CN107145678B - Method for calibrating roughness of river channel plane two-dimensional water flow model - Google Patents
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Abstract
The invention discloses a method for calibrating the roughness of a two-dimensional water flow model of a river channel plane, which comprises the steps of firstly defining roughness zones according to the characteristics of the river channel plane and assigning initial values to the roughness in each zone; selecting the current flow rate of which the roughness is to be calibrated and the corresponding river reach outlet water level; carrying out hydrodynamic calculation by using a river channel plane two-dimensional water flow mathematical model; determining the error between the model calculated value and the measured value of the water level of each monitoring point; judging whether the water level error is small enough; determining a water passing area according to the water depth, and estimating the water level error of each grid point in the water passing area by the water level error interpolation of each monitoring point; adjusting the roughness values of the grid points of the water passing area by a bisection method according to the water level errors of the grid points in the water passing area; further judging whether all the waiting rate fixed flow rates are calibrated; if yes, the roughness rating is completed, and the result of the roughness rating is stored. The method can reduce the man-made interference in the iterative trial calculation process and overcome the defects of unclear flow, harsh conditions, difficult application and the like in the prior art.
Description
Technical Field
The invention relates to the technical field of river dynamics research, in particular to a method for calibrating the roughness of a two-dimensional river channel plane water flow model.
Background
Roughness is an important parameter of a two-dimensional water flow mathematical model (hereinafter referred to as a "two-dimensional water flow model") on a river channel plane, the two-dimensional water flow model can be used for calculating factors such as flow velocity, water level and water depth of a natural river, and the hydraulic factors can be obtained to provide hydraulic conditions for solving the problems of water conservancy, ecology, environment and the like. The two-dimensional water flow model is realized on a computer, is called as river channel plane two-dimensional water flow mathematical model software, the calculation process is essentially a process of solving a discrete plane two-dimensional shallow water equation, besides initial conditions and boundary conditions are required to be given, relevant parameters are also required to be given, wherein the roughness is an important parameter of the two-dimensional water flow model, the river channel roughness is not only related to the roughness of a bed surface, but also related to the river flow plane shape, sediment forming accumulation body and water flow characteristics, and is a comprehensive hydraulic friction coefficient, and the parameter directly determines the rationality of a model calculation result.
In the prior art, three methods are mainly used for calibrating the roughness of a two-dimensional water flow model of a river channel plane: the method comprises the steps of iterative trial algorithm, empirical distribution method and theoretical calculation method. However, the three methods have the defects of unclear flow, harsh conditions, difficult application and the like, no experience or theoretical formula can directly calculate the roughness distribution of the planar two-dimensional bed surface at present, and the traditional iterative trial calculation process mainly depends on manual intervention, has no certain rule and strong subjectivity, and roughness values obtained by different personnel in a ratio are different even if the same model is used for processing the same river reach.
Disclosure of Invention
The invention aims to provide a method for calibrating the roughness of a two-dimensional water flow model of a river channel plane, which can reduce artificial interference in an iterative trial calculation process and overcome the defects of unclear flow, harsh conditions, difficult application and the like in the prior art.
The embodiment of the invention provides a method for calibrating the roughness of a two-dimensional water flow model of a river channel plane, which comprises the following steps:
step 1: defining roughness partitions according to the characteristics of the river channel plane, and assigning initial values to the roughness in each partition by using a roughness initial value function;
step 2: selecting the current flow of which the roughness is to be calibrated and the corresponding river reach outlet water level, and using the current flow as a trial calculation input condition of a river course plane two-dimensional water flow mathematical model;
and step 3: carrying out hydrodynamic calculation by using a river channel plane two-dimensional water flow mathematical model according to the trial calculation input conditions to obtain model calculation values of the water levels of all monitoring points;
and 4, step 4: determining the error between the model calculated value and the measured value of the water level of each monitoring point;
and 5: judging whether the water level error of each monitoring point in the step 4 is small enough; if yes, executing step 8; if not, executing the step 6;
step 6: determining a water passing area according to the water depth, and estimating the water level error of each grid point in the water passing area by the water level error interpolation of each monitoring point;
and 7: determining the adjustment direction of the roughness according to the size and the sign of the water level error of each grid point in the water passing area, adjusting the roughness values of the grid points in the water passing area by a bisection method, and returning to the step 3 for processing;
and 8: further judging whether all the waiting rate fixed flow rates are calibrated; if yes, executing step 9; if not, returning to the step 2, and carrying out roughness rating of the next flow level;
and step 9: the roughness rating was completed and the results of the roughness rating were saved.
According to the technical scheme provided by the invention, the method can reduce the artificial interference in the iterative trial calculation process, overcomes the defects of unclear flow, harsh conditions, difficult application and the like in the prior art, and improves the roughness calibration efficiency while ensuring the reasonable roughness value of the two-dimensional water flow model in the river plane.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for calibrating roughness of a two-dimensional river plane water flow model according to an embodiment of the present invention;
fig. 2 is a schematic diagram of water levels at two monitoring points in an example of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the present invention will be further described in detail with reference to the accompanying drawings, and as shown in fig. 1, a schematic flow chart of a method for rating the roughness of a two-dimensional river channel plane water flow model provided by the embodiment of the present invention is shown, where the method includes:
step 1: defining roughness partitions according to the characteristics of the river channel plane, and assigning initial values to the roughness in each partition by using a roughness initial value function;
in the step, the defining of the roughness partition according to the characteristics of the river channel plane is to define the roughness partition according to the bed sand composition and vegetation type factors of the river channel plane to be treated, and then to assign initial values to the roughness in each partition according to a roughness initial value function.
For natural river channels, the bed surface characteristics of river channels, islands, beaches and cardiac beaches are often different, so that roughness partitions are divided according to the bed surface characteristics, river reach satellite pictures can be referred to, and if site survey data exists, the roughness partitions can be accurately performed.
After the roughness division is carried out on the researched river reach, the initial roughness values n of different areas can be determined according to the existing hydraulic achievement0The value ranges of (A) are shown in Table 1 belowThe following steps:
TABLE 1 Natural river roughness n0Value of
After the rough rate partition is carried out, for each partition with different rough rate value intervals, the process of assigning initial values to the rough rates in each partition by using a rough rate initial value function is as follows:
the specific form of the roughness initial value function established is as follows:
in the above formula, n0(x, y) is the initial roughness value at the midpoint (x, y) of the plane; zx,yIs the bed surface elevation at point (x, y), ZmaxAnd ZminThe maximum bed surface elevation value and the minimum bed surface elevation value of the current roughness partition are respectively; n ismaxAnd nminThe maximum and minimum acceptable roughness values for the current roughness partition, respectively.
The essence of the above formula is that the elevation of the bed surface is taken as a basis, linear interpolation is carried out on the roughness of each coordinate point in a roughness partition, and the roughness values are considered to be smaller at the lower part of the elevation of the bed surface in the same roughness partition.
Step 2: selecting the current flow of which the roughness is to be calibrated and the corresponding river reach outlet water level, and using the current flow as a trial calculation input condition of a river course plane two-dimensional water flow mathematical model;
in this step, a typical flow rate is selected as the current flow rate of the roughness to be measured, and the river reach outlet water level corresponding to the flow rate is determined, and the current flow rate and the water level are known measured values, which are used as trial input conditions of the mathematical model of the two-dimensional water flow on the river course plane.
For the same overflowing area in a river reach, when the overflowing flow (water depth) is different, the represented roughness values are also different, so that the roughness values of different incoming water flows need to be considered in the calculation of a two-dimensional river plane water flow mathematical model. After typical flows with different sizes are selected as grading flows, the embodiment of the invention respectively carries out roughness rating on each flow grade, and the grading roughness corresponding to the grading flows can be used for interpolation calculation of roughness values of other flows.
And step 3: carrying out hydrodynamic calculation by using a river channel plane two-dimensional water flow mathematical model according to the trial calculation input conditions to obtain model calculation values of the water levels of all monitoring points;
and 4, step 4: determining the error between the model calculated value and the measured value of the water level of each monitoring point;
in the step, the specific process is as follows: after the model calculation value of the water level of each monitoring point is obtained, the model calculation value is compared with the actually measured water level of each monitoring point, and an error value between the model calculation value and the actually measured water level is calculated.
And 5: judging whether the water level error of each monitoring point in the step 4 is small enough; if yes, executing step 8; if not, executing the step 6;
step 6: determining a water passing area according to the water depth, and estimating the water level error of each grid point in the water passing area by the water level error interpolation of each monitoring point;
in the step, only the roughness of the water passing area influences the water level of the monitoring point, so that the water passing area under the current flow condition can be determined according to the water depth value output in the trial calculation process of the two-dimensional water flow model, and thus, the roughness adjusting area on the river channel plane can be accurately determined.
The water level error of each grid point is the basis of roughness adjustment, and because only the monitoring point has the calculated error value of the water level, and the water level errors of other non-monitoring points in the water passing area need to be interpolated and estimated by using a two-dimensional interpolation method, the embodiment of the invention adopts an inverse distance weighting method to estimate the water level error of each grid point in the water passing area, and the specific calculation formula is as follows:
in the above formula, e0Is an estimate of the water level error at non-monitored points in the water passing region, eiThe water level error calculation value of the ith monitoring point of the water passing area is obtained, and I is the total number of the monitoring points in the water passing area; d0,iIs the distance between the currently processed non-monitoring point and the ith monitoring point; k is an index whose value is such that e0The estimation error of (2) is small, and k can be 1 in the practical application process.
And 7: determining the roughness adjusting direction according to the size and the sign of the water level error of each grid point in the water passing area, adjusting the roughness value of the grid point in the water passing area by a bisection method, and returning to the step 3 for processing;
in this step, after obtaining the water level error of each grid point in the water passing region, the roughness value of each grid point in the water passing region may be calibrated by using a dichotomy roughness adjustment formula, where the dichotomy roughness adjustment formula is as follows:
in the above formula, nx,yRepresents the roughness value at the current point (x, y), and k +1 in the superscript represent the number of iterations; n isi,minRepresents the minimum advisable roughness value of the ith roughness partition to which the current point (x, y) belongs; n isi,maxRepresenting the maximum admissible roughness value of the i-th roughness partition to which the current point (x, y) belongs;
when the calculated value of the water level is higher, the point roughness is reduced; when the calculated water level value is lower, the point roughness is increased.
And after the roughness values of all the points in the water passing area are adjusted, repeating the steps 3-7 until the water level calculation errors of all the monitoring points meet the precision requirement under the current flow rate condition.
And 8: further judging whether all the waiting rate fixed flow rates are calibrated; if yes, executing step 9; if not, returning to the step 2, and carrying out roughness rating of the next flow level;
and step 9: the roughness rating was completed and the results of the roughness rating were saved.
The following detailed description will be made of the application of the above calibration method by specific examples:
firstly, a plane two-dimensional water flow mathematical model of a bending branch river reach is established, two monitoring points exist in the river reach, and then water levels and corresponding flow rates of different scenes in the river reach are calculated, as shown in the following tables 2 and 3:
TABLE 2 calculation of design flood levels in river reach
TABLE 3 calculation of river reach design flood flow
After the calculation conditions are complete, the roughness of each level of flow in table 3 is calibrated by the method described in the embodiment of the invention. The water levels at the two monitoring points under each flow are calculated by a well-calibrated model, as shown in fig. 2, which is a schematic diagram of the water levels at the two monitoring points in the example of the present invention, as can be seen from fig. 2: after the roughness is rated by the method of the embodiment of the invention, the calculated values of the water levels of the monitoring points 1 and 2 are basically consistent with the measured values, which shows that the method for rating the roughness of the two-dimensional water flow model of the river channel plane is feasible.
In summary, the method of the embodiment of the present invention has the following advantages:
(1) the method has clear process for rating the roughness, loose conditions and easy implementation, can realize the roughness rating by a machine, has less artificial interference, and greatly reduces the subjectivity of manual trial calculation;
(2) according to the method, the roughness of the plane river channel is divided into regions according to the characteristics of the bed surface, the roughness of each region is selected from an initial value and is rated in a roughness reasonable value range specified by hydraulics, and the reasonability of the rated roughness can be comprehensively ensured;
(3) after each round of trial calculation, the water passing area is determined according to the water depth information, the adjustment space of the roughness can be accurately determined, the calculated amount is greatly reduced, meanwhile, a dichotomy roughness adjustment formula is provided based on the monotonic relation between the roughness and the water level, and the convergence speed is higher.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (6)
1. A method for calibrating roughness of a two-dimensional water flow model of a river channel plane is characterized by comprising the following steps:
step 1: defining roughness partitions according to the characteristics of the river channel plane, and assigning initial values to the roughness in each partition by using a roughness initial value function;
step 2: selecting the current flow of which the roughness is to be calibrated and the corresponding river reach outlet water level, and using the current flow as a trial calculation input condition of a river course plane two-dimensional water flow mathematical model;
and step 3: carrying out hydrodynamic calculation by using a river channel plane two-dimensional water flow mathematical model according to the trial calculation input conditions to obtain model calculation values of the water levels of all monitoring points;
and 4, step 4: determining the error between the model calculated value and the measured value of the water level of each monitoring point;
and 5: judging whether the water level error of each monitoring point in the step 4 is smaller than a set threshold value or not; if yes, executing step 8; if not, executing the step 6;
step 6: determining a water passing area according to the water depth, and estimating the water level error of each grid point in the water passing area by the water level error interpolation of each monitoring point;
and 7: determining the roughness adjusting direction according to the size and the sign of the water level error of each grid point in the water passing area, adjusting the roughness value of the grid point in the water passing area by a bisection method, and returning to the step 3 for processing;
and 8: further judging whether all the waiting rate fixed flow rates are calibrated; if yes, executing step 9; if not, returning to the step 2, and carrying out roughness rating of the next flow level;
and step 9: the roughness rating was completed and the results of the roughness rating were saved.
2. A method for calibrating roughness of a two-dimensional river channel plane water flow model according to claim 1, wherein in the step 1, the defining of the roughness partition according to the characteristics of the river channel plane specifically comprises:
and defining a roughness zone according to the bed sand composition and vegetation type factors of the river channel plane to be treated.
3. A method for calibrating roughness of a two-dimensional river channel plane water flow model according to claim 1, wherein in the step 1, the initial roughness value function is used to assign initial roughness values to the partitions, and specifically comprises:
the specific form of the roughness initial value function established is as follows:
in the above formula, n0(x, y) is the initial roughness value at the midpoint (x, y) of the plane; z is a radical ofx,yIs the bed surface elevation at point (x, y), zmaxAnd zminThe maximum bed surface elevation value and the minimum bed surface elevation value of the current roughness partition are respectively; n ismaxAnd nminThe maximum and minimum acceptable roughness values for the current roughness partition, respectively.
4. A method for calibrating roughness of a two-dimensional water flow model of a river channel plane according to claim 1, wherein in the step 4, the determining an error between the calculated value and the measured value of the model of the water level at each monitoring point specifically comprises:
after the model calculation value of the water level of each monitoring point is obtained, the model calculation value is compared with the actually measured water level of each monitoring point, and an error value between the model calculation value and the actually measured water level is calculated.
5. A method for calibrating roughness of a two-dimensional water flow model in a river course plane according to claim 1, wherein in the step 6, the estimating of the water level error of each grid point in the water passing area by interpolation of the water level error of each monitoring point specifically comprises:
estimating the water level error of each grid point in the water passing area by adopting an inverse distance weight method, wherein the specific calculation formula is as follows:
in the above formula, e0Is an estimate of the water level error at non-monitored points in the water passing region, eiThe calculated value of the water level error of the ith monitoring point in the water passing area is obtained, and l is the total number of the monitoring points in the water passing area; d0,iIs the distance between the currently processed non-monitoring point and the ith monitoring point; k is an index whose value is such that e0The estimation error of (2) takes a small value.
6. A method for calibrating roughness of a two-dimensional river channel plane water flow model according to claim 1, wherein in the step 7, the adjusting roughness values of grid points of the water passing area by dichotomy specifically comprises:
the dichotomy roughness adjustment formula is as follows:
in the above formula, nx,yRepresents the roughness value at the current point (x, y), and k +1 in the superscript represent the number of iterations; n isi,minRepresents the minimum advisable roughness value of the ith roughness partition to which the current point (x, y) belongs; n isi,maxRepresenting the maximum admissible roughness value of the i-th roughness partition to which the current point (x, y) belongs;
when the calculated value of the water level is higher, the point roughness is reduced; when the calculated water level value is lower, the point roughness is increased.
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