CN113343601A - Dynamic simulation method for water level and pollutant migration of complex water system lake - Google Patents
Dynamic simulation method for water level and pollutant migration of complex water system lake Download PDFInfo
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Abstract
The invention discloses a dynamic simulation method for water level and pollutant migration of a complex water system lake, which comprises the following steps: s1: collecting lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data; s2: constructing a lake hydrodynamic water quality model; s3: calibrating and verifying the lake hydrodynamic water quality model; s4: assimilating the calibrated and verified lake hydrodynamic water quality model; s5: and dynamically simulating the lake water level and the water quality by utilizing the assimilated lake hydrodynamic water quality model. The invention relates to a dynamic refined simulation method for water level and pollutant migration of a lake with a complex water system, which is suitable for ecological protection and water resource comprehensive management of lakes with complex water system connectivity and multiple functional requirements.
Description
Technical Field
The invention belongs to the technical field of lake comprehensive management, and particularly relates to a dynamic simulation method for water level and pollutant migration of a complex water system lake.
Background
The lake is used as an important carrier of water resources, has irreplaceable effects in aspects of flood control, water resource regulation and configuration, water quality purification, ecological wetland protection, biological species diversity maintenance and the like, and is inseparable from human life. Every country in the world has an indefinite number of lake resources, but the vast country of China also builds that the lake resources are typically rich in lakes, and the large and small lakes are countless, so that a lot of fresh water resources are stored in the lakes, and better support is provided for water resource development and utilization, navigation transportation, fishery breeding development, irrigation of irrigation areas, water resource regulation and storage and the like in China. The health of the lake is an important guarantee for realizing flood control safety of a drainage basin, also an important guarantee for realizing sustainable utilization of water resources, and further an important guarantee for realizing sustainable development of regional ecological environment.
Lakes are generally managed as "reservoirs" as large-scale storage areas, but are different from reservoirs. The common point is that the water storage areas are large-scale water storage areas and have good storage regulation function; the different place is that the reservoir is constructed manually, so the inflow and outflow situation is single, the controllability is strong, and the storage and release process of water resources can be realized through the regulation of a reservoir gate; the lakes exist in river network water systems as natural resources, particularly the lakes which are connected with a plurality of river channels and run through a plurality of rivers and the sea, the inflow and outflow situations are very complex, most of the lakes are shallow water type, the landform is complex, the lakes are easily influenced by changeable environment, meanwhile, with the development of social economy, cross-basin water transfer engineering is produced in order to solve the problem of uneven water resource distribution, in order to save the engineering cost, the lakes with better water system communication are selected as the regulation and storage lakes for water transfer, and therefore higher challenges are further provided for water level simulation and pollutant migration process simulation of the lakes. The original lake simulation method is no longer applicable, so the invention provides a dynamic refined simulation method for the water level and the pollutant migration of the lake with the complex water system.
Disclosure of Invention
The invention aims to solve the problem of accurately realizing lake simulation, and provides a dynamic simulation method for the water level and pollutant migration of a complex water system lake.
The technical scheme of the invention is as follows: a dynamic simulation method for the water level and pollutant migration of a complex water system lake comprises the following steps:
s1: collecting lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s2: constructing a lake hydrodynamic water quality model according to collected lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s3: calibrating and verifying the lake hydrodynamic water quality model;
s4: assimilating the calibrated and verified lake hydrodynamic water quality model;
s5: and dynamically simulating the lake water level and the water quality by utilizing the assimilated lake hydrodynamic water quality model.
Further, step S2 includes the following sub-steps:
s21: carrying out hydraulic parameter identification based on lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s22: building a lake two-dimensional hydrodynamic model and a lake water quality model based on the hydraulic parameters;
s23: and converting the two-dimensional lake hydrodynamic model by adopting an orthogonal curve coordinate, and taking the converted lake hydrodynamic model and the converted lake water quality model as a lake hydrodynamic water quality model.
Further, in step S21, the specific method for identifying the hydraulic parameters is as follows: sampling from the acquired data by utilizing a Latin hypercube sampling method, calculating a decisive coefficient of the sampled data by utilizing a standard rank stepwise regression method, and using a parameter of which the decisive coefficient is greater than a set threshold value to construct a lake two-dimensional hydrodynamic water quality model to finish hydraulic parameter identification; the calculation formulas of the Latin hypercube sampling method and the standard rank stepwise regression method are respectively as follows:
wherein Q ishA random number representing the h' th subinterval in the collected data, and Q representing [0,1 ] in the collected data]Uniformly distributed random numbers in between, N represents the number of subintervals, R2The coefficient of certainty is represented by a coefficient of certainty,
regression score representing output target valueAnalyzing a total variance, wherein V represents the total variance of the output target value;
in step S22, the expression of the lake two-dimensional hydrodynamic model is:
wherein, ζ is the lake depth, namely the distance between the lake datum plane and the lake surface, and the unit is m; h is the total depth of the lake; h is the depth of water below the lake datum level, and the unit is m; u and v are the average flow velocities along the x and y axes, respectively, in m3S; f is the coefficient of the Coriolis force,
fWis the wind resistance coefficient; c is the thank existance coefficient, C1/n (zeta + h)1/6Wherein n is the roughness coefficient; a. thexAnd AyVortex viscosity along the x-axis and y-axis, respectively; p is the static pressure in Pa (pascal); t is duration in units of s; w is the wind speed 10m above the lake surface, WxAnd WyThe wind speeds are 10m higher than the lake water surface along the x axis and the y axis respectively, and the unit is m/s; g is the acceleration of gravity in m/s2；τxx，τyxAnd τxyThe shearing stress corresponding to 0 degree, 90 degrees and 45 degrees on the xy coordinate axis respectively; and also, CdIs the wind drag coefficient;
in step S22, the expression of the lake water quality model is:
wherein p represents the concentration of pollutants, k represents the lake degradation coefficient and has the unit of s-1；DxDenotes the diffusion coefficient along the x-axis, DyThe diffusion coefficient along the y axis is shown, S represents a pollution source item showing the pollution load of the lake, and the unit is g/(m)2S); hf (p) represents a contaminant concentration change process;
in the water quality equation for simulating the transport, diffusion and digestion process of pollutants discharged into lakes, on the right side of the equation, the first and second are both diffusion terms, i.e., DxAnd DyAre the diffusion coefficients in the directions of the x-axis and the y-axis, respectively, in m2S; the third on the right side of the equation is a biochemical reaction term which can be regarded as the total derivative of the ecological variable with time, and not only can reflect the physical, chemical and biological change processes of the variable in the lake, but also can describe the dynamic relation of pollutants among the changes of the characteristics of the hydrological weather, hydrodynamic force and water quality.
In step S23, the expression of the orthogonal curve coordinate is:
wherein the content of the first and second substances,
xξtransformed coordinate of Cartesian coordinate x representing an irregular area (Ω) on new coordinate ξ - η, yξTransformed coordinate, g, of Cartesian coordinate y representing an irregular area (Ω) on new coordinate xi- ηξRepresenting the side length of a zeta axis of an orthogonal grid in a zeta-eta coordinate system;
in step S23, the expression of the lake water power model is:
wherein, gηRepresenting side lengths, A, of the eta axes of an orthogonal grid in a xi-eta coordinate systemξIndicating the viscosity of the vortex along the xi axis, AηIndicating the viscosity of the vortex along the η axis.
Further, in step S3, the specific method for calibrating and verifying the lake water dynamic model includes: utilizing the daily water level observed quantity of the lake water level station length series to rate the hydrodynamic parameters of the lake hydrodynamic model, and obtaining the lake roughness, the wind dragging force coefficient and the wind resistance coefficient when the fitting degree of the water level measured value and the observed value is optimal; calculating the simulation precision of the lake water dynamic model by using a Nash efficiency coefficient method, and verifying the reliability of the lake water dynamic model; the hydrodynamic parameters of the lake hydrodynamic model comprise lake roughness, a wind drag coefficient and a wind resistance coefficient.
Further, in step S3, the specific method for calibrating and verifying the water quality parameters of the lake water quality model is as follows: taking the longitudinal diffusion coefficient, the transverse diffusion coefficient, the comprehensive attenuation coefficient of characteristic pollutants, the dry water depth and the wet water depth of the lake as water quality parameters of a lake water quality model, and utilizing the monitoring data of the lake water quality station to monitor the pollutant concentration to calibrate the water quality parameters of the lake water quality model to obtain the water quality parameters such as the comprehensive attenuation coefficient of the pollutants, the longitudinal diffusion coefficient and the transverse diffusion coefficient of the lake, the dry water depth of the lake and the wet water depth of the lake when the fitting degree of the measured value of the pollutant concentration and the observed value is optimal; according to the daily pollutant concentration observation data of the lake water quality station length series, the simulation precision of the lake water quality model is calculated by using a Nash efficiency coefficient method, and the reliability of the lake water quality model is verified.
Further, in step S3, a Nash efficiency coefficient is calculated by the Nash efficiency coefficient method, and the Nash efficiency coefficient E is converted into a Nash efficiency coefficientnsAs the simulation precision, the calculation formula is as follows:
wherein Q iss,iRepresents the ith observation, Qm,iThe (i) th analog value is represented,
represents the observed mean.
Further, in step S4, the specific method for assimilating the lake hydrodynamic model includes: the water level and flow (without vertical variation) of the lake are taken as state variables, the lake roughness and wind drag force coefficient are taken as parameters to be assimilated, the process belongs to a multi-state variable and multi-parameter assimilation process, the water level value and flow value of a lake measuring station are taken as observed values, and the state variables and the parameters to be assimilated of the lake hydrodynamic model are assimilated by the water level value and flow value of the lake measuring station through an ensemble Kalman filtering method.
Further, in step S4, the specific method for assimilating the lake water quality model is as follows: taking lake characteristic pollutants (main pollutants in lakes) as state variables, taking comprehensive attenuation coefficients and diffusion coefficients of the pollutants as parameters to be assimilated, wherein the process is a single-state variable multi-parameter assimilation process, taking a lake water quality station pollutant concentration value as an observed value, and assimilating the state variables and the parameters to be assimilated of a lake water quality model by using a lake water quality station pollutant concentration value through an ensemble Kalman filtering method.
The invention has the beneficial effects that:
(1) the invention relates to a dynamic refined simulation method for water level and pollutant migration of a lake with a complex water system, which is suitable for ecological protection and water resource comprehensive management of lakes with complex water system connectivity and multiple functional requirements.
(2) The invention has the advantages that an assimilation model for the complex water system lake is established, the improvement of the simulation method for the lake water level and the pollutant change process is realized, a decision maker can select reasonable regulation and control measures timely and accurately, the efficient utilization of lake water resources is facilitated, and method support is provided for the multipurpose complex water system lake water resource optimization scheduling scheme.
Drawings
FIG. 1 is a flow chart of a dynamic simulation method of water level and pollutant migration in a complex water system lake;
FIG. 2 is a flow chart of the model assimilation of lake hydrodynamic water quality.
Detailed Description
The embodiments of the present invention will be further described with reference to the accompanying drawings.
As shown in FIG. 1, the invention provides a dynamic simulation method for water level and pollutant migration of a complex water system lake, which comprises the following steps:
s1: collecting lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s2: constructing a lake hydrodynamic water quality model according to collected lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s3: calibrating and verifying the lake hydrodynamic water quality model;
s4: assimilating the calibrated and verified lake hydrodynamic water quality model;
s5: and dynamically simulating the lake water level and the water quality by utilizing the assimilated lake hydrodynamic water quality model to realize the quantification of the lake water level and the water quality.
In the embodiment of the present invention, step S2 includes the following sub-steps:
s21: carrying out hydraulic parameter identification based on lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s22: building a lake two-dimensional hydrodynamic model and a lake water quality model based on the hydraulic parameters;
s23: and converting the two-dimensional lake hydrodynamic model by adopting an orthogonal curve coordinate, and taking the converted lake hydrodynamic model and the converted lake water quality model as a lake hydrodynamic water quality model.
And (4) finishing the construction of the lake hydrodynamic water quality model by adopting various data collected in the step S1, and finishing the calibration and verification of the lake hydrodynamic water quality model by combining the identification of lake hydraulic parameters.
The lake hydrodynamic water quality model comprises a hydrodynamic model and a water quality model. The hydrodynamic model can realize deduction of a lake flow field and simulation of a water level change process, namely the lake outlet and the lake inlet can be used as boundary conditions of the hydrodynamic model, and by setting hydraulic parameters, flow velocity change rules, flow direction characteristics in different lake regions and lake level spatial distribution rules in the lake outlet region are simulated by using the constructed hydrodynamic equation. The water quality model is used for simulating the dynamic change processes of transport, diffusion, degradation and the like of pollutants in a water body, the simulation of the lake water quality is related to the hydrodynamic conditions in the lake region, namely, the simulation of the lake flow field is an important basis for the evolution simulation of the pollutants in the lake region, and the precision of the hydrodynamic simulation can have great influence on the precision of the water quality model.
In the embodiment of the present invention, in step S21, the specific method for performing hydraulic parameter identification is as follows: sampling from the acquired data by utilizing a Latin hypercube sampling method, calculating a decisive coefficient of the sampled data by utilizing a standard rank stepwise regression method, and using a parameter of which the decisive coefficient is greater than a set threshold value to construct a lake two-dimensional hydrodynamic water quality model to finish hydraulic parameter identification; the calculation formulas of the Latin hypercube sampling method and the standard rank stepwise regression method are respectively as follows:
wherein Q ishA random number representing the h' th subinterval in the collected data, and Q representing [0,1 ] in the collected data]Uniformly distributed random numbers in between, N represents the number of subintervals, R2The coefficient of certainty is represented by a coefficient of certainty,
a regression analysis total variance representing the output target value, V representing the total variance of the output target value;
in step S22, the expression of the lake two-dimensional hydrodynamic model is:
whereinζ represents the lake depth, namely the distance between the lake datum level and the lake surface, and is expressed in m; h represents the total depth of the lake, u represents the average flow velocity along the x-axis, and the unit is m3S; v represents the average flow velocity along the y-axis in m3S; t represents the duration in units of s; g represents the acceleration of gravity in m/s2(ii) a C represents the metabolic coefficient, C is 1/n (delta + h)1/6N represents a roughness coefficient, AxRepresents the viscosity of the vortex along the x-axis, p represents the static pressure in Pa (pascal), f represents the coeliac force coefficient, and f is 2 ω sin Φ; f. ofWDenotes the wind resistance coefficient, W denotes the wind speed 10m above the lake surface, WxRepresenting the wind speed 10m above the lake water surface along the x-axis, in m/s; a. theyDenotes the vortex viscosity, W, along the y-axisyRepresenting the wind speed 10m above the lake water surface along the y-axis, in m/s; h represents the depth of water below the reference level of the lake and has the unit of m;
in step S22, the expression of the lake water quality model is:
wherein p represents the concentration of pollutants, k represents the lake degradation coefficient and has the unit of s-1；DxDenotes the diffusion coefficient along the x-axis, DyThe diffusion coefficient along the y axis is shown, S represents a pollution source item showing the pollution load of the lake, and the unit is g/(m)2S); hf (p) represents a contaminant concentration change process;
in the water quality equation for simulating the transport, diffusion and digestion process of pollutants discharged into lakes, on the right side of the equation, the first and second are both diffusion terms, i.e., DxAnd DyAre the diffusion coefficients in the directions of the x-axis and the y-axis, respectively, in m2S; the third on the right side of the equation is a biochemical reaction term which can be regarded as the total derivative of the ecological variable with time, not only can reflect the physical, chemical and biological change processes of the variable in the lake, but also can describe the hydrological, hydrodynamic and water states of pollutantsDynamic relationships between qualitative feature changes.
In step S23, the expression of the orthogonal curve coordinate is:
wherein the content of the first and second substances,
xξtransformed coordinate of Cartesian coordinate x representing an irregular area (Ω) on new coordinate ξ - η, yξTransformed coordinate, g, of Cartesian coordinate y representing an irregular area (Ω) on new coordinate xi- ηξRepresenting the side length of a zeta axis of an orthogonal grid in a zeta-eta coordinate system;
in step S23, the expression of the lake water power model is:
wherein, gηRepresenting side lengths, A, of the eta axes of an orthogonal grid in a xi-eta coordinate systemξIndicating the viscosity of the vortex along the xi axis, AηIndicating the viscosity of the vortex along the η axis.
In order to solve the above equations accurately, the equations may be converted using orthogonal curve coordinates. The irregular area (Ω) in the cartesian x-y coordinate system can be transformed into a new coordinate system, which is designated as the ξ - η coordinate system, while the irregular area (Ω) now becomes a rectangular area (Ω'). And dividing equal-coordinate grid nodes in the rectangular region (omega'), wherein each grid node has a corresponding node in an x-y coordinate system.
For a large lake, a large number of hydraulic parameters can reduce the parameter calibration efficiency of a lake hydrodynamic model, so that the model collapses in the parameter calibration process. On the basis of ensuring the simulation accuracy of the lake water power model, a standard rank stepwise regression model is selected to be matched with a Latin sampling method (LHS) to analyze the sensitivity of each hydraulic parameter to the output variable of the model, so that the hydraulic parameters with higher sensitivity are identified and subjected to key calibration, the parameter calibration efficiency of the lake water power model is improved, and the calculation safety of the model is ensured.
The two-dimensional hydrodynamic model comprises a plurality of parameters, such as time step length, time step length number, dry and wet boundaries, density functions (temperature related functions), vortex viscosity, lake bottom roughness, water temperature, salinity, Taoton law constant, Taoton law wind constant, time zone standard meridian, extinction coefficient, critical wind speed, wind resistance coefficient and wind drag coefficient, and for a complex water system lake, the parameters influencing hydrodynamic simulation precision comprise the dry and wet boundaries, the time step length, the vortex viscosity, the lake bottom roughness, the water temperature, the salinity, the extinction coefficient, the critical wind speed, the wind resistance coefficient and the wind drag coefficient. Therefore, sensitivity analysis is carried out on the lake hydraulic parameters through a standard rank stepwise regression model and an LHS method, so that important hydraulic parameters are identified, the parameter calibration efficiency of the hydrodynamic model is improved under the condition of ensuring the simulation precision of the model, and the calculation safety of the model is ensured.
The standard rank stepwise regression is to convert the original data into a rank coefficient matrix, standardize the obtained rank coefficient matrix to resolve the nonlinear relation between the input value and the output value, and finally obtain a Standard Regression Coefficient (SRC) and a determinant coefficient R which can reflect the sensitivity of the model2. The SRC may exhibit a degree of contribution of each input value to the overall output result variance, with a larger SRC absolute value indicating a higher sensitivity of the model to the input values. R2Then it may represent the feasibility of the regression model analysis, R2The larger the value, the more feasible the regression model analysis, in general, R2>0.7 shows that the feasibility meets the requirement, and the regression analysis result is reliable.
The expressions of the standard rank stepwise regression model are respectively:
wherein i is 1,2,3 …, n; j is 1,2,3 …, m; j is the number of parameters, and m is 4 in the calculation; n is the number of samples and needs to be obtained through trial calculation; b0Is a general regression coefficient; bjRegression coefficients corresponding to each parameter;
is an estimate of the model output; x is the number ofijIs the realization of the ith sample of the jth model input parameter.
Due to the difference in dimension between the parameters, bjThe value is not directly reflective of the parameter sensitivity, so a standard rank conversion of the above equation is required to obtain:
in the formula (I), the compound is shown in the specification,
is an input parameter xijThe average deviation of the average of the deviation of the average of the deviation of the average of,
is an input parameter xijA standard deviation of (d);
is the output target value yiThe average deviation of the average of the deviation of the average of the deviation of the average of,
is the output target value yiA standard deviation of (d);
is a Standard Regression Coefficient (SRC) which can be used to measure the uncertainty contribution degree of the parameter to the output target value, and the larger the absolute value of the SRC is, the larger the parameter is, the output is represented by the parameterThe greater the uncertainty contribution of the result.
It should be noted that the regression model is built based on a linear relationship between the input target and the output target, but this becomes more complicated when the relationship between the targets is non-linear. If the input parameters of the lake water power model and the output target values are in a nonlinear relationship, the linear regression equation cannot provide an accurate regression relationship. To solve this problem, the above equation needs to be regularized, i.e. the input parameters of the model and the corresponding output data are converted into corresponding rank sequences, each variable of the input and output data is ordered from the first bit with the minimum to the maximum value, and finally the sensitivity of the parameters can be measured by the SRC squared value or the absolute value of the variable. The total variance of the model output target value and the corresponding regression analysis total variance are respectively as follows:
in this case, the decisive coefficients that can be used to measure the reliability of the regression model are:
assuming that the parameters are independent of each other and each parameter is uniformly distributed, the equation
Can become:
in this case, the decisive factor R2To convert to:
in addition, in order to ensure that the samples input into the standard rank stepwise regression model are random, a Latin Hypercube Sampling method (LHS) is adopted to improve the Sampling efficiency, so that the optimal calculation result is obtained by using the minimum number of samples. The LHS method is a multi-bit layered sampling method, and can eliminate repeated invalid sampling work, namely, through sampling times trial calculation, a variable probability density function is equally divided to obtain N subintervals, and finally sampling with the same probability is completed in the N independent subintervals. Random number Q in h-th subintervalhCan be expressed as:
wherein h is 1,2, …, N; qhIs the random number of the h sub-interval, which is more than (h-1)/N and less than h/N; q is at [0,1 ]]Uniformly distributed random numbers in between.
Through parameter identification, important hydraulic parameters required by the lake hydraulic power model can be obtained.
In trial calculation of different Latin sampling times 50, 100, 200, 300, 400 and 500, when the sampling time is 200 times, the condition that the minimum sampling time obtains the optimal calculation result can be met, and therefore, the Latin sampling time is set to be 200 times. When the lake hydrodynamic model takes the flow velocity as an output target, the determinant coefficient R of the standard rank stepwise regression model2All exceed 0.7, wherein 94 percent of R2When the flow rate sensitivity of the hydraulic parameters to the lake exceeds 0.9, the result indicates that the model result is reliable, and the results show that the hydraulic parameters are sorted by roughness (46.15%), a wind drag coefficient (31.02%), a wind resistance coefficient (12.46%), a lake eddy viscosity (2.15%), a critical wind speed (1.92%), a time step (1.73%), a dry-wet boundary (1.56%), a water temperature (1.22%), a salinity (1.12%) and an extinction coefficient (0.67%) in sequence according to the lake bottom terrain and wind field variation, namely that the change of the surface flow rate of the Hongze lake is mainly determined by the lake bottom terrain and the wind field variationMelting; when the lake hydrodynamic model takes the water level as an output target, the deterministic coefficient R of the standard rank stepwise regression model2Also exceeds 0.7 in which 90% of R2When the water level sensitivity of the hydraulic parameters to the lake is determined to be more than 0.9, the model result is reliable, and the analysis result shows that the hydraulic parameters to the lake water level sensitivity are sorted in sequence into roughness (64.13%), a wind drag coefficient (17.76%), a wind resistance coefficient (11.38%), lake vortex viscosity (2.15%), a dry-wet boundary (1.32%), a critical wind speed (1.08%), a time step (0.97%), water temperature (0.83%), salinity (0.26%) and an extinction coefficient (0.12%), namely that the water level change of the Mingzhu mainly depends on the topography of the bottom of the lake. From this, the roughness (n) and the wind drag coefficient (C) are shownd) Coefficient of wind resistance (f)W) The method is the most important hydraulic parameter influencing the lake water power simulation, the emphasis needs to be set, and other hydraulic parameters can be obtained through an empirical formula.
In the embodiment of the present invention, in step S3, the specific method for calibrating and verifying the lake water dynamic model includes: utilizing the daily water level observed quantity of the lake water level station length series to rate the hydrodynamic parameters of the lake hydrodynamic model, and obtaining the lake roughness, the wind dragging force coefficient and the wind resistance coefficient when the fitting degree of the water level measured value and the observed value is optimal; calculating the simulation precision of the lake water dynamic model by using a Nash efficiency coefficient method, and verifying the reliability of the lake water dynamic model; the hydrodynamic parameters of the lake hydrodynamic model comprise lake roughness, a wind drag coefficient and a wind resistance coefficient. The actually measured water level value in the verification period of each lake water level station and the simulated water level process Nash efficiency coefficient are both above 0.60, which indicates that the water power model is reliable.
And (4) utilizing daily water level observation data of the lake water level station length series to calibrate the model parameters to obtain hydraulic parameters such as lake roughness, wind dragging force coefficient, wind resistance coefficient and the like when the fitting degree of the water level measured value and the observed value is optimal. Meanwhile, the reliability of the hydrodynamic model is verified by using daily water level observation data of a lake water level station leader series, and a Nash efficiency coefficient (E) is adoptedns) The simulation accuracy of the hydrodynamic model is evaluated. The actually measured water level value of each lake water level station in the verification period and the simulated water level process Nash efficiency coefficient are both 0.6Above 0, this indicates that the hydrodynamic model is reliable.
In the embodiment of the present invention, in step S3, the specific method for calibrating and verifying the water quality parameters of the lake water quality model is as follows: taking the longitudinal diffusion coefficient, the transverse diffusion coefficient, the comprehensive attenuation coefficient of characteristic pollutants, the dry water depth and the wet water depth of the lake as water quality parameters of a lake water quality model, and utilizing the monitoring data of the lake water quality station to monitor the pollutant concentration to calibrate the water quality parameters of the lake water quality model to obtain the water quality parameters such as the comprehensive attenuation coefficient of the pollutants, the longitudinal diffusion coefficient and the transverse diffusion coefficient of the lake, the dry water depth of the lake and the wet water depth of the lake when the fitting degree of the measured value of the pollutant concentration and the observed value is optimal; according to the daily pollutant concentration observation data of the lake water quality station length series, the simulation precision of the lake water quality model is calculated by using a Nash efficiency coefficient method, and the reliability of the lake water quality model is verified. The coefficient of Nash efficiency of the actually measured pollutant concentration value and the simulated pollutant concentration value in the verification period of each lake water quality station is over 0.60, which indicates that the water quality model is reliable.
In the embodiment of the present invention, in step S3, the Nash efficiency coefficient is calculated by the Nash efficiency coefficient method, and the Nash efficiency coefficient E is calculatednsAs the simulation precision, the calculation formula is as follows:
wherein Q iss,iRepresents the ith observation, Qm,iThe (i) th analog value is represented,
represents the observed mean. EnsThe closer to 1, the closer to the measured value the analog value is; ensThe more deviation from 1, the more deviation from the measured value of the simulation value; if EnsLess than 0 indicates that the simulation result is not authentic.
Aiming at the lake and river network model, actual measurement runoff of a lake entering river (gate) is selected as a lake inflow boundary (upper boundary), and actual measurement water level of a lake exiting river (gate) is selected as a lake outflow boundary (lower boundary). And selecting the monitoring concentration of representative pollutants of the lake-entering rivers (gates) as the upper boundary of the water quality model, and selecting the monitoring concentration of representative pollutants of the lake-entering rivers (gates) as the lower boundary of the water quality model.
Setting the space step length of a model grid through lake and river network data, dividing grid nodes, and selecting a model to calculate time length. For large complex water system lakes, the step length of the grid space is selected between 100 and 500m, and the calculation time is selected between 60s and 60 min.
Using the Nash efficiency coefficient (E)ns) The simulation precision of the hydrodynamic water quality model is evaluated. Calibrating hydraulic parameters of the hydrodynamic model by using daily water level observation data of the lake water level station leader series, and verifying the simulation effect of the hydrodynamic model; and (4) utilizing serial monthly observation data of the lake water quality station leader to calibrate the water quality model parameters and verify the simulation effect of the water quality model. Wherein the coefficient of Nash efficiency (E)ns) Above 0.6, the model simulation effect is reasonable and reliable. Coefficient of Nash efficiency (E)ns) The expression is as follows:
in the formula, Qs,iIs the ith observation, Qm,iFor the (i) th analog value,
are observed averages. EnsThe closer to 1, the closer to the measured value the analog value is; ensThe more deviation from 1, the more deviation from the measured value of the simulation value; if EnsLess than 0 indicates that the simulation result is not authentic.
In the embodiment of the present invention, in step S4, a specific method for assimilating the lake hydrodynamic model includes: the water level and flow (without vertical variation) of the lake are taken as state variables, the lake roughness and wind drag force coefficient are taken as parameters to be assimilated, the process belongs to a multi-state variable and multi-parameter assimilation process, the water level value and flow value of a lake measuring station are taken as observed values, and the state variables and the parameters to be assimilated of the lake hydrodynamic model are assimilated by the water level value and flow value of the lake measuring station through an ensemble Kalman filtering method.
In the embodiment of the present invention, in step S4, the specific method for assimilating the lake water quality model is as follows: taking lake characteristic pollutants (main pollutants in lakes) as state variables, taking comprehensive attenuation coefficients and diffusion coefficients of the pollutants as parameters to be assimilated, wherein the process is a single-state variable multi-parameter assimilation process, taking a lake water quality station pollutant concentration value as an observed value, and assimilating the state variables and the parameters to be assimilated of a lake water quality model by using a lake water quality station pollutant concentration value through an ensemble Kalman filtering method.
And assimilating the lake hydrodynamic water quality model constructed in the S2 by using an ensemble Kalman filtering method, and improving the simulation precision of the model on the lake water level and the water quality. The lake water level is taken as a state variable, the lake roughness is taken as a parameter needing assimilation, and a lake water level station measured value is taken as an assimilation model observation value, and after the state variable and the model parameter are assimilated simultaneously, the improvement of the lake water level simulation precision of the hydrodynamic model is realized. The lake representative pollutant concentration is used as a state variable, the representative pollutant comprehensive attenuation coefficient and the diffusion coefficient are used as parameters needing assimilation, and the actual measurement value of the lake water quality station is used as an assimilation model observation value, so that the lake pollutant concentration simulation precision of the water quality model is improved after the state variable and the model parameters are assimilated at the same time.
Considering that the nonlinear change of the lake hydrodynamic water quality model causes difficulty in meeting the Gaussian distribution condition, determining to adopt an ensemble Kalman filtering method to respectively carry out single assimilation on the model state variable and carry out double assimilation on the model state variable and the model parameter. The ensemble Kalman filtering method (EnKF) is a ductility method combining ensemble theory and mathematical statistics, can lead model simulation errors to dynamically extend along with a model by drawing up simulation errors in optimal interpolation, gets rid of the dynamic change of the simulation errors, and can cut out accompanying operators through the mean value of variables and an error covariance matrix corresponding to the mean value, thereby leading a nonlinear change system to quickly realize a data assimilation process. The EnKF method comprises state prediction, error prediction, variable analysis and variable analysisThe error is calculated in two parts. Assuming that there are N state variables, the matrix formed by them is X ═ X1,X2,....,XN]After Gaussian white noise is inserted into the state variable matrix X, a group of initial variable sets containing M variables is randomly generated from the matrix X considering the initial state error by using the Monte Carlo method
Where t represents the time of assimilation, and i represents a random variable in the set (i ═ 1, 2. Meanwhile, a simulation model is set, and the error covariance matrix of the model at the assimilation time t is YtThen, the state variable prediction equation, the model driving data generation equation and the parameter to be assimilated generation equation are respectively as follows:
wherein f (·) is a model operator;
a state variable predicted value of a random variable i at the moment t + 1;
a state variable analysis value of a random variable i at the time t; j is the number of parameters to be assimilated, J is 1, 2. Thetad～N(0,θ)，σp～N(0,σ)；
In order to assimilate the parameter j,
by setting at an initial beta0(j) Adding N (0, sigma) Gaussian white noise to generate;
for the model driving data at the time t, the driving data mainly concerned in this paper are lake inflow runoff, lake outflow runoff, wind field, initial lake water level,
by at an initial vtAdding N (0, theta) Gaussian white noise to generate; deltatFor model uncertainty error disturbance at time t, δt～N(0,Yt) Typically, the variance value corresponds to 10% of the state variable analog value.
Setting a matrix of observation error covariance at t +1 in the updating process as Zt+1And updating the predicted value of the state variable and the model parameter by using the observed value at the time t +1, wherein the respective updating equations are as follows:
in the formula (I), the compound is shown in the specification,
and
kalman gain matrices for updating state variables and updating parameters, respectively; o ist+1Is the value of the observed variable, epsilon, at time t +1t+1For observing error perturbations,. epsilont+1～N(0,Zt+1) (ii) a h (-) is an observation variable operator, representing
To model utilization of Ot+1Mapping of the obtained output results;
a state variable analysis value of parameter j at time t + 1;
is the predicted value of the state variable of the parameter j at the time t.
The kalman gain matrix for updating the state variables may be calculated by the following equation:
in the formula, H is a matrix expression of an observation variable operator H (·);
is the time of k +1
The prediction error covariance of (a);
is the time of k +1
And with Ot+1Model output variables of
The prediction error covariance of (a);
utilizing O for time k +1t+1The model of (2) outputs a prediction error covariance of the variable;
and forecasting the ensemble average value for the state variable at the moment k + 1. In order to eliminate the dimension disaster problem of the state variable, calculation is not needed
By calculation only
And
a kalman gain matrix of the state variables is obtained.
Averaging the updated state variables to obtain the corresponding optimal estimation value
(average value of state variable analysis set at time k + 1), and the corresponding estimation error covariance
(covariance of state variable analysis set at time k + 1),
and
expression (2)Comprises the following steps:
the Kalman gain matrix of the updated parameters, the updated optimal estimation value of the parameters and the estimation error covariance corresponding to the updated parameters can also adopt equations
Sum equation
The calculation is performed by simply replacing the expression of the state variables in the equation with the expression of the assimilation required parameters, but in contrast to this, the observation value set is generated by adding N (0, ω) white gaussian noise to the observation value before calculating the kalman gain matrix of the updated parameters. In addition, in order to avoid problems such as stop of calculation of an assimilation model, excessive fitting of a model simulation result and an actual measurement value and the like caused by excessive parameter assimilation updating, a parameter smoothing method is adopted, a smoothing factor which is more than 0 and less than 1 is introduced to smooth a parameter set to be assimilated, and the processed parameter prediction set is as follows:
in the formula (I), the compound is shown in the specification,
in order to be a smoothing factor, the method,
the smaller the value is, the weaker the smoothing effect of updating the parameters is, and when the value is equal to zero, the smoothing effect does not exist;
and
respectively a forecast set of the time parameter j at the k +1 moment and an analysis set of the time parameter j at the k moment.
The number of the assimilation collections of the model has little influence on the assimilation effect, the set number is excessively large, the calculation efficiency of the assimilation model is slowed, and the set number is excessively small, so that the state variables or the model parameters cannot be sufficiently assimilated, and the final simulation precision of the model is influenced. And optimizing parameters such as a model assimilation collection number, an observation error, a simulation error, an observation step length and the like by adopting a Root Mean Square Error (RMSE) and a variable consistency Index (IOA).
In the formula, CkIn order to be an analog value of the analog value,
for the measured value, n is the total number of data sets. The smaller the RMSE index value, the larger the IOA index value, the better the assimilation effect.
And selecting 8 sets of 30, 60, 90, 120, 200, 240, 300 and 500 to perform model assimilation trial calculation, and evaluating assimilation results under different sets by using RMSE indexes and IOA indexes, namely evaluating the fitting degree between the assimilated state variables and observed values, so as to respectively obtain the optimal set number, observation errors, simulation errors and observation step size equivalent model parameters of the hydrodynamic model and the water quality model.
The working principle and the process of the invention are as follows: aiming at the characteristics of multiple parameters and slow rate of a two-dimensional lake hydrodynamic water quality model, the sensitivity of lake hydraulic parameters is analyzed by using a standard rank regression and Latin sampling method, so that important characteristic hydraulic parameters are identified, and the parameter rate efficiency of the two-dimensional lake hydrodynamic water quality model is improved; meanwhile, aiming at the problem of simulation precision of the lake two-dimensional hydrodynamic water quality model, the lake hydrodynamic model and the water quality model are assimilated by adopting an integrated Kalman filtering method, so that the fine simulation of the water quality evolution process of the lake with the complex water system is realized. Firstly, collecting lake regional weather, river network conditions, boundary condition data, lake water level, runoff in and out and water quality data; then, constructing, rating and verifying a lake hydrodynamic water quality model; then carrying out lake hydrodynamic water quality model assimilation; and finally, performing dynamic fine simulation on the lake water level and the water quality.
The invention has the beneficial effects that:
(1) the invention relates to a dynamic refined simulation method for water level and pollutant migration of a lake with a complex water system, which is suitable for ecological protection and water resource comprehensive management of lakes with complex water system connectivity and multiple functional requirements.
(2) The invention has the advantages that an assimilation model for the complex water system lake is established, the improvement of the simulation method for the lake water level and the pollutant change process is realized, a decision maker can select reasonable regulation and control measures timely and accurately, the efficient utilization of lake water resources is facilitated, and method support is provided for the multipurpose complex water system lake water resource optimization scheduling scheme.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (8)
1. A dynamic simulation method for the water level and the pollutant migration of a complex water system lake is characterized by comprising the following steps:
s1: collecting lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s2: constructing a lake hydrodynamic water quality model according to collected lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s3: calibrating and verifying the lake hydrodynamic water quality model;
s4: assimilating the calibrated and verified lake hydrodynamic water quality model;
s5: and dynamically simulating the lake water level and the water quality by utilizing the assimilated lake hydrodynamic water quality model.
2. The dynamic simulation method of the water level and the pollutant migration of the complex water system lake according to claim 1, wherein the step S2 comprises the following sub-steps:
s21: carrying out hydraulic parameter identification based on lake topographic and geomorphic data, river network data, boundary condition data, lake water level, runoff in and out, water quality data, lake region meteorological data and hydrological data;
s22: building a lake two-dimensional hydrodynamic model and a lake water quality model based on the hydraulic parameters;
s23: and converting the two-dimensional lake hydrodynamic model by adopting an orthogonal curve coordinate, and taking the converted lake hydrodynamic model and the converted lake water quality model as a lake hydrodynamic water quality model.
3. The method for dynamically simulating the water level and the pollutant migration of a complex water system lake according to claim 2, wherein in the step S21, the specific method for identifying the hydraulic parameters is as follows: sampling from the acquired data by utilizing a Latin hypercube sampling method, calculating a decisive coefficient of the sampled data by utilizing a standard rank stepwise regression method, and using a parameter of which the decisive coefficient is greater than a set threshold value to construct a lake two-dimensional hydrodynamic water quality model to finish hydraulic parameter identification; the calculation formulas of the Latin hypercube sampling method and the standard rank stepwise regression method are respectively as follows:
wherein Q ishA random number representing the h' th subinterval in the collected data, and Q representing [0,1 ] in the collected data]Uniformly distributed random numbers in between, N represents the number of subintervals, R2The coefficient of certainty is represented by a coefficient of certainty,
a regression analysis total variance representing the output target value, V representing the total variance of the output target value;
in step S22, the expression of the lake two-dimensional hydrodynamic model is:
where ζ represents the lake depth, H represents the total lake depth, u represents the average flow velocity along the x-axis, v represents the average flow velocity along the y-axis, t represents the duration, g represents the gravitational acceleration, C represents the metabolic coefficient, axRepresents the viscosity of the vortex along the x-axis, p represents the static pressure, f represents the coriolis force coefficient, and f is 2 ω sin Φ; f. ofWDenotes the wind resistance coefficient, W denotes the wind speed 10m above the lake surface, WxRepresenting the wind speed along the x-axis 10m above the lake surface, AyDenotes the vortex viscosity, W, along the y-axisyThe wind speed at 10m above the water level of the lake along the y axis is shown, and h represents the water depth below the reference level of the lake;
in step S22, the expression of the lake water quality model is:
wherein p represents the concentration of the pollutants, k represents the lake degradation coefficient, DxDenotes the diffusion coefficient along the x-axis, DyThe diffusion coefficient along the y axis is shown, S is a pollution source item for displaying the pollution load of the lake, and HF (p) is a pollutant concentration change process;
in step S23, the expression of the orthogonal curve coordinate is:
wherein x isξThe transformed coordinate, y, of the Cartesian coordinate x representing the irregular area Ω on the new coordinate xi- ηξThe transformed coordinate of Cartesian coordinate y representing the irregular area Ω on the new coordinate ξ - η, gξRepresenting the side length of a zeta axis of an orthogonal grid in a zeta-eta coordinate system;
in step S23, the expression of the lake water power model is:
wherein, gηRepresenting side lengths, A, of the eta axes of an orthogonal grid in a xi-eta coordinate systemξIndicating the viscosity of the vortex along the xi axis, AηIndicating the viscosity of the vortex along the η axis.
4. The method for dynamically simulating the water level and pollutant migration in a complex water system lake according to claim 2, wherein the specific method for calibrating and verifying the lake hydrodynamic model in the step S3 is as follows: calibrating hydrodynamic parameters of the lake hydrodynamic model by using the daily water level observed quantity of the lake water level station length series; calculating the simulation precision of the lake water dynamic model by using a Nash efficiency coefficient method, and verifying the reliability of the lake water dynamic model; the hydrodynamic parameters of the lake hydrodynamic model comprise lake roughness, a wind dragging force coefficient and a wind resistance coefficient.
5. The method for dynamically simulating the water level and the pollutant migration of a complex water system lake according to claim 2, wherein in the step S3, the specific method for calibrating and verifying the water quality parameters of the lake water quality model comprises the following steps: taking the longitudinal diffusion coefficient, the transverse diffusion coefficient, the comprehensive attenuation coefficient of characteristic pollutants, the dry water depth and the wet water depth of the lake as the water quality parameters of the lake water quality model, and utilizing the monitoring data of the pollutant concentration of the lake water quality station to calibrate the water quality parameters of the lake water quality model; according to the daily pollutant concentration observation data of the lake water quality station length series, the simulation precision of the lake water quality model is calculated by using a Nash efficiency coefficient method, and the reliability of the lake water quality model is verified.
6. The method for dynamically simulating the water level and pollutant migration in a complex water-based lake according to claim 5, wherein in step S3, a Nash efficiency coefficient is calculated by using a Nash efficiency coefficient method, and the Nash efficiency coefficient E is calculatednsAs the simulation precision, the calculation formula is as follows:
wherein Q iss,iRepresents the ith observation, Qm,iThe (i) th analog value is represented,
represents the observed mean.
7. The method for dynamically simulating the water level and pollutant migration in a complex water system lake according to claim 2, wherein in the step S4, the specific method for assimilating the lake hydrodynamic model is as follows: the lake water level and the lake flow are used as state variables, the lake roughness and the wind drag force coefficient are used as parameters needing assimilation, the lake measuring station water level value and the flow value are used as observed values, and the state variables and the parameters needing assimilation of the lake hydrodynamic model are assimilated through the lake measuring station water level value and the flow value by using an ensemble Kalman filtering method.
8. The method for dynamically simulating the water level and pollutant migration of a complex water system lake according to claim 2, wherein in the step S4, the specific method for assimilating the lake water quality model comprises: taking the lake characteristic pollutants as state variables, taking the comprehensive attenuation coefficient and diffusion coefficient of the pollutants as parameters needing assimilation, taking the pollutant concentration value of a lake water quality station as an observed value, and assimilating the state variables and the parameters needing assimilation of the lake water quality model by using the pollutant concentration value of the lake water quality station through an ensemble Kalman filtering method.
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