CN110837684A - Drainage basin water quality real-time simulation method based on general calculation - Google Patents
Drainage basin water quality real-time simulation method based on general calculation Download PDFInfo
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Abstract
A watershed water quality real-time simulation method based on general calculation comprises the following steps: dividing basin grids under a general computing framework; parallelization design of a basin water quality model; wherein step S1 includes executing the contents listed in 1.1, 1.2 and 1.3 in sequence; 1.1 basin grid division of a grid pattern; 1.2, defining a simulation grid; 1.3, constructing a grid neighborhood topology; step S2 includes executing the contents listed in 2.1, 2.2, 2.3, 2.4 and 2.5 in sequence; 2.1 general calculation of basic requirements for a water quality model; 2.2 simulating the attribution of the grid; 2.3 designing a hydrodynamic parallel algorithm of a simulation grid; 2.4 design of a water quality simulation parallel algorithm of a simulation grid. The simulation method of the invention can not only simulate the water quality in real time, but also achieve the ideal effect of simulation precision.
Description
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
The water quality model can be used for water quality simulation, water ecological risk evaluation, water quality prediction and forecast by describing the motion and migration transformation rules of environmental pollutants in water, and is a powerful tool for realizing water pollution control, water environment health assessment and watershed water resource planning. In recent decades, a lot of research work has been carried out by many scholars at home and abroad in the aspect of water quality simulation. The two-dimensional model takes pollutant diffusion along the horizontal direction as a research target, is suitable for water quality simulation of large rivers, and is a key research direction of water quality simulation of a current river basin.
The two-dimensional water quality model is a complex process which is iterated simultaneously in time and space, the pollutant diffusion process is approximately regarded as a sequence formed by a large number of time slices, the pollutant diffusion is calculated for each time slice grid by grid, and the simulation of the pollution process of the area is completed through the iteration of the time slices. When the simulated space range is larger, the grid division is finer, the calculated amount is multiplied, and the real-time performance of water quality simulation is influenced. General purpose computing is used as a current advanced graph computing technology, and compared with traditional CPU computing, the computing performance of 1-2 orders of magnitude can be improved in the aspect of parallel processing. The method is introduced into water quality simulation, can greatly improve the water quality simulation performance and efficiency, and is an important means for simulating the water quality of the basin in the future. However, under the current hardware condition of the graphics card, the size of data sent to the GPU at one time is limited. For a large watershed, after the grid space scale is fine to a certain scale, the GPU is difficult to read in at one time. Therefore, how to realize real-time simulation of water quality in a basin range on the premise of not reducing simulation accuracy becomes a key problem which needs to be solved by water quality simulation.
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 spatial distribution and the time variation of the water quality of the whole river channel cannot be obtained through simulation.
Disclosure of Invention
The invention provides a real-time watershed water quality simulation method based on general calculation, which comprises the following steps:
step S1: dividing basin grids under a general computing framework;
step S2: parallelization design of a basin water quality model;
wherein step S1 includes executing the contents listed in 1.1, 1.2 and 1.3 in sequence;
preferably, 1.1 grid-patterned watershed meshing.
1.2 definition of simulation grid
1.3 construction of mesh neighborhood topology
Step S2 includes executing the contents listed in 2.1, 2.2, 2.3, 2.4 and 2.5 in sequence;
preferably, 2.1 general purpose calculations are used to model the basic requirements for water quality;
2.2 simulating the attribution of the grid;
2.3 designing a hydrodynamic parallel algorithm of a simulation grid;
2.4 design of a water quality simulation parallel algorithm of a simulation grid;
more preferably, said 2.3 includes three calculations, namely:
i-simulation grid water depth calculation
II Water velocity calculation for simulation grid
Parallel computing process for hydrodynamic simulation on III time slice
More preferably, in III, the hydrodynamic simulation is performed in two steps over a time slice to ensure parallelism of the hydrodynamic calculations. In the first step, the water velocity is incrementally calculated. Firstly, calculating the water yield increment of a simulation grid according to the water supply amount of a water source point, then carrying out water velocity increment simulation, and calculating the new water depth and water velocity of each grid unit; and secondly, calculating the water flow migration. 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.
More preferably, said 2.4 includes four simulation and calculation processes, namely:
water quality simulation in i water velocity increment link
ii water quality simulation in waterflow migration links
iii pollutant diffusion simulation
iv parallel computing process for water quality simulation on time slice
Preferably, the watershed meshing of the grid pattern is 1.1
In the grid mode, the watershed is divided into rectangular grids with equal size according to a certain resolution, and each unit in the grids is called a pixel. And taking the grid pixels as volume microelements in the two-dimensional water quality model.
The grid division method of the existing water quality simulation mainly adopts a regular grid method and an irregular grid method. The method is simple and convenient for general calculation realization by taking the time slice as a unit.
Preferably, 1.2 the definition of the simulation grid
A maximum water body range is set for the channel and it is assumed that water and contaminant motion is limited to pixels within this range during the simulation period. Based on the image elements, the image elements in the watershed range are divided into two types, one type is a water body image element, and the other type is an external image element.
In the two-dimensional water quality model, each pixel needs to exchange water and pollutants with surrounding 8 neighborhood pixels, and the relevant attributes of external pixels adjacent to the water body need to be stored in a video memory at the same time. The external pixels adjacent to the water body are called boundary pixels, and the grid participating in the water quality simulation comprises two parts, namely the water body pixels and the boundary pixels; the water body pixels are grid units for actual water quality calculation, and the boundary pixels are grid units for providing adjacent attributes for adjacent water body pixels.
The set of simulation grids is represented by equation (1):
M＝{cellid|1≤id≤Nm} (1)
in the formula (1), NmSimulating the number of grids in the set; id is the serial number stored in the set for each simulation grid, and is used for uniquely identifying each simulation grid.
In the general calculation of the invention, the terrain, water depth, water speed and pollutant concentration required by water quality simulation are all expressed as lengthNmThe number of the simulation grids determines the video memory size required by the water quality simulation of the watershed.
Preferably, the 1.3 mesh neighborhood topology is constructed
The simulation grid needs the attribute information of the surrounding 8 neighborhood grids during pollutant diffusion and migration calculation. Therefore, on the basis of simulating grid division, a grid neighborhood topology is also constructed.
For each simulation grid, 8 neighborhoods of the simulation grid are coded according to a certain sequence, and the serial numbers of the neighborhood grids in the simulation grid set are recorded in sequence.
In order to facilitate general calculation of water quality simulation, the neighborhood topology of the simulation grid is also represented by an array. Since one simulation grid has 8 neighborhood codes, the size of the neighborhood topology array is N m8 times of the total weight of the product. In order to facilitate the retrieval of the neighborhood grids, the neighborhood topology arrays are sequentially stored according to the sequence of the serial numbers of the simulation grids.
Preferably, the basic requirements of the 2.1 general calculation on the water quality model are:
in the general computing process, the whole task is divided into a large number of computing units which can be parallel, and each computing unit is independently completed by one kernel. Therefore, the general computing requires that the computing units are relatively independent, the computing result of each computing unit does not affect other computing units, and the execution result of the task is independent of the execution sequence of the computing units.
The two-dimensional water quality model decomposes the contaminant diffusion process into equally spaced time slices over time. In each time slice, the water quality simulation is decomposed into simulation calculation with the micro elements as basic units, and the pollutant concentration simulated by the micro elements in the previous time slice is used as the initial concentration of the next time slice.
And realizing watershed water quality simulation through iteration of time slices. Because the calculation of the time slice is serial, the water quality simulation is realized by general calculation, and the core lies in the calculation independence of each simulation grid on one time slice, namely in the water quality simulation process, the simulation grid can only modify the attribute of the simulation grid, but can not modify the attributes of other grids.
The above-mentionedTime sliceThe time interval represented by one frame of basin water quality simulation is indicated. Over a time slice, the water flow and contaminants of each simulation grid spread only into the 8-neighborhood simulation grid.
Preferably, the 2.2 simulation grid is attributed
Wherein, in order to realize the general calculation of water quality simulation, the attribute of the simulation grid is expressed as a tuple, as shown in formula (2):
cell＝{H，s，b，Wf，vf，cf，Wt，vt，ct} (2)
in the formula (2), H is the terrain height of the grid; s is a grid type and is divided into a water body grid and a boundary pixel; b is neighborhood topology information of the grid; wf、vf、cfRespectively representing the initial water depth, water speed and pollutant concentration of the grid on the time slice; wt、vt、ctThe grid's end water depth, water velocity and contaminant concentration over the time slice are shown, respectively.
On a time slice, { W over analog gridf，vf，cfCalculating to obtain { W of the time slicet，vt，ct}. The next time slice is exchanged when it is calculated. The mechanism avoids the mutual influence of the calculation results of the simulation grids, ensures the independence of the calculation units and lays a data foundation for the water quality simulation of general calculation.
Preferably, the hydrodynamic parallel algorithm design of the 2.3 simulation grid
Wherein, the hydrodynamic model is the basis of the water quality model. And simulating the water depth and water speed of the grid through a hydrodynamic model, and simulating the diffusion, migration and attenuation of pollutants according to the water depth and the water speed.
Let the time slice sequence number be n, the time slice time series t is expressed as formula (3):
t＝{tnn≥1} (3)
the time difference Δ t between adjacent time slices is expressed by formula (4):
Δt＝tn+1-tn(4)
on a time slice, the hydrodynamic simulation core of the simulation grid lies in the calculation of water depth and water speed. For any simulation grid of the watershed, the simulation grid is represented as a central grid r, and 8 neighborhood grids of the simulation grid are represented as b.
Preferably, the hydrodynamic simulation over a time slice is performed as follows:
i-simulation grid water depth calculation
In the grid mode, the water body simulating the grid is regarded as a cubic water column. Since the analog mesh is one pixel in a grid pattern. Setting the pixel resolution as C, the water volume V of the simulation grid is calculated by the formula (5):
Vr＝WrC2(5)
as can be seen from the equation (5), the grid water amount and the water depth are in a linear relationship. And when the grid water depth is calculated, all input and output water quantities are converted into the water depth. According to the principle of water balance, tn+1Depth of water in the grid r at time
See formula (6):
in the formula (6), the reaction mixture is,
for simulating the initial water depth of the grid over a time slice ξr、
Water supply of the simulation grids and water inflow of the neighborhood grids on the time slice respectively represent water income of the grids;
and
respectively the lower seepage quantity, evaporation quantity and water outflow quantity of the simulation grid on the time sliceWater expenditure on the grid of the meter.
In the water quality model only considering main stream river channel grid, the upstream main stream inflow, the branch inflow and the sewage outlet are assumed to be a water source point positioned in the river channel, the precipitation in the river channel finally enters the simulated river reach in the mode of upstream water inflow and branch inflow and convergence, the precipitation amount on the river channel only accounts for a very small part of the whole river channel, so the precipitation item is ignored in the model, for the water source point of the river channel, the flow is taken as a unit to be input into the model, the flow of a certain water source point is set to be ξ (the unit is m)3/s), the water depth ξ of the grid where the water source point is located is increased by the water supply on the time slicerSee formula (7):
evaporation and infiltration are important water expenditure links in simulation of the grid. The river infiltration rate and evaporation rate are set as constants in the model, and
on a time slice after multiplication
wherein, (Δ x, Δ y) is the deviation of the neighborhood grid coordinate relative to 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 (9):
according to the mass conservation law, the water depth output by the time slice due to the water flow migration of the central grid is expressed by the formula (10):
in the formula (10), the compound represented by the formula (10),
representing a central grid tnAnd tn+1The water depth at that moment;
representing a neighborhood grid tnThe water depth at that moment;
respectively represent tnThe proportion of water quantity flowing into the central grid r from the neighborhood grid b at the moment;
represents tnAnd (5) the proportion of the residual water quantity of the central grid at the moment.
According to the formula (9), 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 speed at any position of the watershed is considered to be less than or equal tovmax. In the actual simulation, when the water speed exceeds vmaxWhen it is set to vmax. Thus, vmaxThe time slice interval of water quality simulation is determined, see formula (11):
according to equation (11), the number of time slices N that need to be iterated per hour is:
II Water velocity calculation for simulation grid
As surface water flows on a slope or a riverbed, surface runoff is subjected to pressure gradient force, surface friction force and the like besides the action of gravity. The speed increment in the horizontal direction is generated on the simulation grid by gravity and pressure gradient force, and the water body height difference is simulated approximately by the central grid and the neighborhood grid. Setting the height difference of the water body of the neighborhood grid relative to the central grid as delta HbThe velocity vector increment Δ V generated by the neighborhood grid to the center grid on the time slice is represented by equation (13):
in equation (13), α is a positive constant relating to water density, gravitational acceleration, friction, and the like, and is calibrated from the real watershed hydrological data.
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 (2):
in equation (14), σ is a coefficient of friction ratio and is calibrated by actual hydrological data of the watershed.
On a time slice, if the grid water velocity is less than vmaxThen only part of the grid water flows out, and simultaneously part of the water quantity of 8 adjacent grids is also accommodated. According to the law of conservation of momentum, the output speed of the grid due to water flow migration is shown in formula (15):
parallel computing process for hydrodynamic simulation on III time slice
In order to ensure the parallelism of the hydrodynamic calculation, the hydrodynamic simulation on the time slice is carried out in two steps. In the first step, the water velocity is incrementally calculated. Firstly, calculating the water yield increment of a simulation grid according to the water supply amount of a water source point, then carrying out water velocity increment simulation, and calculating the new water depth and water velocity of each grid unit; and secondly, calculating the water flow migration. 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, the 2.4 simulation grid water quality simulation parallel algorithm design comprises:
and coupling the water quality simulation with a hydrodynamic model, and adding pollutant migration, diffusion and attenuation calculation in the links of water velocity increment and water flow migration.
Water quality simulation in i water velocity increment link
The water supply point is not only the supply point for the water stream but also the supply point for the contaminants. And setting the sewage discharge concentration of the water source point to be delta (the unit is mg/l), and then, the output concentration on the time slice after the water source point discharges sewage is shown as the formula (16):
in the formula (16),respectively represent tnAnd tn+1The pollutant concentration of the central grid at the moment;
is tnAnd (4) the pollution discharge concentration of the central grid at the moment.
In the water velocity increment link, pollutant degradation is considered at the same time. 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 of formula (17):
kn＝1-(1-kd)1/(24×N)(17)
combining formula (16) and formula (17), the pollutant output concentration is:
ii water quality simulation in waterflow migration links
During the water flow migration, the pollutants are migrated along with the water flow. Assuming that the pollutants are uniformly distributed in the simulation grid, the grid pollutant concentration is expressed by formula (19) due to water flow migration according to the mass conservation law:
in the formula (I), the compound is shown in the specification,
for the neighborhood grid b at tnThe contaminant concentration at the moment.
iii pollutant diffusion simulation
In the two-dimensional water quality model, the central grid r diffuses towards the neighborhood grid b, so that pollutants in the central grid are reduced; the neighborhood grid b diffuses towards the center grid r, resulting in an increase in center grid contamination. Setting the diffusion coefficient of the pollutants to be a constant E, the actual migration amount of the pollutants caused by the diffusion of the two adjacent grid cells 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 area of the two water columns (figure 3), and the height W of the water columnbrIs represented by formula (20):
Wbr＝max(min(Hr+Wr，Hb+Wb)-max(Hr，Hb)，0) (20)
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 slicenSee formula (21):
combining formula (20) and formula (21), the concentration of the center mesh pollutant after diffusion is formula (22):
because the pollutant overlapping areas of the adjacent 2 grids are the same, the result of the independent calculation of the central grid still meets the pollutant mass conservation in the time slice pollutant diffusion simulation process.
iv parallel computing process for water quality simulation on time slice
Preferably, in order to ensure the parallelism of the water quality simulation calculation, the water quality simulation on the time slice is carried out in three steps, namely water velocity increment calculation, water flow migration calculation and pollutant diffusion simulation. The pollutant concentration output in each step is used as the initial pollutant concentration in the next step. And outputting the pollutant concentration after the pollutant diffusion simulation is completed as the initial concentration of the next time slice.
Drawings
FIG. 1 is a watershed water quality simulation grid division of a preferred embodiment of the real-time watershed water quality simulation method based on general computation according to the present invention;
FIG. 2 is an example of an 8-neighborhood encoding of the center grid of the embodiment shown in FIG. 1;
FIG. 3 is a view of the contaminant diffusion overlap region of the embodiment of FIG. 1;
FIG. 4 is a comparison graph of the simulated concentration and the measured concentration of the water quality monitoring section of the bridge in the embodiment of FIG. 1;
FIG. 5 is a diagram illustrating the comparison between the simulated concentration and the measured concentration of the water quality monitoring section of the ocean wave river in the embodiment shown in the figure;
Detailed Description
Watershed meshing under 1 general computing framework
1.1 watershed meshing of grid patterns
The two-dimensional water quality model divides a water body area into a large number of micro volume units (referred to as 'infinitesimal' for short) which are seamlessly connected on the plane on the space, and realizes the water quality simulation of the watershed through the pollutant simulation calculation of the infinitesimal. Array operation is a basic mode of general computation, and in order to simplify data input of general computation, a watershed is divided according to a grid mode. In the grid mode, the watershed is divided into rectangular grids with equal size according to a certain resolution, and each unit in the grids is called a pixel. And taking the grid pixels as volume microelements in the two-dimensional water quality model.
And dividing rectangular grids by using a basin external rectangle, wherein the quantity of the grids in each row and each column is equal. Although the dividing method is easy to process by a computer, all grids in a rectangular range are included in water quality simulation calculation, and the size and the spatial resolution of a watershed which can be calculated under the condition of the video memory of the existing computer are limited.
1.2 definition of simulation grid
A maximum water body range is set for the channel and it is assumed that water and contaminant motion is limited to pixels within this range during the simulation period. Based on the image elements, the image elements in the watershed range are divided into two types, one type is a water body image element, and the other type is an external image element. Because the water body pixels only occupy a small part of the full watershed range in reality, if the water body pixels are only put into the video memory for operation, the watershed water quality simulation with a larger range and higher resolution is supported under the same video memory.
However, in the two-dimensional water quality model, each pixel needs to exchange water and pollutants with surrounding 8 neighborhood pixels, and the relevant attributes of the external pixels adjacent to the water body need to be stored in the video memory at the same time. The external pixels adjacent to the water body are called boundary pixels, and the grid participating in the water quality simulation comprises two parts, namely water body pixels and boundary pixels, as shown in fig. 1. The water body pixels are grid units for actual water quality calculation, and the boundary pixels are grid units for providing adjacent attributes for adjacent water body pixels.
The set of simulation grids is represented by equation (1):
M＝{cellid|1≤id≤Nm} (1)
in the formula (1), NmSimulating the number of grids in the set; id is the serial number stored in the set for each simulation grid, and is used for uniquely identifying each simulation grid.
In the general calculation, the terrain, water depth, water speed and pollutant concentration required by water quality simulation are all expressed as length NmThe number of the simulation grids determines the video memory size required by the water quality simulation of the watershed. Table 1 gives the number of simulation grids for different spatial resolutions of the experimental watershed. As can be seen from table 1, the number of simulation grids is less than 1% of the total number of the grids, and the proportion of the simulation grids decreases continuously with the increase of the resolution, and is not limited to be close to the proportion of the water body in the whole watershed. Therefore, the simulation grid is defined in the watershed, the video memory requirement of water quality simulation calculation is reduced, and a foundation is laid for the water quality simulation general calculation of the watershed scale.
1.3 construction of mesh neighborhood topology
The simulation grid needs the attribute information of the surrounding 8 neighborhood grids during pollutant diffusion and migration calculation. Therefore, on the basis of simulating grid division, a grid neighborhood topology is also constructed. For each simulation grid, 8 neighborhoods of the simulation grid are coded according to the sequence shown in fig. 2, and the serial numbers of the neighborhood grids in the simulation grid set are recorded in sequence.
In order to facilitate general calculation of water quality simulation, the neighborhood topology of the simulation grid is also represented by an array. Since one simulation grid has 8 neighborhood codes, the size of the neighborhood topology array is N m8 times of. In order to facilitate the retrieval of the neighborhood grids, the neighborhood topology arrays are sequentially stored according to the sequence of the serial numbers of the simulation grids.
Parallelization design of basin water quality model
2.1 general calculation of basic requirements for Water quality model
General purpose computing was originally designed to handle the large number of parallel operations in game video, with the number of cores of the GPU far exceeding that of the CPU. Because the cache size of each core is relatively small, and the number of digital logic operation units is relatively small and simple, the general computation is more suitable for simple and repeated parallel operation. In a general computing process, an overall task is divided into a large number of computing units which can be parallel, and each computing unit is independently completed by one kernel. Therefore, the general computing requires that the computing units are relatively independent, the computing result of each computing unit does not affect other computing units, and the execution result of the task is independent of the execution sequence of the computing units.
The two-dimensional water quality model decomposes the contaminant diffusion process into equally spaced time slices over time. In each time slice, the water quality simulation is decomposed into simulation calculation with the micro elements as basic units, and the pollutant concentration simulated by the micro elements in the previous time slice is used as the initial concentration of the next time slice. And realizing watershed water quality simulation through iteration of time slices. Because the calculation of the time slice is serial, the water quality simulation is realized by general calculation, and the core lies in the calculation independence of each simulation grid on one time slice, namely in the water quality simulation process, the simulation grid can only modify the attribute of the simulation grid, but can not modify the attributes of other grids.
2.2 Attribution of simulation grid
To achieve general computation of water quality simulation, the attributes of the simulation grid are expressed as a tuple, as in equation (2):
cell＝{H，s，b，Wf，vf，cf，Wt，vt，ct} (2)
in the formula (2), H is the terrain height of the grid; s is a grid type and is divided into a water body grid and a boundary pixel; b is neighborhood topology information of the grid; wf、vf、cfRespectively representing the initial water depth, water speed and pollutant concentration of the grid on the time slice; wt、vt、ctThe grid's end water depth, water velocity and contaminant concentration over the time slice are shown, respectively.
On a time slice, { W over analog gridf，vf，cfCalculating to obtain { W of the time slicet，vt，ct}. The next time slice is exchanged when it is calculated. The mechanism avoids the mutual influence of the calculation results of the simulation grids, ensures the independence of the calculation units and lays a data foundation for the water quality simulation of general calculation.
2.3 hydrodynamic parallel algorithm design of simulation grid
The hydrodynamic model is the basis of the water quality model. And simulating the water depth and water speed of the grid through a hydrodynamic model, and simulating the diffusion, migration and attenuation of pollutants according to the water depth and the water speed.
Let the time slice sequence number be n, the time slice time series t is expressed as formula (3):
t＝{tnn≥1} (3)
the time difference Δ t between adjacent time slices is expressed by formula (4):
Δt＝tn+1-tn(4)
on a time slice, the hydrodynamic simulation core of the simulation grid lies in the calculation of water depth and water speed. For any simulation grid of the watershed, the simulation grid is represented as a central grid r, and 8 neighborhood grids of the simulation grid are represented as b. Hydrodynamic simulation over a time slice proceeds as follows:
i-simulation grid water depth calculation
In the grid mode, the water body simulating the grid is regarded as a cubic water column. Since the analog mesh is one pixel in a grid pattern. Setting the pixel resolution as C, the water volume V of the simulation grid is calculated by the formula (5):
Vr＝WrC2(5)
as can be seen from the equation (5), the grid water amount and the water depth are in a linear relationship. When the grid water depth is calculated, all input and output water quantities are uniformly rotatedAnd changing to water depth. According to the principle of water balance, tn+1Depth of water in the grid r at time
See formula (6):
in the formula (6), the reaction mixture is,
for simulating the initial water depth of the grid over a time slice ξr、
Water supply of the simulation grids and water inflow of the neighborhood grids on the time slice respectively represent water income of the grids;and
the lower seepage quantity, the evaporation quantity and the water outflow quantity of the simulation grid on the time slice respectively represent the water consumption of the grid.
In the water quality model only considering main stream river channel grid, the upstream main stream people stream, the branch stream inlet and outlet and the sewage outlet are assumed to be a water source point positioned in the river channel, the precipitation in the river channel finally enters the simulated river section through the upstream water inlet and branch stream inlet and outlet modes, the precipitation amount on the river channel only occupies a small part of the whole river channel, so the precipitation item is ignored in the model, for the water source point of the river channel, the flow is taken as a unit to input the model, the flow of a certain water source point is set to be ξ (the unit is m)3/s), the water depth ξ of the grid where the water source point is located is increased by the water supply on the time slicerSee formula (7):
evaporation and infiltration are important water expenditure links in simulation of the grid. The river infiltration rate and evaporation rate are set as constants in the model, and
on a time slice after multiplication
wherein, (Δ x, Δ y) is the deviation of the neighborhood grid coordinate relative to 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 (9):
according to the mass conservation law, the water depth output by the time slice due to the water flow migration of the central grid is expressed by the formula (10):
in the formula (10), the compound represented by the formula (10),
representing a central grid tnAnd tn+1The water depth at that moment;
representing a neighborhood grid tnThe water depth at that moment;respectively represent tnThe proportion of water quantity flowing into the central grid r from the neighborhood grid b at the moment;represents tnAnd (5) the proportion of the residual water quantity of the central grid at the moment.
According to the formula (9), 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 of water quality simulation is determined, see formula (11):
according to equation (11), the number of time slices N that need to be iterated per hour is:
II Water velocity calculation for simulation grid
As surface water flows on the slope or the riverbed, surface runoff is subjected to pressure gradient in addition to the action of gravityForce, surface friction, etc. The speed increment in the horizontal direction is generated on the simulation grid by gravity and pressure gradient force, and the water body height difference is simulated approximately by the central grid and the neighborhood grid. Setting the height difference of the water body of the neighborhood grid relative to the central grid as delta HbThe velocity vector increment Δ V generated by the neighborhood grid to the center grid on the time slice is represented by equation (13):
in equation (13), α is a positive constant relating to water density, gravitational acceleration, friction, and the like, and is calibrated from the real watershed hydrological data.
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 (2):
in equation (14), σ is a coefficient of friction ratio and is calibrated by actual hydrological data of the watershed.
On a time slice, if the grid water velocity is less than vmaxThen only part of the grid water flows out, and simultaneously part of the water quantity of 8 adjacent grids is also accommodated. According to the law of conservation of momentum, the output speed of the grid due to water flow migration is shown in formula (15):
parallel computing process for hydrodynamic simulation on III time slice
In order to ensure the parallelism of the hydrodynamic calculation, the hydrodynamic simulation on the time slice is carried out in two steps. In the first step, the water velocity is incrementally calculated. Firstly, calculating the water yield increment of a simulation grid according to the water supply amount of a water source point, then carrying out water velocity increment simulation, and calculating the new water depth and water velocity of each grid unit; and secondly, calculating the water flow migration. 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.
2.4 Water quality simulation parallel algorithm design of simulation grid
And coupling the water quality simulation with a hydrodynamic model, and adding pollutant migration, diffusion and attenuation calculation in the links of water velocity increment and water flow migration.
Water quality simulation in i water velocity increment link
The water supply point is not only the supply point for the water stream but also the supply point for the contaminants. And setting the sewage discharge concentration of the water source point to be delta (the unit is mg/l), and then, the output concentration on the time slice after the water source point discharges sewage is shown as the formula (16):
in the formula (16),respectively represent tnAnd tn+1The pollutant concentration of the central grid at the moment;
is tnAnd (4) the pollution discharge concentration of the central grid at the moment.
In the water velocity increment link, pollutant degradation is considered at the same time. 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 of formula (17):
kn＝1-(1-kd)1/(24×N)(17)
combining formula (16) and formula (17), the pollutant output concentration is:
ii water quality simulation in waterflow migration links
During the water flow migration, the pollutants are migrated along with the water flow. Assuming that the pollutants are uniformly distributed in the simulation grid, the grid pollutant concentration is expressed by formula (19) due to water flow migration according to the mass conservation law:
in the formula (I), the compound is shown in the specification,
for the neighborhood grid b at tnThe contaminant concentration at the moment.
iii pollutant diffusion simulation
In the two-dimensional water quality model, the central grid r diffuses towards the neighborhood grid b, so that pollutants in the central grid are reduced; the neighborhood grid b diffuses towards the center grid r, resulting in an increase in center grid contamination. Setting the diffusion coefficient of the pollutants to be a constant E, the actual migration amount of the pollutants caused by the diffusion of the two adjacent grid cells 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 area of the two water columns (figure 3), and the height W of the water columnbrIs represented by formula (20):
Wbr＝max(min(Hr+Wr，Hb+Wb)-max(Hr，Hb)，0) (20)
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 slicenSee formula (21):
combining formula (20) and formula (21), the concentration of the center mesh pollutant after diffusion is formula (22):
because the pollutant overlapping areas of the adjacent 2 grids are the same, the result of the independent calculation of the central grid still meets the pollutant mass conservation in the time slice pollutant diffusion simulation process.
iv parallel computing process for water quality simulation on time slice
In order to ensure the parallelism of water quality simulation calculation, the water quality simulation on the time slice is carried out in three steps, namely water velocity increment calculation, water flow migration calculation and pollutant diffusion simulation. The pollutant concentration output in each step is used as the initial pollutant concentration in the next step. And outputting the pollutant concentration after the pollutant diffusion simulation is completed as the initial concentration of the next time slice.
2.5 Water quality simulation Performance evaluation based on general calculation
In order to verify the water quality simulation performance of the general calculation, the same computer is adopted to carry out a water quality simulation test of 2 years and one hour for the middle trip of the peony river, wherein the CPU is Inter (R) core (TM) i7-7700HQ, and the display card is NVIDIA GeForce GTX 1070. Both the CPU and GPU water quality simulation adopt parallel calculation. The test results are shown in table 2.
As can be seen from table 2, when the total number of the simulation grids is within 20000, both the GPU and the CPU can complete watershed water quality simulation, and the GPU is about 10 times faster than the CPU; with the improvement of the resolution of the drainage basin, the grid scale and the iteration times per hour are multiplied, the time consumed by a CPU is more and more, the total time of 2-year water quality simulation can be estimated only by the time required by the water quality simulation of a plurality of hours, and the GPU can still meet the requirement of real-time simulation of the water quality of the drainage basin.
Interpolating the flow and concentration of the main flowing point, the branch inflow junction and the drainage point from 2012, 5 and 1 to 2014, 4 and 30 to obtain the hourly flow and concentration of each water source point. And (4) obtaining the hourly river ammonia nitrogen concentration distribution within the simulation time period through time slice iterative calculation. 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. 4. As can be seen from FIG. 4, the model not only can simulate the water quality in real time, but also can achieve a more ideal effect in terms of simulation precision.
TABLE 1 simulation mesh number and ratio under different grid resolution conditions
TABLE 2 watershed water quality simulation time under different grid resolution conditions
Because two-dimensional water quality simulation belongs to calculation intensive operation, and the contradiction between high-precision grid division and the bottleneck of calculation performance is difficult to reconcile, the introduction of general calculation is urgently needed to improve the performance and efficiency of basin water quality simulation. The invention takes the general calculation as a frame, takes the river channel and the edge grid as simulation grids aiming at the space scale of the drainage basin, reduces the grid scale and lays a foundation for the fine water quality simulation of the drainage basin. And then, aiming at the parallelization requirement of general calculation on data, parallelization design is carried out on each stage of water quality simulation, including water velocity increment, water flow migration and pollutant diffusion simulation. Through the water quality simulation of 2 years in the midstream of the peony river, the method proves that the simulation efficiency is improved while the water quality simulation precision is ensured.
Claims (10)
1. A watershed water quality real-time simulation method based on general calculation is characterized by comprising the following steps:
step S1: dividing basin grids under a general computing framework;
step S2: parallelization design of a basin water quality model;
wherein step S1 includes executing the contents listed in 1.1, 1.2 and 1.3 in sequence;
1.1 basin grid division of a grid pattern;
1.2, defining a simulation grid;
1.3, constructing a grid neighborhood topology;
step S2 includes executing the contents listed in 2.1, 2.2, 2.3, 2.4 and 2.5 in sequence;
2.1 general calculation of basic requirements for a water quality model;
2.2 simulating the attribution of the grid;
2.3 designing a hydrodynamic parallel algorithm of a simulation grid;
2.4 design of a water quality simulation parallel algorithm of a simulation grid.
2. The real-time watershed water quality simulation method based on general computation as claimed in claim 1, wherein the 2.3 includes three computations, namely:
i-simulation grid water depth calculation
II Water velocity calculation for simulation grid
And III, performing parallel computation flow of hydrodynamic simulation on the time slice.
3. The method for simulating watershed water quality based on general computation according to claim 2, wherein in III, to ensure the parallelism of the hydrodynamic computation, the hydrodynamic simulation on the time slice is performed in two steps: step one, water velocity increment calculation, namely calculating the water increment of a simulation grid according to the water supply quantity of a water source point, then performing water velocity increment simulation, and calculating the new water depth and water velocity of each grid unit; secondly, calculating water flow migration; 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.
4. The real-time simulation method of watershed water quality based on general computation according to any one of claims 1 to 3, wherein the 2.4 comprises four simulation and computation processes:
i water quality simulation in a water speed increment link;
ii water quality simulation in a water flow migration link;
iii pollutant diffusion simulation;
iv parallel computing process of water quality simulation on time slices.
5. The real-time watershed water quality simulation method based on general computation of claim 4, wherein 1.1 watershed gridding in a grid pattern: under the grid mode, the drainage basin is divided into rectangular grids with equal size according to a certain resolution, and each unit in the grids is called as a pixel; and taking the grid pixels as volume microelements in the two-dimensional water quality model.
6. The method for simulating watershed water quality based on general computation according to claim 5, wherein 1.2 the definition of simulation grid: setting a maximum water body range for the river channel, and assuming that the motion of water and pollutants is limited to pixels in the range in a simulation period; based on the image elements, the image elements in the watershed range are divided into two types, one type is a water body image element, and the other type is an external image element.
7. The method for real-time simulation of watershed water quality based on general computation of claim 6, wherein in the two-dimensional water quality model, each pixel needs to exchange water and pollutants with surrounding 8 neighborhood pixels, and the relevant attributes of the external pixels adjacent to the water body need to be stored in the video memory at the same time; the external pixels adjacent to the water body are called boundary pixels, and the grid participating in the water quality simulation comprises two parts, namely the water body pixels and the boundary pixels; the water body pixels are grid units for actual water quality calculation, and the boundary pixels are grid units for providing adjacent attributes for adjacent water body pixels.
8. The method for simulating watershed water quality based on general computation of claim 7,
the set of simulation grids is represented by equation (1):
M＝{cellid|1≤id≤Nm} (1)
in the formula (1), NmSimulating the number of grids in the set; id is the serial number stored in the set for each simulation grid, and is used for uniquely identifying each simulation grid；
The length of the landform, the water depth, the water speed and the pollutant concentration required by the water quality simulation is NmThe number of the simulation grids determines the video memory size required by the water quality simulation of the watershed.
9. The method for simulating watershed water quality based on general computation according to claim 1, wherein 1.3 the construction of the grid neighborhood topology: when the pollutant is diffused and migrated in the simulation grid, a grid neighborhood topology is also constructed on the basis of the simulation grid division; for each simulation grid, 8 neighborhoods of the simulation grid are coded according to a certain sequence, and the serial numbers of the neighborhood grids in the simulation grid set are recorded in sequence.
10. The real-time simulation method of watershed water quality based on general computation of any one of claims 1 to 3 or any one of claims 5 to 9, wherein the basic requirements of 2.1 general computation on the water quality model are as follows:
in the general computing process, the whole task is divided into a large number of computing units which can be parallel, each computing unit is independently completed by one kernel, the general computing requires that the computing units are relatively independent, the computing result of each computing unit does not influence other computing units, and the execution result of the task is unrelated to the execution sequence of the computing units;
the two-dimensional water quality model decomposes the pollutant diffusion process into time slices at equal intervals in time;
in each time slice, the water quality simulation is decomposed into simulation calculation with the infinitesimal as a basic unit, and the pollutant concentration simulated by the infinitesimal in the previous time slice is used as the initial concentration of the next time slice;
realizing watershed water quality simulation through iteration of time slices; the water quality simulation is realized by general calculation, and the core lies in the calculation independence of each simulation grid on a time slice, namely in the water quality simulation process, the simulation grid can only modify the attribute of the simulation grid, but can not modify the attributes of other grids; over a time slice, the water flow and contaminants of each simulation grid spread only into the 8-neighborhood simulation grid.
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