CN110532673B - Watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation - Google Patents
Watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation Download PDFInfo
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Abstract
The invention discloses a watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation, which comprises the following steps of: constructing and programming a model on a Matlab2015b platform, determining a specific basin, and giving inflow conditions of the basin in the basin by taking a production confluence model with no extra water loss in a basin system as a starting point to ensure that the model can work under the conditions of system closure and variable inflow; the river basin is taken as a whole, the influence of the climate change outside the river basin where the river basin is located on the river basin surface source pollution state is considered, a set of lumped semi-empirical river basin surface source pollution model is developed and constructed to integrate and mathematically analyze the river basin surface source pollution-climate effect, river basin surface source pollution dynamic under the climate change is analyzed from the time domain angle, a reasonable treatment scheme is favorably formulated, the pollution of agricultural river basin surface sources is conveniently controlled, and the method plays a positive role in constructing a clean river basin.
Description
Technical Field
The invention relates to the field of agricultural environmental pollution, in particular to a watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation.
Background
Along with the development of scientific technology, the pollution problem of a drainage basin becomes a serious problem, in the prior art, in the simulation process of agricultural drainage basin area source pollution, the intensity and the sensitivity difference of drainage basin area source pollution effects of a main typical drainage basin area under climate change are difficult to estimate, the influence of the climate change outside the drainage basin where the drainage basin is located on the drainage basin area source pollution state cannot be considered, the adaptability of a model is poor, and the research cost is high, so that the drainage basin area source pollution simulation method based on one-dimensional water flow evolution process simulation is provided to solve the problems in the prior art.
Disclosure of Invention
Aiming at the problems, the invention provides a watershed surface source pollution simulation method based on one-dimensional water flow evolution process simulation, which takes a watershed as a whole, considers the influence of climate change outside the watershed where the watershed is located on the watershed surface source pollution state, develops and constructs a set of lumped semi-empirical watershed surface source pollution model to integrate and mathematically analyze the watershed surface source pollution-climate effect, analyzes the watershed surface source pollution dynamic state under the climate change from the time domain angle, is favorable for formulating a reasonable management scheme, is convenient for controlling the pollution of the agricultural watershed surface source, and plays an active role in constructing a clean watershed.
In order to solve the problems, the invention provides a watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation, which comprises the following steps of:
the method comprises the following steps: constructing and programming a model on a Matlab2015b platform, determining a specific basin, and giving inflow conditions of the basin in the basin by taking a production confluence model with no extra water loss in a basin system as a starting point to ensure that the model can work under the conditions of system closure and variable inflow;
step two: increasing rainfall in the model, and simulating a unit process line and a basin inflow process:
(1) Rainfall device
According to literature research, daily rainfall events are statistically defined as a random process subject to poisson distribution, and the probability function of the random process satisfies the following definition:
where λ is the average incidence of random events per unit time (or unit area); e is the base of the natural logarithm, 2.718; k is 0,1,2, \ 8230n, n, in the stage of model example verification, rainfall adopts actual rainfall data, in the stage of model construction and test, due to the long-term climate change requirement and the limitation of future data, daily rainfall is described by a Poisson distribution function fitted by local rainfall data, daily rainfall is generated according to set rainfall intensity, rainfall duration and the distribution function, and the shape and scale parameters of the Poisson distribution function are obtained by adopting statistical approximation optimized by Root Mean Square Error (RMSE);
(2) Unit process line
According to some basic assumptions, a unit process line obtained by analyzing rainfall of a basin and flow process data at an outlet section corresponding to the rainfall is used for estimating a flow process from the rainfall process, the basin unit process line is assumed to obey gamma distribution of two parameters, and a Probability Density Function (PDF) of the unit process line is as follows:
wherein x is a random variable, gamma (a) is a gamma function, a and b are a shape parameter and a proportion parameter respectively, when a is larger, gamma distribution is very close to normal distribution, the gamma distribution only has the density of positive real numbers, and after rainfall and unit process lines are given, inflow is generated through a convolution algorithm;
(3) Convolution algorithm, fast fourier transform and watershed inflow
Calculating the process that the net rain generated in the drainage basin at different moments converges to the drainage basin as the inflow flow of the drainage basin, and finishing the process by superposing the rainfall process and the instantaneous unit process line through a convolution formula, wherein the formula can be expressed as follows:
where P is precipitation, UH is the unit process line, I (t) is the basin inflow rate as a function of time, and τ is the time interval; sigma is a space factor of a basin area (Aws) product coefficient and a runoff coefficient (Cr), the Cr is assumed to be a constant, the SCS method allows C to depend on rainfall intensity, total rainfall in a basin is redistributed according to a unit process line at the inflow position of the basin through a convolution formula, each position of rainfall or other inflow of the basin is superposed with a basin surface source pollution unit response, the inflow rate (superposed basin rainfall and basin surface source pollution units) finally converged into the basin after superposition effect is obtained, the superposition effect of multiple rains on the basin surface source pollution unit is considered at the same time, and the convolution operand is simplified through Fourier transform (FFT);
step three: evapotranspiration, simulation of lateral water loss and infiltration processes were added to the model:
(1) Evapotranspiration device
Simulated evapotranspiration, defined by the ratio of its initial evapotranspiration to the difference in vapour pressure (Malek et al, 2018), obtained from statistical historical estimates, the ratio of the difference in vapour pressure being defined by the ratio of the difference in vapour pressure to the difference in relative vapour pressure, the reference difference in vapour pressure being defined as 1 when not considering climate changes, the corresponding effect of heating up being simplified by controlling the ratio of the difference in vapour pressure to the air temperature according to set climate warming conditions, whereby the evapotranspiration of the basin is described by its potential evapotranspiration and precipitation functions, the amount of transpiration is defined as zero when a rainfall event occurs due to surface air saturation, the difference in Vapour Pressure (VPD) being described according to the ASCE standard reference evapotranspiration formula (Wang et al, 2018), defined by the air temperature (T), the Relative Humidity (RH) on the basis of the actual vapour pressure (ea) and the saturated vapour pressure (es), the specific formula being as follows:
es =0.6108 x exp (17.27 x T/(T + 237.3)) formula (3-4)
ea = RH/100 es formula (3-5)
VPD = ea-es formula (3-6);
(2) Term of transverse water loss
A transverse water loss term is introduced aiming at a basin in a subtropical humid and hot climate area, and generally comprises the following steps:
wherein x is a basin; AET (x) is the annual actual evapotranspiration of a certain type of land cover downslope x; p (x) is the annual precipitation in basin x; AET (x)/P (x) is an approximation of the Budyko curve; PET (x) is the potential evapotranspiration volume of the watershed x, ω is the improved, dimensionless amount of vegetation available and the annual expected precipitation,
PET(x)＝K c l x ·ET 0 (x) In the formula (3-8), land utilization/coating types in the lx basin x; kc is the intrinsic evapotranspiration coefficient of the vegetation under a certain land utilization/cover type in the watershed x, ET0 (x) is the relative evapotranspiration amount of the watershed x,
AET(x)＝Min(K c (l x )·ET 0 (x) P (x) formula (3-9)
In the formula, m is a month and takes the value of 1-12; kcm is the monthly average coefficient of the crop, ETom is the corresponding relative evapotranspiration,
wherein LAI is the leaf area index,
introducing a water loss parameter, tc, into the module, and considering a transverse water exchange water loss coefficient, W, defining:
tc = Kc + W type (3-12)
The water exchange loss comprises a transverse water exchange water loss (Wc) and a vertical water exchange water loss (Wv), the transverse loss is mainly considered, the transverse outward leakage and the downward leakage are carried out through a basin, namely the sum of the infiltration processes in the formula (3-12), and according to the research result of documents, the transverse water loss and the basin water depth have the following relationship,
Wc＝0.09755(Z-1.405) 6.3068 formula (3-13)
Wherein Wc is the amount of water lost by side permeation (water loss by transverse water exchange), and m 3 D; z is the water level, m,
since vertical leakage losses are not taken into account, there are:
W c w type (3-14)
Thus, formula (3-6) can be rewritten as:
tc = Kc + Wc formula (3-15)
Equations (3-8), (3-9) can be written as:
PET(x)＝Wc(lx)*ET 0 (x) Formula (3-16)
AET(x)＝Min(Tc(lx))*ET 0 (x) P (x)) formula (3-17;
(3) Infiltration of water
The process of infiltration is defined by Richards infiltration (Richards, 1931).
Where K is the hydraulic conductivity coefficient, h is the head of water due to capillary action, z is the elevation above the vertical reference plane, θ is the volumetric water content, t is the time,
the water level of the drainage basin after water storage is h, and the function and the state of the drainage basin are determined by adopting the critical water level of the drainage basin;
step four: the simulation of the evolution process of water flow and pollutants is added in the model:
(1) General equation of water flow and pollutant evolution system
Assuming no groundwater flow and pollutant impact, the system total flow equation is satisfied:
the inflow and outflow differences of the system meet the following conditions:
combining the above two formulas, there are:
by definition there is an inflow rate that satisfies:
q = AV = (bh) V formula (3-22)
From this the classical form of mass conservation is deduced:
in addition, two approximate calculation modes of water flow and pollutants are adopted for the flowing modes of the water flow and the pollutants in the drainage basin, the motion wave approximate calculation combining a continuity equation and a Manning equation is adopted for stable and uniform water flow and pollutants, the shallow water non-uniform and unsteady momentum equations combining the continuity equation and the Saint-Venn equation are adopted for unsteady and non-uniform water flow and pollutants for approximate calculation,
(2) Stable and uniform water flow and pollutants
For a steady uniform flow:
sigma F = ma =0 type (3-24)
Further, ρ (bh Δ x) gtan (θ) = τ (h Δ x) 2+ τ (b Δ x) formula (3-25)
Where ρ (bh Δ x) gtan (θ) is the gravity term, τ (h Δ x) 2 is the side friction force, τ (b Δ x) is the ground friction, τ is the shear or friction stress, ρ is the water density, g is the gravitational acceleration, based on the assumption that sin (θ) = tan (θ) = S, where S is the slope;
(3) Manning formula
In the formula, n is a Manning coefficient (mainly possible values are as follows), V is an area average velocity, rh is a hydraulic radius, and therefore, a continuity equation, a Manning formula and a relation of the hydraulic radius and a water head h are combined under the condition of stable and uniform water flow and pollutants:
since b > h, R h H is approximately equal to
(4) Unsteady non-uniform water flow and pollutants
For unsteady non-uniform water flow and pollutants, approximate calculations are performed using shallow water non-uniform and unsteady momentum equations of a combination of continuity equations and saint-wien equations, and under non-uniform flow conditions, static Pressure differences (CSP) may result in force imbalances, in addition to fluid weights (WG, weight) and surface friction stresses (FR) used in the deductive talent formula, i.e.,
WG = (ρ A Δ x) gS formula (3-28)
FR＝(PgAΔx)S f Formula (3-30)
Where Sf is the frictional loss per unit weight of fluid per unit length of channel, and therefore,
recombination of
Meanwhile, sf can be approximated by a variant formula of the Manning formula,
furthermore, under the condition of unsteady non-uniform flow water flow and pollutants, the continuous equation and the Saint Vietnam equation of the basin non-point source pollution process are combined to be as follows:
therefore, the evolution process of the watershed water flow and the pollutants is finally completed by solving the outflow flow velocity V and the water head h, and after the operation of each part is completed, the watershed non-point source pollution convergence process is simulated;
step five: changing the river basin non-point source pollution condition of river basin inflow and river basin attribute conditions such as vegetation coverage and the like in the simulation process, considering the effective contribution area of the river basin to the river basin, increasing the climate change driving scene and the response of the river basin non-point source pollution process brought by the climate change driving scene, then establishing a long-time sequence weather condition driven dynamic river basin non-point source pollution model, and clarifying the important influence of the climate change and the river basin attribute on the river basin non-point source pollution process by combining the step debugging model.
The further improvement lies in that: and step two and step three are integrated into the simulation of the basin runoff generation process of basin rainfall.
The further improvement lies in that: in step two (1), a typical rainfall event is selected according to two principles: the rainfall is not performed 5 days before and 10 days after the single rainfall event, which is to eliminate the cumulative effect of historical rainfall events and ensure the normal basic flow of a drainage basin, and then the generated daily rainfall is reduced into a rainfall time sequence with the scale below the day according to a certain time step, dt and the scale according to the duration of the rainfall, a corresponding time interval and the given annual rainfall.
The further improvement lies in that: in the step (2), the vertical loss is vertical infiltration of the water surface in the drainage basin, mainly including the storage amount of the soil layer in the drainage basin and the supplement of underground water when the drainage basin is completely dried and then is used for storing water again, and is closely related to the buried depth of the underground water, when the aquifer is saturated, the vertical loss is reduced, and the drainage basin definition is considered, so that the water is not continuously lost for a long time until the drainage basin is permanently dried, and the vertical loss is not considered.
The further improvement lies in that: in the third step (3), the critical water level of the drainage basin is used to determine the function and state of the drainage basin, in this case, the average water level is set as its critical value to compare the variation amplitude with the corresponding driving force for a long time, and meanwhile, the model assumes that the drainage of the drainage basin is frictionless, the water flow and pollutant process is defined by the manning formula, the water flow and pollutant outflow speed is V, and finally, the inflow and outflow of the drainage basin and drainage basin system are respectively calculated, and whether the conservation law of mass of the whole system is maintained is checked.
The further improvement is that: in the fourth step, after the operation of each part is completed, the basin area source pollution confluence process is simulated, so that basin attribute conditions such as basin area source confluence process pollution conditions and vegetation coverage of basin inflow in the simulation are changed, the evolution process of pollutants is analyzed, and the effective contribution area of the basin is considered.
The further improvement is that: and in the fifth step, the factors of basin seepage, precipitation, evapotranspiration, transverse seepage water and climate change are combined in the process of debugging the model.
The beneficial effects of the invention are as follows: the river basin is taken as a whole, the influence of the climate change outside the river basin where the river basin is located on the surface source pollution state of the river basin is considered, a set of lumped semi-empirical river basin surface source pollution model is developed and constructed to integrate and mathematically analyze the surface source pollution-climate effect of the river basin, the surface source pollution dynamic state of the river basin under the climate change is analyzed from the time domain angle, the long-term average value information provided by the time domain change is reliable, and reasonable adjustment can be made on the aspects of model calculation complexity, data requirements, research area characteristics, result accuracy and the like according to the requirements of research problems on the basis of the general river basin surface source pollution rule to improve the adaptability and research cost of the model.
Detailed Description
In order to make the technical means, objectives and functions of the invention easy to understand, the invention will be further described with reference to the following embodiments.
The embodiment provides a watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation, which comprises the following specific steps:
the method comprises the following steps: constructing and programming a model on a Matlab2015b platform, determining a specific basin, and giving inflow conditions of the basin in the basin by taking a production confluence model without extra water loss of a basin system as a starting point to ensure that the model can work under the conditions of system closure and variable inflow;
step two: increasing rainfall in the model, and simulating a unit process line and a basin inflow process:
(1) Rainfall device
According to literature research, daily rainfall events are statistically determined to be a random process subject to Poisson distribution, and a probability function of the random process meets the following definition:
where λ is the average incidence of random events per unit time (or unit area); e is the base of the natural logarithm, 2.718; k is 0,1,2, \8230n, in the model instance verification phase, rainfall adopts actual rainfall data, in the model construction and test phase, due to the long-term climate change requirement and the limitation of future data, daily rainfall is described by a poisson distribution function fitted by local rainfall data, daily rainfall is generated according to set rainfall intensity, rainfall duration and distribution function, the shape and scale parameters of the poisson distribution function are obtained by adopting statistical approximation optimized by Root Mean Square Error (RMSE), and meanwhile, a typical rainfall event is selected according to two principles: the method comprises the following steps that (1) rain is not produced 5 days before and 10 days after a single rainfall event, so that the accumulated effect of historical rainfall events is eliminated, normal base flow of a drainage basin is ensured, and then, according to the duration of rainfall, corresponding time intervals and given annual rainfall, the generated daily rainfall is reduced to form a rainfall time sequence with the scale below days according to a certain time step length, dt and scale;
(2) Unit process line
According to some basic assumptions, a unit process line obtained by analyzing rainfall of a basin and flow process data at an outlet section corresponding to the rainfall is used for estimating a flow process from the rainfall process, the basin unit process line is assumed to obey gamma distribution of two parameters, and a Probability Density Function (PDF) of the unit process line is as follows:
wherein x is a random variable, gamma (a) is a gamma function, a and b are a shape parameter and a proportion parameter respectively, when a is larger, gamma distribution is very close to normal distribution, the gamma distribution only has the density of positive real numbers, and after rainfall and unit process lines are given, inflow is generated through a convolution algorithm;
(3) Convolution algorithm, fast fourier transform and watershed inflow
The method is characterized in that the net rain generated in the drainage basin at different moments is calculated and converged to the drainage basin to be used as the process of inflow flow of the drainage basin, and the process is completed by a method of superposing a rainfall process and an instantaneous unit process line through a convolution formula, wherein the formula can be expressed as follows:
where P is precipitation, UH is the unit process line, I (t) is the basin inflow rate as a function of time, and τ is the time interval; sigma is a space factor of a basin area (Aws) product coefficient and a runoff coefficient (Cr), the Cr is assumed to be a constant, C is allowed to depend on the rainfall intensity by an SCS method, total rainfall in the basin is redistributed at a basin inflow position according to a unit process line through a convolution formula, each position of the basin rainfall or other incoming water is superposed with a basin surface source pollution unit response, the inflow rate (superposed basin rainfall and basin surface source pollution units) finally converged into the basin after superposition effect is obtained, the superposition effect of multiple rains on the basin surface source pollution unit is considered at the same time, and the convolution operand is simplified by utilizing Fourier transform (FFT);
step three: increasing evapotranspiration, lateral water loss and infiltration process simulation in the model:
(1) Evaporation device
Simulated evapotranspiration, defined by the ratio of its initial evapotranspiration to the difference in vapour pressure (Malek et al, 2018), obtained from statistical historical estimates, the ratio of the difference in vapour pressure being defined by the ratio of the difference in vapour pressure to the difference in relative vapour pressure, the reference difference in vapour pressure being defined as 1 when not considering climate changes, the corresponding effect of heating up being simplified by controlling the ratio of the difference in vapour pressure to the air temperature according to set climate warming conditions, whereby the evapotranspiration of the basin is described by its potential evapotranspiration and precipitation functions, the amount of transpiration is defined as zero when a rainfall event occurs due to surface air saturation, the difference in Vapour Pressure (VPD) being described according to the ASCE standard reference evapotranspiration formula (Wang et al, 2018), defined by the air temperature (T), the Relative Humidity (RH) on the basis of the actual vapour pressure (ea) and the saturated vapour pressure (es), the specific formula being as follows:
es =0.6108 x exp (17.27 x T/(T + 237.3)) formula (3-4)
ea = RH/100 es formula (3-5)
VPD = ea-es formula (3-6);
(2) Term of transverse water loss
A transverse water loss term is introduced aiming at a basin in a subtropical humid and hot climate area, and generally comprises the following steps:
wherein x is a watershed; AET (x) is the annual actual evapotranspiration of a certain type of land cover lower basin x; p (x) is the annual precipitation in basin x; AET (x)/P (x) is an approximation of the Budyko curve; PET (x) is the potential evapotranspiration volume of the watershed x, ω is the improved, dimensionless amount of vegetation available and the annual expected precipitation,
PET(x)＝K c l x ·ET 0 (x) Formula (3-8)
In the formula, land utilization/cover type in lx basin x; kc is the inherent evapotranspiration coefficient of the vegetation in the watershed x under a certain land utilization/cover type, ET0 (x) is the relative evapotranspiration amount of the watershed x,
AET(x)＝Min(K c (l x )·ET 0 (x) P (x) formula (3-9)
In the formula, m is a month and takes the value of 1-12; kcm is the monthly average coefficient of the crop, ETom is the corresponding relative evapotranspiration,
wherein LAI is the leaf area index,
introducing a water loss parameter, tc, into the module, and considering a transverse water exchange water loss coefficient, W, defining:
tc = Kc + W type (3-12)
The water exchange loss comprises two parts of transverse water exchange water loss (Wc) and vertical water exchange water loss (Wv), wherein the vertical loss is vertical infiltration of a water surface in a basin when the basin is completely dried and then is used for storing water again, mainly the storage amount of a soil layer in the basin and replenishing underground water, and has a close relation with the buried depth of the underground water, when an aquifer is saturated, the vertical loss is reduced, the basin definition is considered, the water is not continuously drained to be permanently dried for a long time, the vertical loss is not considered, the transverse loss is mainly considered, the transverse outward leakage and the downward leakage pass through the basin are the sum of downward seepage processes in the formula (3-12), and according to the research result of documents, the transverse water loss and the basin water depth have the following relation,
Wc＝0.09755(Z-1.405) 6.3068 formula (3-13)
Wherein Wc is the water loss by side permeation (water loss by transverse water exchange), and m3/d; z is the water level, m,
since vertical leakage losses are not taken into account, there are:
W c w type (3-14)
Thus, the formula (3-6) can be rewritten as:
tc = Kc + Wc formula (3-15)
Formulas (3-8), (3-9) can be written as:
PET(x)＝Wc(lx)*ET 0 (x) Formula (3-16)
AET(x)＝Min(Tc(lx))*ET 0 (x) P (x)) formula (3-17;
(3) Infiltration in the lower part of the body
The process of infiltration is defined by Richards infiltration (Richards, 1931).
Where K is the hydraulic conductivity coefficient, h is the head of water caused by capillary action, z is the elevation above the vertical datum level, θ is the volumetric water content, t is the time,
the method comprises the following steps of (1) after a watershed stores water, determining the function and the state of the watershed by adopting the critical water level of the watershed, setting the average water level as the critical value under the condition, comparing the variation amplitude of the average water level with the long-term corresponding driving force, simultaneously, assuming that the outflow of the watershed is frictionless by a model, defining the water flow and pollutant process by a Manning formula, setting the outflow speed of the water flow and pollutant as V, finally, respectively calculating the inflow and outflow of a watershed system, and checking whether the whole mass conservation law of the system is conserved or not;
step four: the simulation of the evolution process of water flow and pollutants is added in the model:
(1) General equation of water flow and pollutant evolution system
Assuming no groundwater flow and pollutant impact, the system total flow equation is satisfied:
the inflow and outflow differences of the system meet the following conditions:
combining the above two formulas, there are:
by definition there is an inflow rate that satisfies:
q = AV = (bh) V formula (3-22)
From this the classical form of mass conservation is deduced:
in addition, two approximate calculation modes of water flow and pollutants are adopted for the flowing modes of the watershed water flow and the pollutants, the motion wave approximate calculation combining a continuity equation and a Manning equation is adopted for stable and uniform water flow and pollutants, the shallow water non-uniform and unsteady momentum equations combining the continuity equation and the Saint-Venen equation are adopted for unsteady and non-uniform water flow and pollutants for approximate calculation,
(2) Stabilizing uniform water flow and pollutants
For a steady uniform flow:
Σ F = ma =0 equation (3-24)
Further, ρ (bh Δ x) gtan (θ) = τ (h Δ x) 2+ τ (b Δ x) formula (3-25)
Where ρ (bh Δ x) gtan (θ) is the gravity term, τ (b Δ x) 2 is the side friction force, τ (b Δ x) is the ground friction, τ is the shear or friction stress, ρ is the water density, g is the gravitational acceleration, based on the assumption that sin (θ) = tan (θ) = S, where S is the slope;
(3) Manning formula
Wherein n is the Manning coefficient (the main possible values are shown in the specification), V is the area average velocity,
rh is the hydraulic radius of the water to be measured,
TABLE 3-1 Manning coefficient Table
Table 3-1 The main tabulated values of Manning’s roughness coefficient
| Surfacing material | Manning coefficient (n) |
| Asphalt | 0.016 |
| Concrete-finishing | 0.012 |
| Channel-cleaning | 0.022 |
| Canal-gravel | 0.025 |
| Channel-weeds | 0.030 |
| Channel-stone, cobble | 0.035 |
| Flood plain-pasture, farmland | 0.035 |
| Plain-low density of flooding | 0.050 |
| Flood plain-medium density | 0.075 |
| Flood plain-high density forest | 0.15 |
| Glass | 0.010 |
| Crushing stone | 0.029 |
| Natural stream-clean and straight | 0.030 |
| Natural stream-most river | 0.035 |
| Natural stream with many and deep weeds | 0.040 |
Thus, under the condition of stable and uniform water flow and pollutants, combining a continuity equation, a Manning formula and a relation of a hydraulic radius and a water head h:
since b > h, R h H is approximately equal to
(4) Unsteady non-uniform water flow and pollutants
For unsteady non-uniform water flow and pollutants, approximate calculations are performed using shallow water non-uniform and unsteady momentum equations of a combination of continuity equations and saint-wien equations, and under non-uniform flow conditions, static Pressure differences (CSP) may result in force imbalances, in addition to fluid weights (WG, weight) and surface friction stresses (FR) used in the deductive talent formula, i.e.,
WG = (rho A. DELTA.x) gS formula (3-28)
FR＝(ρgAΔx)S f Formula (3-30)
Where Sf is the friction loss per unit weight of fluid per unit length of channel, and therefore,
recombination of
Meanwhile, sf can be approximated by a variant formula of the Manning formula,
furthermore, under the condition of unsteady non-uniform flow water flow and pollutants, the continuous equation and the Saint Vietnam equation of the basin non-point source pollution process are combined to be as follows:
therefore, the evolution process of the watershed water flow and the pollutants is finally completed by solving the outflow flow velocity V and the water head h, and after the calculation of each part is completed, the watershed non-point source pollution convergence process is simulated, so that the pollution conditions of the watershed non-point source convergence process of the watershed inflow and the watershed attribute conditions such as vegetation coverage are changed in the simulation, the evolution process of the pollutants is analyzed, and the effective contribution area of the watershed is considered;
step five: in the simulation process, the river basin non-point source pollution condition of river basin inflow and river basin attribute conditions such as vegetation coverage are changed, the effective contribution area of the river basin to the river basin is considered, the climate change driving situation and the response of the river basin non-point source pollution process brought by the climate change driving situation are increased, then a long-time sequence weather condition driven dynamic river basin non-point source pollution model is established, and the important influence of the climate change and the river basin attribute on the river basin non-point source pollution process is clarified by combining the step debugging model.
The river basin is taken as a whole, the influence of the climate change outside the river basin where the river basin is located on the surface source pollution state of the river basin is considered, a set of lumped semi-empirical river basin surface source pollution model is developed and constructed to integrate and mathematically analyze the surface source pollution-climate effect of the river basin, the surface source pollution dynamic state of the river basin under the climate change is analyzed from the time domain angle, the long-term average value information provided by the time domain change is reliable, and reasonable adjustment can be made on the aspects of model calculation complexity, data requirements, research area characteristics, result accuracy and the like according to the requirements of research problems on the basis of the general river basin surface source pollution rule to improve the adaptability and research cost of the model.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are given by way of illustration of the principles of the present invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, and such changes and modifications are within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: constructing and programming a model on a Matlab2015b platform, determining a specific basin, and giving inflow conditions of the basin in the basin by taking a production confluence model with no extra water loss in a basin system as a starting point to ensure that the model can work under the conditions of system closure and variable inflow;
step two: increasing rainfall in the model, and simulating a unit process line and a basin inflow process:
(1) Rainfall device
According to literature research, daily rainfall events are statistically defined as a random process subject to poisson distribution, and the probability function of the random process satisfies the following definition:
wherein λ is the average incidence of random events per unit time or unit area; e is the base of the natural logarithm, 2.718; k is 0,1,2, \ 8230n, in the model example verification stage, rainfall adopts actual rainfall data, in the model construction and test stage, due to the long-term climate change requirement and the limitation of future data, daily rainfall is described by a Poisson distribution function fitted by local rainfall data, daily rainfall is generated according to set rainfall intensity, rainfall duration and the distribution function, and the shape and scale parameters of the Poisson distribution function are obtained by adopting statistical approximation of root mean square error optimization;
(2) Unit process line
The unit process line obtained by analyzing rainfall of the drainage basin and flow process data at the corresponding outlet section is used for calculating the flow process in the rainfall process, the unit process line of the drainage basin is assumed to obey gamma distribution of two parameters, and the probability density function is as follows:
wherein x is a random variable, gamma (a) is a gamma function, a and b are a shape parameter and a proportion parameter respectively, when a is larger, gamma distribution is very close to normal distribution, the gamma distribution only has the density of positive real numbers, and after rainfall and unit process lines are given, inflow is generated through a convolution algorithm;
(3) Convolution algorithm, fast fourier transform and watershed inflow
Calculating the process that the net rain generated in the drainage basin at different moments converges to the drainage basin as the inflow flow of the drainage basin, and finishing the process by superposing the rainfall process and the instantaneous unit process line through a convolution formula, wherein the formula can be expressed as follows:
where P is precipitation, UH is the unit process line, I (t) is the basin inflow rate as a function of time, and τ is the time interval; sigma is a space factor of a basin area product coefficient and a runoff coefficient Cr, cr is assumed to be a constant, C is allowed to depend on precipitation intensity by an SCS method, total precipitation in a basin is redistributed at inflow positions of the basin according to a unit process line through a convolution formula, each position of rainfall or other incoming water of the basin is superposed with a basin area surface source pollution unit response, and the inflow rate of the final inflow basin after superposition effect is obtained, wherein the inflow rate of the final inflow basin comprises: superposing the drainage basin rainfall and drainage basin non-point source pollution units, simultaneously considering the superposition effect of multiple rainings in the drainage basin non-point source pollution units, and simplifying the operation amount of convolution by utilizing Fourier transform;
step three: increasing evapotranspiration, lateral water loss and infiltration process simulation in the model:
(1) Evaporation device
Simulating an evapotranspiration quantity, defined by a ratio of an initial evapotranspiration quantity to a vapor pressure difference, obtaining the initial evapotranspiration quantity from statistical history estimation, wherein the ratio of the vapor pressure difference is defined by the ratio of the vapor pressure difference to a relative vapor pressure difference, when climate change is not considered, the reference vapor pressure difference is defined as 1, and according to a set climate warming condition, the corresponding effect of temperature rise is simplified by controlling the ratio of the vapor pressure difference to air temperature, so that the evapotranspiration of a basin is described by potential evapotranspiration and precipitation functions of the basin, when a rainfall event occurs, the evapotranspiration quantity is defined as zero due to surface air saturation, the vapor pressure difference VPD is described by an ASCE standard reference evapotranspiration formula, and the actual vapor pressure and the saturated vapor pressure es are defined by the air temperature T and the relative humidity RH, and the specific formula is as follows:
es =0.6108 x exp (17.27 x T/(T + 237.3)) formula (3-4)
ea = RH/100 es formula (3-5)
VPD = ea-es formula (3-6);
(2) Term of transverse water loss
A transverse water loss term is introduced aiming at a basin in a subtropical humid and hot climate area, and generally comprises the following steps:
wherein x is a watershed; AET (x) is the annual actual evapotranspiration of a certain type of land cover lower basin x; p (x) is the annual precipitation in basin x; AET (x)/P (x) is an approximation of the Budyko curve; PET (x) is the potential evapotranspiration volume of the watershed x, ω is the improved, dimensionless amount of vegetation available and the annual expected precipitation,
PET(x)＝K c l x ·ET 0 (x) Formula (3-8)
Wherein, land utilization/cover type in lx basin x; kc is the inherent evapotranspiration coefficient of the vegetation in the watershed x under a certain land utilization/cover type, ET0 (x) is the relative evapotranspiration amount of the watershed x,
AET(x)＝Min(K c (l x )·ET 0 (x) P (x) formula (3-9)
In the formula, m is a month and takes the value of 1-12; kcm is the monthly average coefficient of the crop, ETom is the corresponding relative evapotranspiration,
wherein LAI is the leaf area index,
introducing a water loss parameter, tc, into the module, and considering a transverse water exchange water loss coefficient, W, defining:
tc = Kc + W formula (3-12)
The water exchange loss comprises a transverse water exchange water loss Wc and a vertical water exchange water loss Wv, the transverse loss is mainly considered, the transverse outward leakage and the downward leakage are carried out through a basin, namely the sum of the downward leakage process in the formula (3-12), and according to the research result of documents, the transverse water loss and the basin water depth have the following relationship,
Wc＝0.09755(Z-1.405) 6.3068 formula (3-13)
Wherein Wc is the transverse water exchange water loss, m 3 D; z is the water level, m,
since vertical leakage losses are not taken into account, there are:
w type (3-14) is approximately covered by Wc ≈ W
Thus, the formula (3-6) can be rewritten as:
tc = Kc + Wc formula (3-15)
Formulas (3-8), (3-9) can be written as:
PET(x)＝Wc(lx)*ET 0 (x) Formula (3-16)
AET(x)＝Min(Tc(lx))*ET 0 (x) P (x)) formula (3-17;
(3) Infiltration of water
The infiltration process is defined by richedz infiltration.
Where K is the hydraulic conductivity coefficient, h is the head of water due to capillary action, z is the elevation above the vertical reference plane, θ is the volumetric water content, t is the time,
the water level of the drainage basin after water storage is h, and the function and the state of the drainage basin are determined by adopting the critical water level of the drainage basin;
step four: the simulation of the evolution process of water flow and pollutants is added in the model:
(1) General equation of water flow and pollutant evolution system
Assuming no groundwater flow and pollutant impact, the system total flow equation is satisfied:
the inflow and outflow differences of the system meet the following conditions:
the two formulas above are combined, and the method comprises the following steps:
by definition there is an inflow rate that satisfies:
q = AV = (bh) V formula (3-22)
From this the classical form of mass conservation is deduced:
in addition, two approximate calculation modes of water flow and pollutants are adopted for the flowing modes of the water flow and the pollutants in the drainage basin, the motion wave approximate calculation combining a continuity equation and a Manning equation is adopted for stable and uniform water flow and pollutants, the shallow water non-uniform and unsteady momentum equations combining the continuity equation and the Saint-Venn equation are adopted for unsteady and non-uniform water flow and pollutants for approximate calculation,
(2) Stabilizing uniform water flow and pollutants
For a steady uniform flow:
sigma F = ma =0 type (3-24)
Further, ρ (bh Δ x) gtan (θ) = τ (h Δ x) 2+ τ (b Δ x) formula (3-25)
Where ρ (bh Δ x) gtan (θ) is the gravity term, τ (h Δ x) 2 is the side friction force, τ (b Δ x) is the ground friction, τ is the shear or friction stress, ρ is the water density, g is the gravitational acceleration, based on the assumption that sin (θ) = tan (θ) = S, where S is the slope;
(3) Manning formula
Where n is the Manning coefficient, V is the area average velocity, and Rh is the hydraulic radius, thus combining the continuity equation, the Manning equation, and the relationship of hydraulic radius and head h under stable uniform flow and contamination conditions:
since b > h, R h H is approximately equal to
(4) Unsteady non-uniform water flow and pollutants
For unsteady non-uniform currents and pollutants, approximate calculations are performed using shallow non-uniform and unsteady momentum equations of a combination of continuity equations and saint-wien equations, and under non-uniform flow conditions, static pressure differences can result in stress imbalances, i.e.,
WG = (rho A. DELTA.x) gS formula (3-28)
FR＝(ρgAΔx)S f Formula (3-30)
Where Sf is the friction loss per unit weight of fluid per unit length of channel, and therefore,
recombination of
Meanwhile, sf can be approximated by a variant formula of the Manning formula,
furthermore, under the condition of unsteady non-uniform flow water flow and pollutants, the continuous equation and the Saint Vietnam equation of the basin non-point source pollution process are combined to be as follows:
therefore, the evolution process of the watershed water flow and the pollutants is finally completed by solving the outflow flow velocity V and the water head h, and after the calculation of each part is completed, the watershed non-point source pollution convergence process is simulated;
step five: changing the river basin non-point source pollution condition of river basin inflow and the attribute condition of vegetation coverage river basin in the simulation process, considering the effective contribution area of the river basin to the river basin, increasing the climate change driving scene and the response of the river basin non-point source pollution process brought by the climate change driving scene, then establishing a long-time sequence weather condition driven dynamic river basin non-point source pollution model, and clarifying the important influence of climate change and river basin attribute on the river basin non-point source pollution process by combining the step debugging model.
2. The watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation according to claim 1, wherein: the step two and the step three are integrated into the process simulation of basin runoff generation by basin rainfall.
3. The watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation according to claim 1, wherein: in step two (1), a typical rainfall event is selected according to two principles: the rainfall is not rained 5 days before and 10 days after a single rainfall event, which is to eliminate the cumulative effect of historical rainfall events and ensure the normal base flow of a drainage basin, and then the generated daily rainfall is reduced into a rainfall time sequence with the scale below days according to a certain time step, dt and scale according to the duration of rainfall, a corresponding time interval and given annual rainfall.
4. The watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation according to claim 1, wherein: in the step (2), the vertical loss is vertical infiltration of the water surface in the drainage basin, mainly including the storage amount of the soil layer in the drainage basin and the supplement of underground water when the drainage basin is completely dried and then is used for storing water again, and is closely related to the buried depth of the underground water, when the aquifer is saturated, the vertical loss is reduced, and the drainage basin definition is considered, so that the water is not continuously lost for a long time until the drainage basin is permanently dried, and the vertical loss is not considered.
5. The watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation according to claim 1, wherein the method comprises the following steps: in the third step (3), the critical water level of the drainage basin is used to determine the function and state of the drainage basin, in this case, the average water level is set as its critical value to compare the variation amplitude with the corresponding driving force for a long time, and meanwhile, the model assumes that the drainage of the drainage basin is frictionless, the water flow and pollutant process is defined by the manning formula, the water flow and pollutant outflow speed is V, and finally, the inflow and outflow of the drainage basin and drainage basin system are respectively calculated, and whether the conservation law of mass of the whole system is maintained is checked.
6. The watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation according to claim 1, wherein the method comprises the following steps: in the fourth step, after the operation of each part is completed, the watershed non-point source pollution confluence process is simulated, so that the pollution condition of the watershed non-point source confluence process of watershed inflow and the attribute condition of vegetation coverage watershed are changed in the simulation, the evolution process of pollutants is analyzed, and the effective contribution area of the watershed is considered.
7. The watershed non-point source pollution simulation method based on one-dimensional water flow evolution process simulation according to claim 1, wherein: and in the fifth step, the factors of basin seepage, precipitation, evapotranspiration, transverse seepage water and climate change are combined in the process of debugging the model.
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