CN110765676A - Watershed water quality simulation method based on stable flow field - Google Patents

Watershed water quality simulation method based on stable flow field Download PDF

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CN110765676A
CN110765676A CN201910673992.7A CN201910673992A CN110765676A CN 110765676 A CN110765676 A CN 110765676A CN 201910673992 A CN201910673992 A CN 201910673992A CN 110765676 A CN110765676 A CN 110765676A
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陈军
武国正
唐古拉
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Chengdu University of Information Technology
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Abstract

A stable flow field-based watershed water quality simulation method comprises the following steps: step S1: establishing a watershed hydrodynamic model based on a stable flow field; step S2: simulating the water quality of the drainage basin; step S1 includes executing the contents listed in 1.1 and 1.2 in sequence; 1.1 establishing a hydrodynamic model in a grid mode; 1.2 early-stage water regime simulation based on a stable flow field; step S2 includes executing the contents listed in 2.1 and 2.2 in sequence; 2.1 decomposing the two-dimensional finite difference water quality model; 2.2 coupling the water quality model with the hydrodynamic model. The simulation method provided by the invention has the advantages that the simulation precision of the two monitoring sections in practical application reaches more than 85%, and the result can be used for practical river water quality simulation.

Description

Watershed water quality simulation method based on stable flow field
Technical Field
The invention relates to water quality simulation, and has wide application prospects in the aspects of regional disaster prevention and reduction, water pollution control, water environment health assessment, watershed water resource planning and the like.
Background
As a powerful tool for water pollution control, water environment health assessment and watershed water resource planning, a watershed water quality model is always a hot point of research at home and abroad. The water quality model is also called a water quality mathematical model and is a mathematical description of the change rule of the water quality of the water body. It can be used for predicting water quality, researching river pollution and self-purification and controlling pollution discharge. The water quality model can be divided into zero-dimensional, one-dimensional, two-dimensional and three-dimensional models according to the space dimension. Since the zero-dimensional model generalizes the studied environmental unit to a fully mixed reactor without involving information about hydrodynamics, only rough planning estimates can be made for regional water quality; the three-dimensional water quality model comprises the changes of water quality and water flow parameters along the vertical direction, the lateral direction and the longitudinal direction, the simulation process is complex, and the simulation application of the water quality of a general river is less. The two-dimensional model considers the pollutant diffusion in two coordinate directions, is very suitable for pollutant diffusion simulation of large rivers in a drainage basin, is always a research focus of various pollution transmission, and forms a large number of research results at home and abroad.
The SWAT model developed by Jeff Arnold doctor, the agricultural research center of the United States Department of Agriculture (USDA) uses daily time-continuous calculations. The SWAT simulated watershed hydrological process is divided into a land phase (i.e., runoff producing and slope converging portions) of hydrologic cycle and a converging phase (i.e., river converging portion) of hydrologic cycle. The former controls the input amount of water, sand, nutrient substances, chemical substances and the like of the main riverway in each sub-river basin; the latter determines the transportation and movement of materials such as water, sand and the like from the river network to the outlet of the drainage basin. However, the mode of substituting the years of precipitation data into the waterless watershed for repeated iteration by using the SWAT model and taking the final output of the model as the watershed early-stage water regime has the problems of large calculation amount and iteration of simulation errors.
The EFDC (the Environmental Fluid Dynamics code) model is a three-dimensional surface water quality mathematical model developed by John Hamrick and the like of Virginia ocean science research institute of William Mary university, can realize hydrodynamics and water quality simulation of water bodies such as rivers, lakes, reservoirs, wetland systems, estuaries, oceans and the like, and is a multi-parameter finite difference model. The model system comprises modules of hydrodynamic force, silt, toxic substances, water quality, bottom materials, wind waves and the like, wherein flow field calculation is firstly completed in the simulation calculation process to obtain the space-time distribution characteristics of a three-dimensional flow velocity field, and the migration and erosion functions of the silt are calculated on the basis, so that the dynamic change process of various water quality variables influenced by the adsorption of the viscous silt is simulated. The EFDC model requires the input of water depth and contaminant concentration data at all locations in the river. However, because it is difficult to obtain the water depth and concentration at all positions of the river, the water depth and concentration are mainly obtained by interpolation of spatially discrete observation points. The error of spatial interpolation becomes the main source of early stage regimen error in the method. For example, the chinese invention patent with application number 201310066807.0 discloses a watershed hydrology and water quality monitoring system and method based on the internet of things under the influence of hydraulic engineering, which obtains real-time data of the hydrology and water quality of key water areas by additionally installing various fixed and flowing sensors, monitors the field environment by matching with a video technology, transmits monitoring information by using the internet of things, carries out intelligent prediction of the watershed hydrology and water quality through a neural network, and finally realizes key applications such as current situation evaluation, trend evaluation, implementation effect evaluation, extreme event processing and the like through an expert system. The invention can provide real-time, reliable and complete hydrological and water quality information for the watershed under the influence of hydraulic engineering, and realizes the integrated remote protection of the watershed across-region and multi-model. But the simulation of the early stage water regime of the basin has larger error, and the water quality spatial distribution and the time change of the whole river channel cannot be obtained through simulation. .
Disclosure of Invention
The invention provides a stable flow field-based watershed water quality simulation method, which comprises the following steps:
step S1: establishing a watershed hydrodynamic model based on a stable flow field;
step S2: simulating the water quality of the drainage basin;
wherein, step S1 includes executing the contents listed in 1.1 and 1.2 in sequence;
preferably, 1.1 establishing a hydrodynamic model in a grid mode;
1.2 early-stage water regime simulation based on stable flow field
Step S2 includes executing the contents listed in 2.1 and 2.2 in sequence;
preferably, the decomposition of the 2.1 two-dimensional finite difference water quality model;
2.2 coupling the water quality model with the hydrodynamic model;
preferably, the 1.1 includes water balance statistics, advection item simulation, pressure item simulation, external force item simulation, and basin runoff simulation on a time slice.
Preferably, the hydrodynamic model is guided by the Navier-Stokes equation (N-S equation). The N-S equation decomposes fluid motion into advection, pressure and external force terms.
In grid mode, the runoff simulation divides the watershed into equal segments both spatially and temporally. In space, dividing a drainage basin into rectangular meshes with equal sizes according to a certain resolution, and storing and representing the rectangular meshes by adopting grid data of a GIS (geographic information system); in time, the radial flow confluence process is broken up into equally spaced time slices. And on each time slice, the runoff confluence process of the basin is decomposed into simulation calculation with the grid unit as a basic unit, and the simulated water depth and water speed of the grid unit of the previous time slice are used as the initial water depth and water speed of the next time slice. And (4) realizing hydrodynamic simulation of the watershed through iteration of the time slices.
The time slice refers to a time interval represented by one frame of basin water quality simulation. Over a time slice, the water flow and contaminants of each simulation grid spread only into the 8-neighborhood simulation grid.
Let the time slice sequence number be n, the time slice time series t is expressed as formula (1):
t＝{tnn≥1} (1)
the adjacent time slice time difference Δ t is represented by formula (2):
Δt＝tn+1-tn(2)
for any grid cell in the watershed, it is denoted r in the simulation, and its 8-neighborhood grid is denoted b. Grid cell runoff simulation on a time slice is performed as follows:
i water balance
The main sources of water flow of the grid unit are upstream incoming water and precipitation supply; water flow disbursements include downstream sluicing, infiltration, and evaporation. Let tnThe depth of water of the central grid r at the moment
Figure BSA0000186497110000031
The precipitation, the infiltration, the evaporation, the inflow and the outflow on the time slice are respectively
Figure BSA0000186497110000032
And
Figure BSA0000186497110000033
according to the principle of water balance, tn+1Temporal center grid depthIs represented by the formula (3):
in the model, the main stream inflow point and the branch stream inflow sink directly input the flow, so that the flow is ignored
Figure BSA0000186497110000036
An item;
Figure BSA0000186497110000037
setting the infiltration rate and evaporation rate according to the underlap property, and
Figure BSA0000186497110000038
multiplying to obtain;
Figure BSA0000186497110000039
and
Figure BSA00001864971100000310
and calculating according to the water flow velocity vectors of the central grid and the neighborhood grid, and particularly realizing in an advection item link.
II advection term simulation
The advection term indicates that the fluid itself and properties migrate with velocity. And under the grid mode, simulating an advection term by adopting a multi-flow method. Let the water velocity vector of the neighborhood grid b be
Figure BSA00001864971100000311
The ratio S of the amount of water flowing into the center grill rb→rIs represented by formula (4):
Figure BSA00001864971100000312
wherein (Δ x, Δ y) is the deviation of the neighborhood grid coordinate from the central grid coordinate, and the unit is pixel; v. ofmaxRepresenting the maximum velocity scalar allowed over the time slice.
Residual water ratio S of central gridrIs represented by formula (5):
Figure BSA00001864971100000313
according to the mass conservation law, the depth of the central grid water after advection calculation is expressed by the formula (6):
Figure BSA00001864971100000314
in the formula (I), the compound is shown in the specification,
Figure BSA00001864971100000315
representing a central grid tnAnd tn+1The water depth at that moment;
Figure BSA00001864971100000316
representing a neighborhood grid tnThe water depth at that moment;
Figure BSA00001864971100000317
respectively represent tnThe proportion of water quantity flowing into the central grid r from the neighborhood grid b at the moment;represents tnAnd (4) the residual water quantity proportion of the central grid at the moment.
According to the law of conservation of momentum, the water velocity of the central grid after advection calculation
Figure BSA00001864971100000319
Is represented by the formula (7):
Figure BSA00001864971100000320
in the formula (I), the compound is shown in the specification,
Figure BSA00001864971100000321
and
Figure BSA00001864971100000322
respectively represent tnThe water velocity of the time center grid r and the neighborhood grid b.
According to the formula (4) and the formula (5), when the water velocity of the simulation grid is equal to vmaxAnd when the water flows out, the grid water flow on the time slice flows out completely. To ensure the model operates normally, a fixed v is set for the basinmaxAnd the water velocity at any position of the watershed is considered to be less than or equal to vmax. In the actual simulation, when the water speed exceeds vmaxWhen it is set to vmax. Thus, vmaxThe time slice interval for water quality simulation is determined, as shown in formula (8):
according to equation (8), the number of time slices N to be iterated per hour is equation (9):
III pressure term simulation
During the migration of water flow along with the speed, pressure gradient force is generated inside the water flow due to different water pressures. The pressure gradient force adopts an 8-neighborhood approximate calculation method. Let the height of the central grid be HrElevation of neighborhood grid is HbThen the height difference of water body is delta HbIs represented by the formula (10):
Figure BSA0000186497110000043
the velocity vector increment Δ V generated by the neighborhood grid to the center grid on the time slice is represented by equation (11):
in the formula, α is a positive constant relating to water density, gravitational acceleration, frictional force, and the like, and is calibrated by actual hydrological data of the watershed.
IV external force term simulation
As surface water flows on a slope or a riverbed, surface runoff is subjected to surface friction, acting force of adjacent water masses and the like besides the action of gravity. Wherein, gravity is the basic power of runoff, and under the action of gravity, rivers flow from the eminence to low. The water flow flows from one grid to the other grid, and the gravitational potential energy is partially converted into kinetic energy after the height of the water surface is reduced, which is expressed as the increase of the water flow speed; the kinetic energy is converted into gravitational potential energy after the water surface height rises, and the gravitational potential energy is expressed as the reduction of the water flow speed and even the reverse flow. The hydraulic acceleration generated by gravity and the hydraulic acceleration generated by pressure are uniformly expressed by formula (11), namely, the coefficient a in the formula integrates factors such as gravity factor and pressure.
The surface water flow is influenced by the surface friction force, so that the water flow speed is vertically changed. In the runoff confluence simulation process, when the water depth is lower than a given threshold value, the water speed is multiplied by an attenuation coefficient to reduce the water speed. Setting the upper bound depth d of water flow frictionmax(in m) and a lower bound depth of dmin(in m), the attenuation coefficient ε is approximately defined by the equation (12):
Figure BSA0000186497110000051
wherein sigma is a friction proportion coefficient, and the calibration is carried out through actual hydrological data of the basin.
Basin runoff simulation on V time slice
In one time slice, basin runoff simulation is carried out in two steps. First, water balance and hydrodynamic simulation. Firstly, calculating the water yield of each grid unit, then performing pressure item and external force item simulation, and calculating the new water depth and water speed of each grid unit; and secondly, simulating advection terms. And performing water flow migration calculation on the basis of the new water depth and the water speed of the grid unit obtained in the first step, wherein the obtained water depth and water speed are used as the initial water depth and water speed of the next time slice.
Preferably, said 1.2 comprises:
first, the basic assumption of a stable flow field is given: namely, assuming that a basin has a plurality of water source points and the flow rate is constant, the water depth and the water speed at the outlet of the basin finally tend to be stable through continuous iteration of the runoff confluence model. The watershed water flow field at this time is called a steady flow field.
Obviously, no stable water source exists in reality, and a stable flow field cannot exist. But at a specific time point, instantaneous flow exists at a main flow inflow point, a branch flow inflow and convergence point and a sewage discharge point on the main flow channel of the drainage basin. If the instantaneous flow of each water source point at the starting moment of the simulation time period is used as the stable water supply amount, the stable flow field created through the model iteration can be approximately used as the early-stage water regime of the simulation time period.
I hydrodynamic model perfection
Equation (12) uses the water height difference as the only basis for the velocity increment. In a river channel area with unsmooth flowing water, if the simulated water speed is too high, the upstream grid water flow is quickly gathered to the central grid, and the central grid water flow cannot flow downstream in time, so that a large water body height difference is generated in a short time, and further a large speed increment is generated for 8 surrounding grids. Along with the increase of the iteration times, the water flow direction is easy to be abnormal at the positions, and even the phenomenon that the flow velocity directions of adjacent upstream and downstream grids are opposite and frequently alternate occurs, so that the water depth and the water velocity are changed violently. Table 1 shows the grid water velocity and water depth variation over a typical time slice for a grid unit in a region with poor flowing water flow before model completion. As can be seen from table 1, the existing model violates the real runoff convergence rule and cannot accurately simulate the hydrodynamic process of the watershed. Even under stable water supply conditions upstream of the watershed, it is difficult to generate a stable water flow field.
To avoid the above problem, a water flow mixing simulation is added to the model. The water flow mixing simulation comprises two steps of grid unit water speed increment correction and neighborhood grid unit water flow mixing simulation, wherein:
A. grid cell water velocity increment correction
The water velocity increment is reduced after the grid water flow with the water depth of more than 1m is mixed with the surrounding water mass and is in an inverse proportion to the water depth. The correction formula is formula (13):
Figure BSA0000186497110000061
table 1 typical grid water velocity and depth changes before and after model completion
Figure BSA0000186497110000062
B. Neighborhood grid cell water flow mixing simulation
Assuming that each grid cell is mixed with 8 neighborhood grid water flow in each time slice, the momentum conservation law is followed in the mixing process. First, the total momentum and the total water quantity of the central grid and the 8-neighborhood grid are calculated and are divided to obtain the water velocity after the water flow of the central grid is mixed.
C. Runoff confluence simulation process after hydrodynamic model is complete
The runoff confluence simulation after the hydrodynamic model is completed is carried out in three steps, namely water yield balance and hydrodynamic simulation, advection item simulation and water flow mixed simulation. The incremental correction of the water speed of the grid unit is integrated into a first simulation link, and after the hydrodynamic simulation is completed, the new water speed is corrected according to the formula (13); the water flow mixing simulation of the neighborhood grid unit is used as an independent simulation link and is carried out after the advection item simulation is finished.
As can be seen from table 1, after the model is completed, the water flow of the grid unit is continuously accumulated, the water depth is stably increased, the water speed is gradually reduced, the water flow direction is kept stable, and a foundation is laid for establishing a stable flow field.
II early-stage water regime simulation based on stable flow field
Let the water supply amount of a certain water source point be ξ (unit is m)3And/s), the unit of the grid at the position is r, the water yield of the grid r is modified from the formula (3) to the formula (14):
Figure BSA0000186497110000063
in the formula, ξrThe water quantity of the water source point grid on the time slice meets the following requirements:
Figure BSA0000186497110000064
it is apparent that ξ for the mainstream flow point, the branch inflow sink and the blowdown pointrGreater than or equal to 0, and ξ for water intakerIs less than or equal to 0.
In the process of creating the stable flow field, whether the stable flow field is created is quantitatively described by using equation (16).
Figure BSA0000186497110000071
In the formula, W is the depth of the outlet control point of the basin, n is the number of hours of current simulation, h is the number of hours of forward pushing, and A is the accumulated error threshold.
In order to objectively simulate the basin early-stage water regime, a flow sequence which is several hours before a simulation time period is input at a water source point according to the basin confluence time, and a water flow field is established through model iteration to serve as the basin early-stage water regime. In the early stage water regime simulation process of the drainage basin, firstly substituting the first hour flow of the early stage water source point flow sequence into a model to serve as upstream stable water supply, and creating a stable flow field of the drainage basin; on the basis, the upstream flow sequence of the early water source point is iterated hour by hour to simulate the early water regime of the basin.
Preferably, the decomposition of the 2.1 two-dimensional finite difference water quality model comprises:
assuming that there is a volume infinitesimal
Figure BSA0000186497110000072
This volume element has inputs and outputs along the longitudinal (x-axis) and transverse (y-axis) directions. The two-dimensional differential equation for the propagation of a contaminant in a body of water is as follows:
Figure BSA0000186497110000073
in the formula (17), the compound represented by the formula (I),
Figure BSA0000186497110000074
the average contaminant concentration of the microcell (i, j);
Figure BSA0000186497110000075
expressed as diffusion coefficients in x and y directions, respectively, in km2/h；ui，jAnd vi，jRepresenting the water flow velocity in the x and y directions; k is a radical ofi，jRepresents the contaminant degradation coefficient in units of 1/d.
As can be seen from the formula (17), the center infinitesimal tn+1The concentration of the contaminant at the moment is equal to the infinitesimal tnThe pollutant concentration at the moment is added with the pollutant concentration increased from the neighborhood infinitesimal due to diffusion and water flow inflow in unit time, the pollutant concentration reduced by the central infinitesimal due to diffusion and water flow outflow is subtracted, and then the pollutant loss caused by degradation is subtracted.
Preferably, the coupling of the 2.2 water quality model and the hydrodynamic model comprises:
under the grid mode, the volume infinitesimal of the two-dimensional finite difference water quality model is a grid unit. The model is solved step by step according to water yield balance, advection item simulation and water flow mixing simulation, and is the key of coupling of a water quality model and a hydrodynamic model.
Water quality simulation in I water yield balance process
In water quality simulation, the water source point is not only the supply point of the water flow, but also the supply point of the pollutant. And setting the sewage discharge concentration of the water source point to be delta (the unit is mg/l), wherein the output concentration on the time slice after the water source point discharges sewage is expressed as a formula (18):
Figure BSA0000186497110000076
in the formula (I), the compound is shown in the specification,
Figure BSA0000186497110000081
respectively represent tnAnd tn+1The contaminant concentration of the central grid at the time;
Figure BSA0000186497110000082
is tnThe concentration of the blowdown of the center grid at that time.
In the water balance calculation, the pollutant degradation is also considered. The pollutant degradation coefficient is measured in days, and needs to be converted into the degradation rate of the pollutant in a time slice. Let the contaminant degradation coefficient be a constant k in the flow domaindThen in time slice tnOn the rate of degradation of contaminants knIs represented by formula (19):
kn＝1-(1-kd)1/(24×N)(19)
combining formula (18) and formula (19), the pollutant output concentration in the water yield balance process is formula (20):
Figure BSA0000186497110000083
pollutant migration calculation in II advection item simulation process
In the advection term, the grid cells and the neighborhood grid exchange water according to the water speed. Assuming that the central grid and the neighborhood grid pollutants are fully mixed in the water flow migration, the grid pollutant concentration output by advection term simulation is formula (21) according to the mass conservation law:
in the formula (I), the compound is shown in the specification,
Figure BSA0000186497110000085
for the neighborhood grid b at tnThe contaminant concentration at the moment.
III pollutant diffusion simulation of water flow mixing simulation
Pollutant diffusion is simulated in a water flow mixing link. In equation (17), the central grid r diffuses towards the neighborhood grid b, resulting in a reduction of central grid contamination; the neighborhood grid b diffuses towards the center grid r, resulting in an increase in center grid contamination. In the model, the pollutant diffusion coefficient is set to be a constant E, and the actual migration amount of pollutants caused by diffusion of two adjacent grid units is related to the concentration difference of the pollutants.
Regarding the water of two adjacent grid cells as a cubic water column, the height of the water column is equal to the water depth, and the pollutant diffusion is considered to occur in the overlapping region of the two water columns (figure 1), and the height W of the water columnbrIs represented by formula (22):
Wbr＝max(min(Hr+Wr，Hb+Wb)-max(Hr，Hb)，0) (22)
in order to quantitatively describe the pollutant concentration change caused by water flow mixing simulation, the constant E is converted into the outward diffusion distance E of the pollutant on a time slicenAs in formula (23):
Figure BSA0000186497110000086
combining formula (22) and formula (23), the concentration of the center grid contaminant after diffusion is listed in formula (24):
drawings
Fig. 1 is a schematic structural diagram of a pollutant diffusion overlapping area in a preferred embodiment of the stable flow field-based watershed water quality simulation method of the present invention;
FIG. 2 is a cross section and a sewage draining exit of the peony river midstream of the embodiment shown in FIG. 1;
FIG. 3 is a process for creating a stable flow field based on an initial flow rate according to the embodiment shown in FIG. 1;
FIG. 4 is a diagram illustrating the variation of ammonia nitrogen concentration during the creation of a stable flow field in the embodiment of FIG. 1;
FIG. 5 is a comparison of the simulated water level and the measured water level of the peony river two-station in the embodiment shown in the figure;
FIG. 6 is a comparison graph of the simulated concentration and the measured concentration of the water quality monitoring section of the bridge in the embodiment shown in FIG. 1;
FIG. 7 is a comparison graph of simulated concentration and measured concentration of a water quality monitoring section of a wave river section in the embodiment shown in FIG. 1;
Detailed Description
Example 1.1: a watershed water quality simulation method based on a stable flow field takes the middle trip of the peony river as a verification watershed. The peony river is the second major branch of Songhua river, originating from the peony ridge in Changbai mountain of Jilin. The river is in the north-south direction, the total length is 726km, the river width is 100-300 m, the water depth is 1.0-5.0 m, the total fall is 1007 m, and the average slope drop is 1.39 per thousand. The ice season is from 11 middle of the month to 4 middle of the month of the following year. The middle trip of the peony river takes a section of a West pavilion as a starting point, receives a sea wave river and a first steep two branches along the way, and is provided with a hydrological monitoring section (a second station of the peony river), 2 water quality monitoring sections (a section of a warm spring bridge and a section of the sea wave river) and 4 sewage outlets (a sewage outlet, a constant and rich paper industry outlet, a municipal sewage outlet and a sludge outlet of a Hualin town). The monitoring profile and the drain position are shown in fig. 2.
Collecting flow and ammonia nitrogen concentration data of each monitoring section and each drain outlet from 2012, 5, 1 and 2014, 10, 31, simulating a pollution process of the middle trip of the peony river based on topographic data of 90m of a drainage basin, and performing model precision verification by using the actually measured concentration of the water quality monitoring section.
(1) Basin stabilization flow field simulation
And taking 12-23 days 12 and 30 months 4 and 2012 as an early water environment simulation period. The instantaneous flow and concentration at the mid-trip section and the drain outlet of the peony river at 2012, 4, 30 and 12 days are shown in table 2. At vmaxThe initial flow rates of the water source points shown in table 2 were superimposed under the conditions of 2m/s, α ═ 0.12, σ ═ 0.995, h ═ 10h, and a ═ 0.05, and the flow field generation was stabilized after 200 hours of iteration, as shown in fig. 3.
At KdUnder the conditions of 0.05 and 0.08, the ammonia nitrogen concentration is gradually stabilized in the process of generating a stable flow field, as shown in fig. 4.
TABLE 2 initial time instantaneous flow and Ammonia Nitrogen concentration at various Water Source points
Figure BSA0000186497110000091
Figure BSA0000186497110000101
On the basis, flow and concentration sequences of water source points from 12 hours to 23 hours from 4 months to 30 days in 2012 are iterated hour by hour to simulate the early stage water regime of the watershed.
(2) Watershed hydrodynamic simulation
And substituting flow data of each monitoring section and each drain outlet from 2012, 5 month and 1 day to 2014, 4 month and 30 days into the hydrodynamic model to simulate the watershed hydrodynamic process. The simulated water level of the peony-river two-station grid unit hourly is collected, a water level change curve is made, and the water level change curve is compared with the actually measured water level, as shown in fig. 5.
As can be seen from the graph 5, the simulated water level and the actual measured water level of the hydrodynamic model based on the stable flow field have high goodness of fit, and a foundation is laid for improving the simulation precision of the water quality of the drainage basin.
(3) Basin water quality simulation
Interpolating the flow and concentration of the main inflow point, the branch inflow junction and the exhaust point in the simulation time period to obtain the hourly flow and concentration of each water source point. And (3) obtaining the hourly river ammonia nitrogen concentration distribution within the simulation time period by time slice iterative calculation on the basis of the stable flow field of the initial time. The hourly simulated concentration of the water quality monitoring section grid unit is collected, a concentration change curve is made, and the concentration change curve is compared with the actually measured concentration, as shown in fig. 6.
As can be seen from FIG. 6, the model achieves a relatively ideal effect on the fitting effect of the concentration variation trend of the cross section of the bridge in Wenchun and spring and the cross section of the sea wave river. Measured concentration of the cross section
Figure BSA0000186497110000102
And analog concentration
Figure BSA0000186497110000103
The degree of fit RNew is calculated according to equation (25):
Figure BSA0000186497110000104
in the formula, N is the number of the actually measured concentration sequences of the section.
The section simulation accuracy is shown in table 3. As can be seen from table 3, the simulation accuracy of both the two monitoring sections reaches 85% or more, and the results can be used for actual simulation of the river water quality.
TABLE 3 simulation accuracy of water quality monitoring section in simulation period
Figure BSA0000186497110000105

Claims (10)

1. A stable flow field-based watershed water quality simulation method comprises the following steps:
step S1: establishing a watershed hydrodynamic model based on a stable flow field;
step S2: simulating the water quality of the drainage basin;
it is characterized in that step S1 includes executing the contents listed in 1.1 and 1.2 in sequence;
1.1 establishing a hydrodynamic model in a grid mode;
1.2 early-stage water regime simulation based on a stable flow field;
step S2 includes executing the contents listed in 2.1 and 2.2 in sequence;
2.1 decomposing the two-dimensional finite difference water quality model;
2.2 coupling the water quality model with the hydrodynamic model.
2. The stable flow field based watershed water quality simulation method of claim 1, wherein: the 1.1 comprises water balance statistics, advection item simulation, pressure item simulation, external force item simulation and basin runoff simulation on a time slice.
3. The stable flow field based watershed water quality simulation method of claim 2, wherein: the hydrodynamic model is guided by the Navier-Stokes equation (N-S equation). The N-S equation decomposes fluid motion into advection, pressure and external force terms.
4. The watershed water quality simulation method based on the stable flow field as claimed in claim 3, wherein: in a grid mode, runoff simulation divides a watershed into equal segments from the space and the time; in space, dividing a drainage basin into rectangular meshes with equal sizes according to a certain resolution, and storing and representing the rectangular meshes by adopting grid data of a GIS (geographic information system); in time, the radial flow confluence process is broken up into equally spaced time slices. On each time slice, the runoff confluence process of the basin is decomposed into simulation calculation with the grid unit as a basic unit, and the simulated water depth and water speed of the grid unit of the previous time slice are used as the initial water depth and water speed of the next time slice; and (4) realizing hydrodynamic simulation of the watershed through iteration of the time slices.
5. The stable flow field based watershed water quality simulation method of claim 4, wherein: the time slice refers to a time interval represented by simulating one frame of watershed water quality; on a time slice, the water flow and contaminants of each simulation grid only diffuse into the 8-neighborhood simulation grid:
let the time slice sequence number be n, the time slice time series t is expressed as formula (1):
t＝{tnn≥1} (1)
the adjacent time slice time difference Δ t is represented by formula (2):
Δt＝tn+1-tn(2)
for any grid cell in the watershed, it is denoted r in the simulation, and its 8-neighborhood grid is denoted b.
6. The stable flow field based watershed water quality simulation method of claim 5, wherein:
grid cell runoff simulation on a time slice is performed as follows:
i water balance
The main sources of water flow of the grid unit are upstream incoming water and precipitation supply; water flow disbursement includes downstream sluicing, infiltration and evaporation; let tnThe depth of water of the central grid r at the momentPrecipitation on time slicesThe lower seepage amount, the evaporation amount, the inflow amount and the outflow amount are respectively
Figure FSA0000186497100000022
Andaccording to the principle of water balance, tn+1Temporal center grid depth
Figure FSA0000186497100000024
Is represented by the formula (3):
Figure FSA0000186497100000025
in the model, the main stream inflow point and the branch stream inflow sink directly input the flow, so that the flow is ignored
Figure FSA0000186497100000026
An item;setting the infiltration rate and evaporation rate according to the underlap property, and
Figure FSA0000186497100000028
multiplying to obtain;
Figure FSA0000186497100000029
and
Figure FSA00001864971000000210
calculating according to the water flow velocity vectors of the central grid and the neighborhood grid, and particularly realizing in an advection item link;
II advection term simulation
The advection term indicates that the fluid itself and properties migrate with velocity. And under the grid mode, simulating an advection term by adopting a multi-flow method. Let the water velocity vector of the neighborhood grid b be
Figure FSA00001864971000000211
The ratio S of the amount of water flowing into the center grill rb→rIs represented by formula (4):
Figure FSA00001864971000000212
wherein (Δ x, Δ y) is the deviation of the neighborhood grid coordinate from the central grid coordinate, and the unit is pixel; v. ofmaxA scalar quantity representing the maximum speed allowed on the time slice;
residual water ratio S of central gridrIs represented by formula (5):
Figure FSA00001864971000000213
according to the mass conservation law, the depth of the central grid water after advection calculation is expressed by the formula (6):
Figure FSA00001864971000000214
in the formula (I), the compound is shown in the specification,
Figure FSA00001864971000000215
representing a central grid tnAnd tn+1The water depth at that moment;
Figure FSA00001864971000000216
representing a neighborhood grid tnThe water depth at that moment;
Figure FSA00001864971000000217
respectively represent tnThe proportion of water quantity flowing into the central grid r from the neighborhood grid b at the moment;
Figure FSA00001864971000000218
represents tnThe proportion of the residual water amount of the central grid at the moment;
according to the law of conservation of momentum, after advection calculationWater velocity of central gridIs represented by the formula (7):
Figure FSA00001864971000000220
in the formula (I), the compound is shown in the specification,
Figure FSA00001864971000000221
and
Figure FSA00001864971000000222
respectively represent tnThe water velocity of the time center grid r and the neighborhood grid b;
according to the formula (4) and the formula (5), when the water velocity of the simulation grid is equal to vmaxWhen the water flows out, all the grid water flows on the time slice flow out; to ensure the model operates normally, a fixed v is set for the basinmaxAnd the water velocity at any position of the watershed is considered to be less than or equal to vmax；
In the actual simulation, when the water speed exceeds vmaxWhen it is set to vmax. Thus, vmaxThe time slice interval for water quality simulation is determined, as shown in formula (8):
according to equation (8), the number of time slices N to be iterated per hour is equation (9):
III pressure term simulation
During the migration of water flow along with the speed, pressure gradient force is generated inside the water flow due to different water pressures. The pressure gradient force adopts an 8-neighborhood approximate calculation method. Let the height of the central grid be HrElevation of neighborhood grid is HbThen the height difference of water body is delta HbIs represented by the formula (10):
Figure FSA0000186497100000033
the velocity vector increment Δ V generated by the neighborhood grid to the center grid on the time slice is represented by equation (11):
Figure FSA0000186497100000034
α is a positive constant related to water density, gravity acceleration, friction force and the like, and is calibrated through actual hydrological data of a basin;
IV external force term simulation
Setting the upper bound depth d of water flow frictionmax(in m) and a lower bound depth of dmin(in m), the attenuation coefficient ε is approximately defined by the equation (12):
Figure FSA0000186497100000035
wherein sigma is a friction proportion coefficient, and the calibration is carried out through actual hydrological data of the watershed;
basin runoff simulation on V time slice
In a time slice, the basin runoff simulation is carried out in two steps, wherein in the first step, water yield and water power simulation: firstly, calculating the water yield of each grid unit, then performing pressure item and external force item simulation, and calculating the new water depth and water speed of each grid unit; step two, advection item simulation: and performing water flow migration calculation on the basis of the new water depth and the water speed of the grid unit obtained in the first step, wherein the obtained water depth and water speed are used as the initial water depth and water speed of the next time slice.
7. The stable flow field based watershed water quality simulation method of claim 6, wherein: the 1.2 comprises:
first, the basic assumption of a stable flow field is given: that is, assuming that there are several water source points in the basin, the flow rate is constant; through continuous iteration of the runoff confluence model, the water depth and the water speed at the outlet of the watershed finally tend to be stable. The watershed water flow field at this time is called a steady flow field.
8. The stable flow field based watershed water quality simulation method of claim 7, wherein: hydrodynamic model refinement involving I
A. Grid cell water velocity increment correction
Supposing that the water velocity increment is reduced after the grid water flow with the water depth of more than 1m is mixed with the surrounding water masses and is in an inverse relation with the water depth; the correction formula is formula (13):
Figure FSA0000186497100000043
B. neighborhood grid cell water flow mixing simulation
Supposing that each grid unit is mixed with 8 neighborhood grid water flow on each time slice, and the momentum conservation law is followed in the mixing process; firstly, calculating the total momentum and the total water quantity of a central grid and 8 adjacent grids, and dividing the total momentum and the total water quantity to obtain the water speed after water flow of the central grid is mixed;
C. runoff confluence simulation process after hydrodynamic model is complete
The runoff confluence simulation after the hydrodynamic model is completed is carried out in three steps, namely water yield and balance, hydrodynamic simulation, advection item simulation and water flow mixed simulation; the incremental correction of the water speed of the grid unit is integrated into a first simulation link, and after the hydrodynamic simulation is completed, the new water speed is corrected according to the formula (13); the mixed simulation of the water flow of the neighborhood grid unit is used as an independent simulation link and is carried out after the simulation of the advection item is finished;
II early-stage water regime simulation based on stable flow field
Let the water supply amount of a certain water source point be ξ (unit is m)3And/s), the unit of the grid at the position is r, the water yield of the grid r is modified from the formula (3) to the formula (14):
Figure FSA0000186497100000041
in the formula, ξrThe water quantity of the water source point grid on the time slice meets the following requirements:
Figure FSA0000186497100000042
it is apparent that ξ for the main stream inflow point, the side stream inflow point and the blow down pointrGreater than or equal to 0, and ξ for water intakerLess than or equal to 0;
in the process of creating the stable flow field, whether the stable flow field is created or not is quantitatively described by adopting an equation (16);
Figure FSA0000186497100000051
in the formula, W is the depth of the outlet control point of the basin, n is the number of hours of current simulation, h is the number of hours of forward pushing, and A is the accumulated error threshold.
9. The stable flow field based watershed water quality simulation method of claim 8, wherein: the decomposition of the 2.1 two-dimensional finite difference water quality model comprises the following steps:
assuming that there is a volume infinitesimal
Figure FSA0000186497100000052
This volume element has inputs and outputs along the longitudinal (x-axis) and transverse (y-axis) directions. The two-dimensional differential equation for the propagation of a contaminant in a body of water is as follows:
Figure FSA0000186497100000053
in the formula (17), the compound represented by the formula (I),
Figure FSA0000186497100000054
the average contaminant concentration of the microcell (i, j);
Figure FSA0000186497100000055
expressed as diffusion coefficients in x and y directions, respectively, in km2/h；ui，jAnd vi，jRepresenting the water flow velocity in the x and y directions; k is a radical ofi，jRepresenting the contaminant degradation coefficient in l/d.
10. The stable flow field based watershed water quality simulation method of claim 9, wherein: the 2.2 coupling of the water quality model and the hydrodynamic model comprises: under the grid mode, the volume infinitesimal of the two-dimensional finite difference water quality model is a grid unit; the model is solved step by step according to water yield balance, advection item simulation and water flow mixing simulation, and is the key of coupling of a water quality model and a hydrodynamic model:
water quality simulation in I water yield balance process
In water quality simulation, the water source point is not only the supply point of the water flow, but also the supply point of the pollutant. And setting the sewage discharge concentration of the water source point to be delta (the unit is mg/l), wherein the output concentration on the time slice after the water source point discharges sewage is expressed as a formula (18):
Figure FSA0000186497100000056
in the formula (I), the compound is shown in the specification,respectively represent tnAnd tn+1The contaminant concentration of the central grid at the time;
Figure FSA0000186497100000058
is tnThe sewage discharge concentration of the central grid at the moment;
in the water balance calculation, the pollutant degradation is also considered. The pollutant degradation coefficient is measured in days, and needs to be converted into the degradation rate of the pollutant in a time slice. Let the contaminant degradation coefficient be a constant k in the flow domaindThen in time slice tnOn the rate of degradation of contaminants knIs represented by formula (19):
kn＝1-(1-kd)1/(24×N)(19)
combining formula (18) and formula (19), the pollutant output concentration in the water yield balance process is formula (20):
pollutant migration calculation in II advection item simulation process
In the advection term, the grid cells and the neighborhood grid exchange water according to the water speed. Assuming that the central grid and the neighborhood grid pollutants are fully mixed in the water flow migration, the grid pollutant concentration output by advection term simulation is formula (21) according to the mass conservation law:
Figure FSA0000186497100000062
in the formula (I), the compound is shown in the specification,
Figure FSA0000186497100000063
for the neighborhood grid b at tnThe concentration of the contaminant at the moment;
III pollutant diffusion simulation of water flow mixing simulation
Pollutant diffusion is simulated in a water flow mixing link. In equation (17), the central grid r diffuses towards the neighborhood grid b, resulting in a reduction of central grid contamination; the neighborhood grid b diffuses towards the center grid r, resulting in an increase in center grid contamination. In the model, the pollutant diffusion coefficient is set to be a constant E, and the actual migration amount of pollutants caused by diffusion of two adjacent grid units is related to the concentration difference of the pollutants.
Regarding the water of two adjacent grid cells as a cubic water column, the height of the water column is equal to the water depth, and the pollutant diffusion is considered to occur in the overlapping region of the two water columns (figure 1), and the height W of the water columnbrIs represented by formula (22):
Wbr＝max(min(Hr+Wr，Hb+Wb)-max(Hr，Hb)，0) (22)
for quantitative water descriptionThe change of the concentration of the pollutants caused by the flow mixing simulation is converted into the distance E of the outward diffusion of the pollutants on the time slice by the constant EnAs in formula (23):
Figure FSA0000186497100000064
combining formula (22) and formula (23), the concentration of the center grid contaminant after diffusion is listed in formula (24):
Figure FSA0000186497100000065
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