculated value and the actual value of the water level does not exceed 10 cm, and the temperature error does not exceed 10%.

[0017] Furthermore, the coordinates are SGZ coordinate system, and the Schmidt stability of different computational grids and different times is expressed as:

[0018]

[0019] Where S j is the Schmidt stability of the grid unit, g is the gravitational acceleration, m is the number of layers in the hydrodynamic-water temperature coupling model, H j is the water depth of grid cell j calculated by the hydrodynamic model at time t, H ij is the thickness of the i-th layer of grid unit j calculated by the hydrodynamic model at time t, z ij is the height from the center of the i-th layer of grid unit j to the water surface calculated by the hydrodynamic model at time t, ρ ij is z calculated by the temperature model at time t ij The density at .

[0020] Furthermore, it also includes:

[0021] The Schmidt stability of the entire lake or reservoir is calculated based on the Schmidt stability of different calculation grids and different times, expressed as:

[0022]

[0023] In the formula, S all is the Schmidt stability of the entire lake or reservoir.

[0024] Furthermore, the meteorological boundary includes atmospheric pressure, atmospheric humidity, atmospheric temperature, water surface shortwave radiation, precipitation, evaporation, cloud cover and geographical location of the meteorological station; the wind boundary includes wind speed, wind direction and the height of the measuring point from the ground; the water temperature boundary includes the water temperature of each layer of the grid computing unit at the lake entrance boundary.

[0025] Furthermore, the coordinates are in the SIG coordinate system, and the Schmidt stability of different computational grids and different times as well as the Schmidt stability of the entire lake or reservoir are expressed as:

[0026]

[0027]

[0028] In the formula, S j is the Schmidt stability of the grid unit, m is the number of layers in the hydrodynamic-water temperature coupling model, n is the number of computational grid units, g is the gravitational acceleration, S all is the Schmidt stability of the entire lake or reservoir, H j is the water depth of grid cell j calculated by the hydrodynamic model at time t, z ij is the height from the center of the i-th layer of grid unit j to the water surface calculated by the hydrodynamic model at time t, ρ ij is z calculated by the temperature model at time t ij The density at .

[0029] A Schmidt stability calculation system based on a mathematical model, comprising:

[0030] The first division module is used to determine the study area based on the geographical location and longitude and latitude coordinates of the target lake or reservoir, and divide the study area into n computational grid units;

[0031] The hydrodynamic calculation module is used to set the initial conditions, boundary conditions and parameters of the hydrodynamic model based on the hydrological data of the target lake or reservoir, and calculate the hydrodynamic data of all grid cells using the hydrodynamic model;

[0032] The temperature calculation module is used to set the temperature model initial conditions, temperature model boundary conditions and temperature parameters based on the meteorological data of the target lake or reservoir, and calculate the temperature data of all grid cells using the temperature model according to the hydrodynamic data and the set temperature model initial conditions, temperature model boundary conditions and temperature parameters;

[0033] The second division module is used to divide the target lake or reservoir into m layers vertically based on the actual water depth of the target lake or reservoir;

[0034] The Schmidt stability calculation module is used to obtain the distribution of the water temperature of the lake or reservoir in different spaces and times based on the hydrodynamic data and temperature data; and to calculate the Schmidt stability of the lake or reservoir in different calculation grids and at different times based on the distribution of the water temperature of the lake or reservoir in different spaces and times.

[0035] The beneficial effects achieved by the present invention are:

[0036] The present invention is easy to operate and apply. It calculates the temperature stratification stability based on the hydrodynamic model and the water temperature model. Compared with the existing technology that estimates the Schmidt stability of the entire lake or reservoir based on the measured data of scattered sampling points of the target lake or reservoir, the technical method of the present invention is based on the calculation grid units and model output results of the entire lake or reservoir, and can perform batch calculations and improve the calculation accuracy of the lake and reservoir regions. The calculation method based on the calculation grid units is conducive to analyzing the spatial distribution of the Schmidt stability of the lake and reservoir, laying a foundation for studying other water environment phenomena of the reservoir and controlling water ecological problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0038] Figure 2 is the result of the Schmidt stability calculation throughout the year;

[0039] Figure 3 is the result of Schmidt stability calculation for the whole reservoir. DETAILED DESCRIPTION

[0040] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0041] Embodiment 1, a Schmidt stability calculation method based on a mathematical model, comprising:

[0042] (1) Based on the geographical location and longitude and latitude coordinates of the target reservoir, the EFDC model was used to reasonably divide the study area into 457 computational grid cells. Based on the hydrological data of the target reservoir, the initial conditions, boundary conditions and hydrodynamic parameters of the hydrodynamic module were set to construct a hydrodynamic model. The initial conditions of the hydrodynamic module included underwater topography, initial water depth and initial water surface elevation, the boundary conditions included inflow and outflow, and the hydrodynamic parameters included the bottom roughness coefficient. The calculation formula of the hydrodynamic module is as follows:

[0043] The momentum equation in the x direction is:

[0044]

[0045] The momentum equation in the y direction is:

[0046]

[0047] The momentum equation in the z direction is:

[0048]

[0049] Continuity equation:

[0050]

[0051] Equation of state:

[0052] ρ=ρ(p,S,T,C)

[0053] Where x, y are the horizontal orthogonal coordinates (meters); z is the vertical coordinate (dimensionless); t is time (seconds); m x , m y is the coordinate transformation coefficient; u, v are the horizontal velocity components in the curvilinear coordinates (m / s); w is the vertical velocity component in the vertical coordinates (m / s); ζ is the water surface elevation relative to the reference height (m); H is the total water depth (m); h is the water depth below the reference height; p is the physical pressure exceeding the hydrostatic pressure of the reference density (m 2 / second); P atm is the standard atmospheric pressure (Pascal); ρ0 is the reference density (kg / m 3 );f is the Coriolis coefficient (1 / second); A H is the horizontal momentum and mass diffusivity (m 2 / second); A v is the vertical turbulent viscosity coefficient (m 2 / second); c p is the vegetation resistance coefficient (dimensionless); D p is the projected vegetation area per unit horizontal area perpendicular to the runoff (dimensionless); S u , S v is the source / sink of horizontal momentum in the x and y directions (m 2 / Second 2 );S h is the source / sink term of the mass conservation equation (m 3 / second); S is salinity (ng / L); T is temperature (Celsius); C is the total amount of inorganic suspended matter (g / m 3 ).

[0054] (2) Based on the meteorological data of the target lake or reservoir, set the initial conditions, boundary conditions and temperature parameters of the temperature module and construct a temperature model; the initial conditions of the temperature module include the initial water temperature, and the boundary conditions include the meteorological boundary, wind boundary and water temperature boundary; the meteorological boundary includes atmospheric pressure, atmospheric humidity, atmospheric temperature, water surface shortwave radiation, precipitation, evaporation, cloud cover and the geographical location of the meteorological station; the wind boundary includes wind speed, wind direction and the ground height of the measurement point; the water temperature boundary includes the water temperature of each layer of the grid calculation unit at the reservoir entry boundary; the temperature parameters include the light attenuation coefficient and the bottom bed temperature diffusion coefficient; based on the actual water depth of the target reservoir, select the SGZ coordinate system and divide the reservoir into 10 layers in the longitudinal direction. The temperature module calculation formula is as follows:

[0055]

[0056] Where: P = m y Hu, Q = m x Hv

[0057] Where P and Q are the mass components in the x and y directions respectively (m 2 / second); A b is the vertical turbulent diffusion coefficient (m 2 / second); I is the solar shortwave radiation (watt / m 2 );S T is the source and sink term of heat exchange (joule / second); the meanings of other parameters are the same as those in the above hydrodynamic module calculation formula.

[0058] (3) After calibration and verification of the hydrodynamic parameters and temperature parameters, the absolute error between the model calculated value and the actual value of the water level is 0.016 m, and the temperature error is 4.78%.

[0059] Table 1 Validation results of reservoir A model

[0060]

[0061]

[0062] Run the model and obtain the distribution of the water temperature of the lake or reservoir in different spaces and times; calculate the Schmidt stability of the lake or reservoir in different computational grids and at different times based on the model operation results; the model operation results at least include the water depth of the desired computational grid unit, the number of layers of the computational grid unit, the water density of the center point of each layer, the height of the center point of each layer from the water surface, and the thickness of each layer; the calculation methods of the Schmidt stability of a single grid and the entire lake (reservoir) are:

[0063]

[0064]

[0065] Where S j To calculate the Schmidt stability of the grid cells (J / m 2 ), S all is the Schmidt stability of the entire lake (reservoir) (J / m 2 ), g is the acceleration due to gravity (9.81 m / s 2 ), n is the number of computational grid units, m is the number of computational grid units, H j is the water depth (m) of the calculated grid cell j, H ij To calculate the thickness (m) of the i-th layer of grid cell j, z ij is the height (m) of the center of the i-th layer of the grid unit j from the water surface, ρ ij For z ij Density at (kg / m 3 );

[0066] Embodiment 2 is different from Embodiment 1 in that the coordinate system is the SIG coordinate system. Since the calculation grid units are evenly layered, the thickness H of the calculation grid unit j is ij And the Schmidt stability calculation formula can be simplified as:

[0067]

[0068]

[0069]

[0070] Where S j To calculate the Schmidt stability of the grid cells (J / m 2 ), S all is the Schmidt stability of the entire lake (reservoir) (J / m 2 ), H j is the water depth (m) of grid cell j, z ij is the height (m) of the center of the i-th layer of the grid unit j from the water surface, ρ ij For z ij Density at (kg / m 3 ).

[0071] The present invention also provides a Schmidt stability calculation system based on a mathematical model, comprising:

[0072] The first division module is used to determine the study area based on the geographical location and longitude and latitude coordinates of the target lake or reservoir, and divide the study area into n computational grid units;

[0073] The hydrodynamic calculation module is used to set the initial conditions, boundary conditions and parameters of the hydrodynamic model based on the hydrological data of the target lake or reservoir, and calculate the hydrodynamic data of all grid cells using the hydrodynamic model;

[0074] The temperature calculation module is used to set the temperature model initial conditions, temperature model boundary conditions and temperature parameters based on the meteorological data of the target lake or reservoir, and calculate the temperature data of all grid cells using the temperature model according to the hydrodynamic data and the set temperature model initial conditions, temperature model boundary conditions and temperature parameters;

[0075] The second division module is used to divide the target lake or reservoir into m layers vertically based on the actual water depth of the target lake or reservoir;

[0076] The Schmidt stability calculation module is used to obtain the distribution of the water temperature of the lake or reservoir in different spaces and times based on the hydrodynamic data and temperature data; and to calculate the Schmidt stability of the lake or reservoir in different calculation grids and at different times based on the distribution of the water temperature of the lake or reservoir in different spaces and times.

[0077] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0078] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0079] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0080] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0081] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A Schmidt stability calculation method based on a mathematical model, characterized in that: include: Determine the study area based on the geographical location and longitude and latitude coordinates of the target lake or reservoir, and divide the study area into n computational grid units; Based on the hydrological data of the target lake or reservoir, the initial conditions, boundary conditions and parameters of the hydrodynamic model are set, and the hydrodynamic data of all grid cells are calculated using the hydrodynamic model; Based on the meteorological data of the target lake or reservoir, the initial conditions, boundary conditions and temperature parameters of the temperature model are set, and the temperature data of all grid cells are calculated using the temperature model according to the hydrodynamic data and the set initial conditions, boundary conditions and temperature parameters of the temperature model; Based on the actual water depth of the target lake or reservoir, the target lake or reservoir is divided into m layers vertically; The distribution of the water temperature of the lake or reservoir in different spaces and times can be obtained based on the hydrodynamic data and temperature data; Calculate the Schmidt stability of the lake or reservoir in different computational grids and at different times based on the distribution of the water temperature of the lake or reservoir in different spaces and times; The coordinates are the SGZ coordinate system, and the Schmidt stability of different computational grids and different times is expressed as: ； In the formula S j is the Schmidt stability of the grid unit, g is the gravitational acceleration, m is the number of layers in the hydrodynamic-water temperature coupling model, H j is the grid unit calculated by the hydrodynamic model at time t j The depth of water, H ij is the grid unit calculated by the hydrodynamic model at time t j No. i The thickness of the layer, z ij is the grid unit calculated by the hydrodynamic model at time t j No. i The height of the center of the layer from the water surface, ρ ij is calculated by the temperature model at time t z ij The density at Also included: Calculate the Schmidt stability of the entire lake or reservoir based on the Schmidt stability of different calculation grids and different times, expressed as: ； In the formula, S all is the Schmidt stability of the entire lake or reservoir; Alternatively, the coordinates are in the SIG coordinate system, and the Schmidt stability for different computational grids and different times and the Schmidt stability for the entire lake or reservoir are expressed as: ； ； In the formula, S j is the Schmidt stability of the grid unit, m is the number of layers in the hydrodynamic-water temperature coupling model, n is the number of computational grid units, g is the gravitational acceleration, S all is the Schmidt stability of the entire lake or reservoir, H j is the grid unit calculated by the hydrodynamic model at time t j The depth of water, z ij is the grid unit calculated by the hydrodynamic model at time t j No. i The height of the center of the layer from the water surface, ρ ij is calculated by the temperature model at time t z ij The density at .

2. The Schmidt stability calculation method based on the mathematical model according to claim 1 is characterized in that: The initial conditions of the hydrodynamic model include underwater topography, initial water depth and initial water surface elevation; the boundary conditions of the hydrodynamic model include inflow into a lake or reservoir and outflow from a lake or reservoir or water level; the hydrodynamic parameters include the roughness coefficient of the lake or reservoir bed.

3. The Schmidt stability calculation method based on mathematical model according to claim 1, characterized in that: The initial conditions of the temperature model include the initial water temperature; the boundary conditions of the temperature model include the meteorological boundary, the wind boundary and the water temperature boundary; the temperature parameters include the light attenuation coefficient and the bottom bed temperature diffusion coefficient.

4. The Schmidt stability calculation method based on mathematical model according to claim 1, characterized in that: Also includes: The hydrodynamic parameters and temperature parameters of the lake or reservoir are calibrated and verified so that the absolute error between the model calculated value and the actual value of the water level does not exceed 10 cm, and the temperature error does not exceed 10%.

5. The Schmidt stability calculation method based on mathematical model according to claim 3 is characterized in that: The meteorological boundary includes atmospheric pressure, atmospheric humidity, atmospheric temperature, water surface shortwave radiation, precipitation, evaporation, cloud cover and the geographical location of the meteorological station; the wind boundary includes wind speed, wind direction and the ground height of the measurement point; the water temperature boundary includes the water temperature of each layer of the grid calculation unit at the lake entry boundary.

6. A Schmidt stability calculation system based on a mathematical model, characterized in that: include: The first division module is used to determine the study area based on the geographical location and longitude and latitude coordinates of the target lake or reservoir, and divide the study area into n computational grid units; The hydrodynamic calculation module is used to set the initial conditions, boundary conditions and parameters of the hydrodynamic model based on the hydrological data of the target lake or reservoir, and calculate the hydrodynamic data of all grid cells using the hydrodynamic model; The temperature calculation module is used to set the temperature model initial conditions, temperature model boundary conditions and temperature parameters based on the meteorological data of the target lake or reservoir, and calculate the temperature data of all grid cells using the temperature model according to the hydrodynamic data and the set temperature model initial conditions, temperature model boundary conditions and temperature parameters; The second division module is used to divide the target lake or reservoir into m layers vertically based on the actual water depth of the target lake or reservoir; The Schmidt stability calculation module is used to obtain the distribution of the water temperature of the lake or reservoir in different spaces and times based on the hydrodynamic data and temperature data; based on the distribution of the water temperature of the lake or reservoir in different spaces and times, the Schmidt stability of the lake or reservoir in different calculation grids and at different times is calculated; The coordinates are the SGZ coordinate system, and the Schmidt stability of different computational grids and different times is expressed as: ； In the formula S j is the Schmidt stability of the grid unit, g is the gravitational acceleration, m is the number of layers in the hydrodynamic-water temperature coupling model, H j is the grid unit calculated by the hydrodynamic model at time t j The depth of water, H ij is the grid unit calculated by the hydrodynamic model at time t j No. i The thickness of the layer, z ij is the grid unit calculated by the hydrodynamic model at time t j No. i The height of the center of the layer from the water surface, ρ ij is calculated by the temperature model at time t z ij The density at Also included: Calculate the Schmidt stability of the entire lake or reservoir based on the Schmidt stability of different calculation grids and different times, expressed as: ； In the formula, S all is the Schmidt stability of the entire lake or reservoir; Alternatively, the coordinates are in the SIG coordinate system, and the Schmidt stability for different computational grids and different times and the Schmidt stability for the entire lake or reservoir are expressed as: ； ； In the formula, S j is the Schmidt stability of the grid unit, m is the number of layers in the hydrodynamic-water temperature coupling model, n is the number of computational grid units, g is the gravitational acceleration, S all is the Schmidt stability of the entire lake or reservoir, H j is the grid unit calculated by the hydrodynamic model at time t j The depth of water, z ij is the grid unit calculated by the hydrodynamic model at time t j No. i The height of the center of the layer from the water surface, ρ ij is calculated by the temperature model at time t z ij The density at .

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