A farmland drainage calculation method and system based on a frequency domain groundwater movement equation

Abstract

The application provides a farmland drainage calculation method and system based on a frequency domain groundwater movement equation, and the method comprises the following steps: establishing a steady-state recharge groundwater movement model and a groundwater flow model, calculating a steady-state groundwater level distribution and a groundwater level response to different frequency infiltration signals; combining crop water demand rules and regional hydrogeological characteristics, comparing and analyzing drainage calculation results under steady-state irrigation and periodic irrigation, and evaluating differences in drainage ditch design parameters; taking an actual rainfall process as a time domain recharge signal, decomposing frequency components of the signal by using a discrete Fourier transform, and extracting different frequency rainfall recharge signals; based on the frequency domain groundwater movement model, simulating groundwater fluctuation processes caused by the signals of different frequencies, and superimposing the processes in the time domain to obtain recharge groundwater dynamic changes and drainage calculation results of the actual rainfall. The application can reduce the engineering quantity of drainage ditch construction, is suitable for periodic irrigation scenarios, and can also be expanded for simulation of non-periodic events.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of groundwater movement simulation, and more particularly to a farmland drainage calculation method and system based on a frequency domain groundwater movement equation. BACKGROUND

[0002] Farmland drainage calculation is an important means to design drainage ditch parameters, simulate seepage fields, and evaluate drainage efficiency based on groundwater dynamics simulation, considering soil water infiltration, groundwater recharge and discharge, and soil water and groundwater evaporation processes. Drainage ditch design needs to consider various natural factors, such as meteorological conditions, groundwater depth, soil texture and its physical properties; at the same time, the influence of human factors, including crop types, farming systems, irrigation systems and irrigation methods, etc. needs to be fully evaluated. On this basis, by analyzing the influence of design parameters such as drainage ditch spacing and ditch depth on drainage efficiency, a scientific and reasonable drainage scheme can be provided.

[0003] In the calculation and research of farmland open ditch drainage, a large number of scholars have carried out systematic work. For example, based on one-dimensional groundwater movement theory, the calculation formula of drainage ditch seepage flow under flooding irrigation conditions is derived by using conformal transformation; considering the influence of evaporation on drainage volume, an analytical solution of groundwater level drawdown rate is derived, and an optimized drainage ditch design spacing is proposed; at the same time, combined with unsteady flow theory, a drainage design index system based on appropriate depth and duration of groundwater level exceeding standard is proposed. In addition, in order to deal with salinization disasters, researchers have also established drainage system design formulas under the condition of salinization control, and further considered the influence of ground slope and evaporation on the drainage process, enriching the theoretical system of open ditch drainage.

[0004] In addition to directly calculating drainage flow based on groundwater dynamics formula for design, farmland drainage research has also developed a series of comprehensive simulation models. For example, SWMS-2D and other numerical simulation models based on accurate solution of control equations have the advantages of rigorous physical basis and strong simulation capability, but their calculation is complex and time-consuming, especially in dealing with long time series or large scale simulation, which is low in efficiency and high in cost, limiting its wide application in practice.

[0005] Traditional drainage calculation is usually based on the assumption of steady-state infiltration, that is, assuming constant irrigation, drainage design is carried out according to the maximum groundwater level rise caused by irrigation and the maximum allowable groundwater depth for crops. However, irrigation is a dynamic process in practice, not a steady-state condition with constant input. The design based on steady-state assumption is often conservative, which may lead to an increase in the amount of drainage ditch construction. Therefore, there is an urgent need for a groundwater flow simulation and drainage design method suitable for any variable recharge conditions.

[0006] Field irrigation is often affected by crop growth period, rotation irrigation system and salt leaching period, and presents significant periodic characteristics. Studies have shown that, after soil moisture decreases, using a high-frequency periodic irrigation mode of once or twice a week can not only improve the efficiency of crop use of shallow groundwater, but also effectively prevent salt accumulation in the root zone, thereby promoting the healthy growth of crops. In a shallow saltwater environment, periodic irrigation is more beneficial to the healthy development of crops such as cotton than continuous irrigation. Under the condition of consistent total irrigation water, periodic irrigation can make the irrigation timing more discrete, which helps to delay the rise of the groundwater level, theoretically allowing the increase of the distance between drainage ditches and reducing the construction cost of the drainage system.

[0007] Therefore, it is necessary to develop a groundwater flow simulation model suitable for periodic irrigation scenarios to provide a theoretical basis and practical guidance for farmland drainage design. Although the existing drainage design based on the steady-state assumption can ensure that the rise of the groundwater level does not exceed the limit, the design distance is conservative, and the construction burden of the drainage system is heavy. Therefore, it is necessary to establish a theoretical system based on the frequency domain groundwater motion equation to simulate the dynamic response of groundwater under periodic irrigation conditions, and then optimize the drainage design. SUMMARY

[0008] The present application aims to solve the technical problems existing in the prior art, and provides a farmland drainage calculation method and system based on the frequency domain groundwater motion equation. The present application converts the traditional steady-state recharge problem to periodic recharge, which helps to analyze the differences in drainage ditch design parameters under different irrigation methods.

[0009] According to a first aspect of the present application, a farmland drainage calculation method based on the frequency domain groundwater motion equation is provided, comprising the following steps:

[0010] A one-dimensional groundwater motion model of groundwater between drainage ditches under the condition of steady-state irrigation recharge of the upper boundary is established, and the corresponding steady-state groundwater level distribution is calculated;

[0011] A one-dimensional frequency domain groundwater flow model under the condition of periodic irrigation recharge of the upper boundary is established, and the response of the groundwater level to different frequency infiltration signals is calculated;

[0012] The differences in drainage ditch design parameters under the conditions of steady-state irrigation and periodic irrigation are compared and analyzed by combining the water requirement law of typical crops in the irrigation area and the regional hydrogeological characteristics;

[0013] The actual rainfall process is taken as a time domain recharge signal, the frequency components of the time domain recharge signal are decomposed by using discrete Fourier transform, and the rainfall recharge signals of different frequencies are extracted;

[0014] Based on the frequency domain groundwater movement model, the groundwater fluctuation process caused by each frequency signal is simulated, and superposition is carried out in the time domain to obtain the dynamic change of the groundwater under the condition of non-periodic events and the corresponding drainage calculation result.

[0015] Based on the above technical solution, the application can also be improved as follows.

[0016] Optionally, the establishment of the one-dimensional groundwater movement model of the upper boundary steady-state irrigation recharge condition between the drainage ditches includes:

[0017] When the stable irrigation condition is stable, the stable irrigation amount is R 0, and the phreatic water is in a steady flow state, at this time, the aquifer is similar to a steady flow water pipe, the exploitation water comes from the recharge source, and the drainage amount q = R 0, and the distribution of the groundwater level between the drainage ditches is:

[0018]

[0019] In the formula, h indicates the simulated groundwater level, h 0 is the initial groundwater level; is the pressure conductivity coefficient of the phreatic aquifer, μ is the instantaneous saturation difference of the groundwater level sudden rise zone, that is, the soil water supply degree L is the interval of the drainage ditch, x is the horizontal distance of the groundwater level simulation point relative to the drainage ditch.

[0020] Optionally, when the steady-state infiltration is steady, the position of the highest groundwater level is located in the middle of the drainage ditch, at this time, the groundwater level is the highest, and the maximum value is h m According to the following formula:

[0021]

[0022] In the formula, h m indicates the position of the middle of the drainage ditch, and the maximum rising height of the simulated groundwater level; is the pressure conductivity coefficient of the phreatic aquifer, μ is the instantaneous saturation difference of the groundwater level sudden rise zone, that is, the soil water supply degree; R 0 is the stable irrigation amount, L is the interval of the drainage ditch.

[0023] Optionally, the establishment of the one-dimensional frequency domain groundwater flow model under the condition of the upper boundary periodic irrigation recharge includes:

[0024] When the recharge amount R When the fluctuation varies periodically, i.e. under periodic irrigation, R When the fluctuation varies periodically in the form of a trigonometric function, the distribution of the fluctuation of the groundwater level between the drainage ditches is:

[0025]

[0026] wherein, h p (x,ω) Table The simulated fluctuating groundwater level is in the form of a complex number, |h p | is the amplitude of the fluctuating groundwater level, is a complex unit; R p (ω) is the amplitude of the fluctuating recharge, ω is the frequency of the fluctuation, wherein it is assumed that T is the fluctuation period, ω= 2 π / T ; is the pressure conductivity coefficient of the phreatic aquifer, μ is the instantaneous saturated difference of the groundwater level surge zone, i.e. the soil water supply degree; L is the spacing of the drainage ditches, x is the horizontal distance of the simulation point of the groundwater level from the drainage ditches, and sinh is the hyperbolic sine function.

[0027] Optionally, the drainage ditch design parameters include the spacing of the drainage ditches; the difference in the drainage ditch design parameters is evaluated by comparing and analyzing the drainage calculation results under the conditions of steady-state irrigation and periodic irrigation in combination with the water demand law of the typical crops in the irrigation area and the regional hydrogeological characteristics.

[0028] For the design of the drainage ditches in the irrigation area, the most unfavorable drainage condition should be taken as the boundary parameter, and the limit drainage ditch spacing is calculated in combination with the highest expected value of the initial groundwater level.

[0029] Optionally, the calculation of the limit drainage ditch spacing in combination with the highest expected value of the initial groundwater level includes the maximum allowable rising amplitude of the groundwater h L The formula is expressed as:

[0030]

[0031] wherein ，h D is the average initial groundwater depth, h p | max is the maximum amplitude of the fluctuating groundwater level,h m,max This represents the maximum rise in groundwater level achieved through steady-state irrigation. h S,min The minimum depth of groundwater level suitable for crop growth.

[0032] Optionally, the step of using the actual rainfall process as a time-domain supply signal, and decomposing the frequency components of the time-domain supply signal using discrete Fourier transform to extract rainfall supply signals of different frequencies includes:

[0033] The time-domain rainfall replenishment signal is obtained by using the discrete Fourier decomposition method. R ( t Decomposed into steady-state supply terms R 0 and a series of fluctuation terms of different frequencies R pj The formula is expressed as follows:

[0034]

[0035] In the formula, R 0 represents the steady-state replenishment component, reflecting the average rainfall replenishment magnitude over the time series; R pj ( ω j ) represents the complex form of the supply fluctuation, | R pj The amplitude represented by | indicates the magnitude of the contribution of supply fluctuations at different frequencies. ω j For the angular frequency of the fluctuation, index j = 1,2… represents the frequency index. For complex units, t For time.

[0036] Optionally, the frequency-domain groundwater movement model simulates the groundwater fluctuation process caused by signals at various frequencies, and superimposes the simulations in the time domain to obtain the dynamic changes of groundwater under non-periodic event conditions and the corresponding drainage calculation results, including:

[0037] The replenishment of rainfall in a non-periodic event is known to be... R ( t The discrete Fourier decomposition method is used to decompose the feed into steady-state replenishment. R 0 and a series of fluctuations At this time, corresponding R ( t The groundwater level can be expressed as:

[0038]

[0039] In the formula, h (x , t ) represents the simulated groundwater level, h 0 is the initial groundwater level; is the phreatic pressure conduction coefficient, μ is the instantaneous saturated difference of the groundwater level sudden rise zone, i.e. the soil water yield L is the spacing of the drainage ditch, x is the horizontal distance of the groundwater level simulation point relative to the drainage ditch; R 0 is the steady-state recharge component, reflecting the average rainfall recharge size in the time series; R pj ( ω j ) is the complex form of the recharge fluctuation, R pj represents the amplitude, indicating the size of the contribution of the recharge fluctuation of different frequencies, ω j is the angular frequency of the fluctuation, and the index j = 1, 2… is the serial number of the frequency, is the complex unit, t is the time; and sinh is the hyperbolic sine function.

[0040] Optionally, the non-periodic event is represented as the recharge of actual rainfall; and the obtained groundwater dynamic change under the non-periodic event condition and the corresponding drainage calculation result further include:

[0041] According to the time series data of the recharge, the simulation data of the groundwater level are obtained, and the drainage ditch drainage capacity and the response time of the groundwater level to recover to a suitable groundwater level under the rainfall condition are calculated.

[0042] According to a second aspect of the present application, a farmland drainage calculation system based on a frequency domain groundwater motion equation is provided, comprising:

[0043] A steady-state recharge motion model establishment module is configured to establish a groundwater motion model under a steady-state recharge condition of the upper boundary;

[0044] A frequency domain recharge motion model establishment module is configured to establish a groundwater motion model under a periodic recharge condition of the upper boundary;

[0045] A frequency component obtaining module is configured to perform frequency domain decomposition on time series recharge data or rainfall data based on a discrete Fourier decomposition method to obtain frequency components of the steady-state recharge and the fluctuating recharge;

[0046] The drainage calculation module calculates the underground water level under steady-state recharge and fluctuation recharge and steady-state recharge motion models and frequency domain recharge motion models, obtains the underground water level signal under different frequencies and superimposes in the time domain.

[0047] Technical effects and advantages of the present application:

[0048] The present application provides a farmland drainage calculation method and system based on a frequency domain underground water motion equation, a one-dimensional underground water flow model suitable for periodic irrigation scenarios is constructed, and the dynamic response characteristics of the underground water level under periodic irrigation and steady-state irrigation under different soil types, underground water parameters, irrigation frequency and drainage ditch spacing conditions are analyzed; compared with steady-state drainage calculation, the farmland drainage calculation method based on the frequency domain underground water motion equation can reduce the engineering quantity of drainage ditch construction; the frequency domain underground water motion model can not only be applied to periodic irrigation scenarios, but also be extended to simulate non-periodic events, and has wide application prospects in agricultural water resource management and drainage system optimization. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the present application or prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0050] Figure 1 A farmland drainage calculation method based on a frequency domain underground water motion equation provided by an embodiment of the present application;

[0051] Figure 2 A schematic diagram of a drainage ditch design provided by an embodiment of the present application;

[0052] Figure 3 A spatial distribution diagram of water head between drainage ditches relative to initial underground water level depth under infiltration conditions provided by an embodiment of the present application, (a) in the diagram shows the spatial distribution of steady-state irrigation water head; (b) in the diagram shows the spatial distribution of water head fluctuation amplitude under periodic irrigation;

[0053] Figure 4 A comparison diagram of the maximum water head rise amplitude in the middle of the drainage ditch under steady-state irrigation and various periodic irrigation conditions provided by an embodiment of the present application h L With the change of drainage ditch spacing L

[0054] Figure 5 ​The effect picture of decomposition and fitting provided by the method for providing rainfall recharge of the embodiment of the present application is shown in the following figure;

[0055] Figure 6 The three-dimensional space-time distribution diagram of the groundwater level under rainfall conditions with respect to distance x and time t is provided for the drainage parameter combination of the embodiment of the present application;

[0056] Figure 7 The diagram of the change of the groundwater level with respect to time under rainfall conditions is provided for the embodiment of the present application; (a) in the diagram shows the change of the groundwater level with respect to time at the midpoint of the drainage ditch; (b) in the diagram shows the spatial distribution diagram of the groundwater level between the drainage ditches at different times. DETAILED DESCRIPTION

[0057] To make the objectives, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described below in connection with the drawings in the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0058] It can be understood that, based on the defects in the background art, the embodiment of the present application proposes a farmland drainage calculation method based on a frequency domain groundwater motion equation, specifically as shown in the following figure, which includes the following steps: Figure 1

[0059] Step 1, considering the steady-state irrigation (infiltration) recharge condition of the upper boundary, that is, the water received by the surface is infiltrated into the aquifer downward when the farmland is irrigated, it is assumed that the soil infiltration reaches a steady state (that is, the infiltration rate is equal to the irrigation recharge, and does not change with time), and this recharge can be simplified as a uniform infiltration flux. A one-dimensional (lateral) groundwater motion model of the groundwater between the drainage ditches under this condition is established, and the corresponding steady-state groundwater level distribution is calculated.

[0060] In the embodiment, the infiltration represents the process of water entering the soil and flowing into the groundwater aquifer after irrigation; considering the steady-state irrigation (infiltration) recharge condition of the upper boundary, that is, starting from the one-dimensional groundwater motion equation, under the condition of horizontal complete ditch drainage, the groundwater flow belongs to unsteady flow. Based on the Dupuit assumption, and assuming that the thickness of the aquifer is uniform and the thickness of the phreatic water layer can be ignored, the equation for the change of the water head in the one-dimensional direction is obtained as:

[0061] (1)

[0062] In the formula, μ is the instantaneous saturation difference of the groundwater level surge zone, that is, the soil water degree, k is the hydraulic conductivity.​R t represents the intensity of infiltration or evaporation, positive for infiltration and negative for evaporation; h represents the simulated groundwater level, x is the horizontal distance of the simulation point of groundwater level to the drainage ditch, t is the time.

[0063] Equation (1) is a second-order nonlinear partial differential equation, which must be linearized to obtain its analytical solution. Figure 2 shows the schematic diagram of drainage ditch design, when the initial groundwater level h 0 is much larger than the amplitude of groundwater level change, the kh in equation (1) can be approximately replaced by the average value of water head h 0, that is, the constant aquifer thickness is considered. h

[0064] Under the condition of homogeneous aquifer, equation (1) can be simplified to a linear partial differential equation:

[0065] (2)

[0066] where a = kh 0 / μ, is called the pressure conductivity coefficient of phreatic aquifer. The initial condition and boundary condition are:

[0067] (3)

[0068] where L is the spacing of drainage ditches.

[0069] Considering the change of water head in one-dimensional direction under stable irrigation, in equation (2) , the stable irrigation amount is R 0, and the underground phreatic water is in a steady flow state. At this time, the aquifer is similar to a steady flow water pipeline, and the exploitation water comes from the recharge source, the drainage amount q = R 0, and the change of groundwater level between drainage ditches is:

[0070] (4)

[0071] where h represents the simulated groundwater level, h 0 is the initial groundwater level; is the pressure conductivity coefficient of phreatic aquifer, μ is the instantaneous saturation difference of groundwater level sudden rise zone, that is, the soil water conductivity L is the spacing of drainage ditches, x ​​The horizontal distance of the simulation point from the drain.

[0072] According to equation (4), when the steady-state infiltration, the highest position of the groundwater level is in the middle of the drain, at this time the groundwater level is the highest, the maximum value h m The maximum height of the groundwater level can be calculated according to the following formula

[0073] (5)

[0074] In the formula, h m The middle position of the drain, the maximum height of the simulated groundwater level; The pressure conductivity coefficient of the phreatic aquifer, μ The instantaneous saturated difference of the groundwater level, that is, the soil water content; R 0 is the stable irrigation amount, L The spacing of the drain.

[0075] According to equation (5), under the condition of steady-state infiltration, the height of the groundwater level increases with the increase of the spacing of the drain.

[0076] Step 2, under the condition of periodic irrigation (infiltration) recharge at the upper boundary, that is, when the farmland irrigation changes with time as a sine wave, a one-dimensional frequency domain groundwater flow model of soil infiltration into the aquifer is established to calculate the response of the groundwater level to different frequency infiltration signals;

[0077] When the recharge amount R is fluctuating, that is, under the condition of periodic irrigation, R It presents a periodic fluctuation in the form of a trigonometric function with an angular frequency of ω, and the amplitude of the fluctuating recharge is R p (ω), the recharge process of the upper boundary can be expressed as a function of time: R p (ω)cos(ω t + φ ), t is the time, φ is the initial phase of the fluctuation, in the complex domain, this expression can be equivalently expressed in complex form: R p ( ω )e iωt . Substitute R p ( ω )e iωt into equation (2) to eliminate the complex term e iωt , we get:

[0078] (6)

[0079] where, h p h(x, ω) is the simulated wave groundwater level, which is a complex number, |h p | A is the amplitude of the wave groundwater level, is the complex unit; R p A(ω) is the amplitude of the wave recharge, ω ω is the frequency of the wave, which is assumed to be T T is the wave period, ω = 2 π / T ; K is the pressure conductivity of the phreatic aquifer, μ Δh is the instantaneous saturation deficit of the wave drawdown zone, i.e., the specific yield of the soil.

[0080] In this case, the boundary condition expressed by equation (3) becomes:

[0081] (7)

[0082] where, L L is the spacing of the drainage ditches.

[0083] The corresponding complex solution of equation (6) under the boundary condition of equation (7), i.e., the distribution of the wave groundwater level between the drainage ditches, is:

[0084] (8)

[0085] where, h p h(x, ω) is the simulated wave groundwater level, which is a complex number, |h p | A is the amplitude of the wave groundwater level, is the complex unit; R p A(ω) is the amplitude of the wave recharge, ω ω is the frequency of the wave, which is assumed to be T T is the wave period, ω= 2 π / T ; K is the pressure conductivity of the phreatic aquifer, μ Δh is the instantaneous saturation deficit of the wave drawdown zone, i.e., the specific yield of the soil. L L is the spacing of the drainage ditches, x x is the horizontal distance of the simulation point of the groundwater level from the drainage ditch. sinh is the hyperbolic sine function, sinh x = ( e x - e-x ) / 2.

[0086] Select parameter combinations: a =3000m 2 / d, μ =0.03, annual irrigation water volume is set at 0.6m, total irrigation time is 75 days, and drainage ditch spacing is... L = 200 m, irrigation cycle T = 30d. Figure 3 This demonstrates the spatial distribution of water head relative to the initial groundwater level depth between drainage ditches under the above parameter settings for both periodic and steady-state irrigation. Figure 3 (a) in the diagram shows the steady-state term. h According to formula (13), the water head reaches its maximum value in the middle of the two drainage ditches, rising by about 0.44 m. Figure 3 (b) shows the fluctuation term. h p The amplitude of the groundwater fluctuation along the ditch direction is the largest in the middle of the drainage ditch, close to 0.42 m, indicating that the amplitude of the groundwater fluctuation caused by periodic irrigation is smaller than the amplitude of the steady-state term.

[0087] Step 3: Combining the water requirement patterns of typical crops in the irrigation area and the regional hydrogeological characteristics, compare and analyze the drainage calculation results under steady-state irrigation and periodic irrigation conditions, and evaluate the differences in drainage ditch design parameters.

[0088] The drainage ditch design parameters include the spacing between drainage ditches. For irrigation area drainage ditch design, the most unfavorable drainage conditions should be used as boundary parameters, combined with the highest expected value of the initial groundwater level, to calculate the ultimate drainage ditch spacing. The design principle is as follows: Let the average initial groundwater depth be... h D =1.70 m, suitable groundwater level range for crop growth h S The maximum allowable rise in groundwater level is 1.30-2.30 m. h L )for:

[0089] (9)

[0090] In the formula, | h p | max This represents the maximum amplitude of the fluctuating groundwater level. h m,max This represents the maximum rise in groundwater level achieved through steady-state irrigation. h S,minThe minimum groundwater level depth suitable for crop growth. Taking the Hetao Irrigation District as an example, under any drainage parameters and irrigation cycle, the maximum head variation in the middle of the drainage ditch must not exceed 0.4 m, i.e. h L <0.4 m.

[0091] Select the parameter combination that is least conducive to drainage in the Hetao Irrigation District: a =3000m 2 / d, μ =0.03, the annual irrigation water volume is set to 0.6m, and the total irrigation time is 75 days. Figure 4 This demonstrates the maximum head rise at the center of the drainage ditch under selected parameter combinations, steady-state irrigation, and five different irrigation cycles. h L Depending on the spacing of the drainage ditch L The relationship between the changes. Under steady-state irrigation conditions, in order to control the rise in groundwater level within 0.4 m, the spacing between drainage ditches... L The distance must be less than 190 m. However, when using a farmland drainage design method based on frequency domain groundwater movement equations, the maximum permissible spacing of drainage ditches increases significantly. For example, during irrigation cycles... T = 10 days, L Up to 204 m; T = 5 days, L Up to 226 m; T = 2 days, L It can be magnified up to 252 m, so the farmland drainage design method based on the frequency domain groundwater movement equation can significantly reduce the amount of engineering work required for drainage ditch construction.

[0092] Step 4: Using the actual rainfall process as the time-domain supply signal, the frequency components of the supply signal are extracted by using Discrete Fourier Transform decomposition, and rainfall supply signals of different frequencies are extracted.

[0093] In this embodiment, the time-domain rainfall replenishment signal is decomposed using the Discrete Fourier Decomposition method. R ( t Decomposed into steady-state supply terms R 0 and a series of fluctuation terms of different frequencies R pj :

[0094] (10)

[0095] In the formula, R 0 represents the steady-state replenishment component, reflecting the average rainfall replenishment magnitude over the time series; R pj ( ω j ) represents the complex form of the supply fluctuation, |R pj | represents the amplitude of the different frequency components of the recharge fluctuation, ω j is the angular frequency of the fluctuation, index j = 1,2… is the order of the frequency, is the complex unit, t is time.

[0096] A 20-day simulation period is considered, in which a storm is assumed to occur from day 5 to 5.5 with a rainfall intensity of 100 mm / day. The time series of the recharge is decomposed according to equation (10) and the first 300 main frequency components are selected to compose the recharge series in time domain. Figure 5 It is shown that the discrete Fourier decomposition method can well reconstruct the time series of the recharge under the idealized storm scenario.

[0097] Step 5, based on the frequency domain groundwater flow model, simulate the groundwater fluctuation process caused by each frequency signal, and superimpose in time domain to obtain the groundwater dynamic change and corresponding drainage calculation results under the condition of non-periodic events;

[0098] The non-periodic event is represented as the recharge of actual rainfall. The recharge of the rainfall with non-periodic events is known R ( t ), which is decomposed into steady-state recharge R 0 and a series of fluctuation recharge At this time, the groundwater level corresponding to R ( t ) can be represented as:

[0099] (11)

[0100] In the formula, h ( x , t ) represents the simulated groundwater level, h 0 is the initial groundwater level; is the pressure conductivity coefficient of the phreatic aquifer, μ is the instantaneous saturated difference of the groundwater level surge zone, i.e. the soil water yield L is the spacing of the drainage ditch, x is the horizontal distance of the groundwater level simulation point from the drainage ditch; R 0 is the steady-state recharge component, reflecting the average rainfall recharge size in time series; R pj ( ω j ) is the complex form of the fluctuation recharge, | represents the amplitude of the different frequency components of the recharge fluctuation, R pj| represents the amplitude, indicating the size of the contribution of the different frequency fluctuations, ω j is the angular frequency of the fluctuations, index j = 1,2… is the serial number of the frequency, is the complex unit, t is time; sinh is the hyperbolic sine function, sinh x = ( e x - e -x ) / 2.

[0101] Finally, according to the time series data of recharge, the simulation data of groundwater level is obtained, and the drainage capacity of the drainage ditch under rainfall and the response time of the groundwater level to recover to the appropriate groundwater level are calculated.

[0102] Taking the Hetao Irrigation District as an example, assuming that a heavy rain occurs from the 5th to the 5th day, considering the rainfall intensity of 100 mm / day in the Hetao Irrigation District within 0.5 days, and selecting the most difficult drainage parameter combination in the Hetao Irrigation District: a =3000m 2 / d, μ =0.03, set the drainage spacing L =200m, the maximum allowable water head change in the middle of the drainage ditch h L <0.4 m. According to formula (11), the groundwater level between the drainage ditches will fall below the maximum allowable depth after 2.5 days of rainfall.

[0103] Figure 6 The three-dimensional space-time distribution of groundwater level with distance x and time t under the above drainage parameter combination under the condition of heavy rain is shown. It is found that the maximum rise of groundwater level reaches about 1.6 m, which is close to the initial average groundwater depth h D =1.7m, indicating that short-term heavy rainfall has a significant impact on groundwater level. Due to the effect of the drainage ditch, the groundwater level falls rapidly after the rain and recovers to the initial depth level within about 7 days after the rain.

[0104] Figure 7The figure of the change of the underground water level with time under the rainfall condition provided by the embodiment of the present application; (a) of the figure shows the change of the underground water level with time at the midpoint of the drainage ditch; (b) of the figure shows the spatial distribution of the underground water level between the drainage ditches at different time; (a) of the figure shows that the underground water level rises rapidly at the beginning of the rainfall (the 5th day) and reaches the peak (about 1.6 m) at the end of the rainfall (the 5.5th day). Then the water level gradually decreases and falls back to the maximum allowed depth at the 7.5th day. (b) of the figure shows the change of the spatial distribution of the underground water at different time sections (1 hour, 4 hours, 12 hours, 1 day, 2 days and 2.5 days) after the rainfall. The results show that the underground water level of most areas (about 30-170 m) of the field has broken the upper limit after 4 hours of the rainfall; the rising water level covers an area of about 10-190 m of the field after 12 hours; the influence range is 20-180 m after 1 day of the rainfall. Until 2.5 days after the rainfall, the underground water level falls back to below the allowed depth, which shows that in this scenario, the drainage ditch needs about 2.5 days to restore the crop root zone to the suitable underground water level.

[0105] Therefore, the embodiment of the present application provides a farmland drainage calculation method based on the frequency domain underground water movement equation. By constructing a one-dimensional underground water flow model suitable for the periodic irrigation scenario, the proposed frequency domain underground water movement method is not only suitable for the periodic irrigation scenario, but also can be extended to the non-periodic infiltration simulation and is suitable for the calculation of the underground water level between the ditches under any non-steady state irrigation scenario. The embodiment of the present application converts the traditional steady state recharge problem to the periodic recharge, which is helpful to analyze the difference of the drainage ditch design parameters (such as the distance between the ditches) under different irrigation modes. The simulation of the Hetao irrigation area as a representative area shows that under the same irrigation water quantity, the periodic irrigation mode can significantly slow down the rising amplitude of the underground water level, can more effectively prevent the crop from being damaged by waterlogging and can improve the regulation and control ability and efficiency of the drainage system. In addition, the frequency domain underground water movement model proposed by the present application is not only suitable for the periodic irrigation scenario, but also can be extended to simulate the non-periodic recharge event. In the sudden scenario such as the rainstorm, the dynamic change of the underground water level can be accurately simulated by the frequency domain reconstruction of the rainfall process, so as to enhance the application reliability and adaptability of the model in the actual farmland drainage.

[0106] According to the second aspect of the present application, a farmland drainage calculation system based on the frequency domain underground water movement equation is provided, comprising:

[0107] The steady state recharge movement model establishing module is used for establishing the underground water movement model under the steady state recharge of the upper boundary;

[0108] The frequency domain recharge movement model establishing module is used for establishing the underground water movement model under the periodic recharge of the upper boundary;

[0109] The frequency component obtaining module is configured to obtain frequency components of the steady recharge and the fluctuant recharge by performing frequency domain decomposition on the time series recharge data or the rainfall data based on a discrete Fourier decomposition method.

[0110] The drainage calculation module is configured to calculate the steady recharge and the fluctuant recharge in the underground water level based on the steady recharge and the fluctuant recharge and the steady recharge motion model and the frequency domain recharge motion model, and obtain the underground water level signals at different frequencies and superimpose the signals in the time domain.

[0111] It can be understood that the agricultural field drainage calculation system based on the frequency domain groundwater motion equation provided by the present application corresponds to the agricultural field drainage calculation method based on the frequency domain groundwater motion equation provided by the above-mentioned embodiments, and the related technical features of the agricultural field drainage calculation system based on the frequency domain groundwater motion equation can refer to the related technical features of the agricultural field drainage calculation method based on the frequency domain groundwater motion equation, which will not be repeated here.

[0112] According to a third aspect of the present application, an electronic device is provided, comprising an obtainer, a processor, a display and outputter, and a computer program stored in a memory and executable on the processor, wherein the processor executes the program to perform the method for calculating the surface net flux based on the frequency domain soil moisture equation.

[0113] In addition, the logical instructions in the memory described above can be implemented in the form of a software function unit and sold or used as an independent product, which can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in the embodiments of the present application. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0114] Although the preferred embodiments of the present application have been described, those skilled in the art can make further changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including all changes and modifications falling within the scope of the present application.

[0115] Finally, it should be noted that the above only describes the preferred embodiments of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art will appreciate that the technical solutions described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalent features, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A farmland drainage calculation method based on a frequency domain groundwater motion equation, characterized by, include: A one-dimensional groundwater movement model between drainage ditches is established under the condition of steady-state irrigation recharge at the upper boundary, and the corresponding steady-state groundwater level distribution is calculated. This includes: under stable irrigation conditions, with a stable irrigation volume of R0, the groundwater is in a steady flow state. In this case, the aquifer is similar to a steady-flow water conveyance pipe, the extracted water comes from the recharge source, the drainage volume is q = R0, and the groundwater level distribution between the drainage ditches is as follows: wherein, h S represents the simulated groundwater level, h 0 is the initial groundwater level; K is the pressure conductivity coefficient of the phreatic aquifer, μ is the instantaneous saturation deficit of the groundwater level in the phreatic aquifer, i.e. the soil water content L is the distance between the drainage ditches, x is the horizontal distance of the groundwater level simulation point from the drainage ditch; A one-dimensional frequency domain groundwater flow model is established under the condition of periodic irrigation recharge at the upper boundary, and the response of groundwater level to infiltration signals of different frequencies is calculated. This includes: when the recharge amount R fluctuates, i.e., under the condition of periodic irrigation, R exhibits periodic fluctuations in the form of a trigonometric function over time. In this case, the distribution of groundwater level fluctuations between drainage ditches is as follows: where h p (x, ω) represents the simulated fluctuating groundwater level, which is in complex form, |h p | is the amplitude of the fluctuating groundwater level, is the complex unit; R p (ω) is the amplitude of the fluctuating recharge, ω is the frequency of the fluctuation, which is assumed to be T is the fluctuation period, ω=2 π / T ; is the pressure conductivity of the phreatic aquifer, μ is the instantaneous saturation deficit of the groundwater level, i.e., the soil water yield; L is the spacing of the drainage ditches, x is the horizontal distance of the simulated point of the groundwater level from the drainage ditches, and sinh is the hyperbolic sine function. Based on the water requirement patterns of typical crops in the irrigation area and the regional hydrogeological characteristics, the drainage calculation results under steady-state irrigation and periodic irrigation conditions are compared and analyzed to evaluate the differences in drainage ditch design parameters. The actual rainfall process is used as the time-domain supply signal. The frequency components of the time-domain supply signal are decomposed by discrete Fourier transform, and rainfall supply signals of different frequencies are extracted. Based on the frequency domain groundwater movement model, the groundwater fluctuation process caused by signals of various frequencies is simulated and superimposed in the time domain to obtain the dynamic changes of groundwater under non-periodic event conditions and the corresponding drainage calculation results.

2. The method of claim 1, wherein the method is characterized by: When steady-state infiltration, the highest position of the groundwater level is located in the middle of the drain, at which time the groundwater level is the highest, the maximum value h m This is calculated according to the following formula: wherein h m is the maximum height of groundwater level rise in the middle of the drain; is the pressure conductivity coefficient of the phreatic aquifer, μ is the instantaneous saturated-unsaturated difference, i.e. the soil water content, in the groundwater level sudden rise zone; R 0 is the stable irrigation amount, L is the spacing of the drains.

3. The method of claim 1, wherein the method is characterized by: The drainage ditch design parameters include the spacing between drainage ditches; the evaluation of the differences in drainage ditch design parameters, by combining the water requirement patterns of typical crops in the irrigation area and the regional hydrogeological characteristics, and comparing and analyzing the drainage calculation results under steady-state irrigation and periodic irrigation conditions, includes: For the design of drainage ditches in irrigation areas, the most unfavorable drainage conditions should be used as boundary parameters, and the maximum expected value of the initial groundwater level should be combined to calculate the ultimate drainage ditch spacing.

4. The method of claim 3, wherein the method is characterized by: The calculation of the limit ditch spacing including the maximum allowable rise of groundwater in combination with the highest expected value of the initial groundwater level is expressed by the formula: h L The formula is expressed as: where ，h D is the average initial groundwater depth, h p | max is the maximum amplitude of fluctuating groundwater level, h m,max is the maximum rise in groundwater level resulting from steady-state irrigation, h S,min is the minimum groundwater depth for suitable crop growth.

5. The method of claim 1, wherein the method is characterized by: The step of using the actual rainfall process as a time-domain supply signal, and decomposing the frequency components of the time-domain supply signal using discrete Fourier transform to extract rainfall supply signals of different frequencies includes: The time domain rainfall recharge signal is decomposed into a steady state recharge term R ( t ) and a series of fluctuating terms of different frequencies by the discrete Fourier decomposition method R 0 R pj , which is expressed by the following formula: where R 0 is the steady-state recharge component, reflecting the average recharge from rainfall over the time series; R pj ω j is the complex form of the recharge fluctuation, R pj represents the amplitude, indicating the contribution of the recharge fluctuation of different frequencies, ω j is the angular frequency of the fluctuation, with index j = 1, 2… is the serial number of the frequency, is the complex unit, t is time.​ 6. The method of claim 1, wherein the method is characterized by: The frequency-domain groundwater movement model simulates the groundwater fluctuation process caused by signals at various frequencies, and superimposes the data in the time domain to obtain the dynamic changes of groundwater under non-periodic event conditions and the corresponding drainage calculation results, including: The recharge of rainfall, which is a non-periodic event, is given by R ( t ), which is decomposed into steady recharge R 0 and a series of fluctuating recharge , where the groundwater level corresponding to R ( t ) can be expressed as: where, h ( x , t ) denotes the simulated groundwater level, h 0 is the initial groundwater level; is the phreatic aquifer pressure conductivity, μ is the instantaneous saturation deficit of the groundwater level in the phreatic aquifer, i.e. the soil water content L is the distance between the drainage ditches, x is the horizontal distance of the groundwater level simulation point from the drainage ditch; R 0 is the steady-state recharge component, reflecting the average rainfall recharge over time; R pj ( ω j ) is the complex form of the recharge fluctuation, R pj | represents the amplitude, indicating the contribution of different frequencies of the recharge fluctuation, ω j is the angular frequency of the fluctuation, with the index j = 1,2… being the frequency number, is the complex unit, t is the time; sinh is the hyperbolic sine function.

7. The method of claim 1, wherein the method is characterized by: The non-periodic event is represented by actual rainfall replenishment; obtaining the dynamic changes of groundwater and corresponding drainage calculation results under non-periodic event conditions also includes: Based on the time series data of the replenishment, simulated data of the groundwater level were obtained, and the drainage capacity of the drainage ditch and the response time for the groundwater level to recover to a suitable level under rainfall conditions were calculated.

8. A farmland drainage calculation system based on the frequency-domain groundwater motion equation, used for the farmland drainage calculation method based on the frequency-domain groundwater motion equation in any one of claims 1 to 7, characterized in that, The system includes: The steady-state recharge motion model establishment module is used to establish a groundwater motion model under the upper boundary steady-state recharge condition. This includes: under stable irrigation conditions, with a stable irrigation volume of R0, the groundwater is in a steady flow state. In this case, the aquifer is similar to a steady-flow water conveyance pipe, the extracted water comes from the recharge source, the drainage volume is q = R0, and the groundwater level distribution between the drainage ditches is as follows: wherein, h S represents the simulated groundwater level, h 0 is the initial groundwater level; K is the pressure conductivity coefficient of the phreatic aquifer, μ is the instantaneous saturation deficit of the groundwater level in the phreatic aquifer, i.e. the soil water content L is the distance between the drainage ditches, x is the horizontal distance of the groundwater level simulation point from the drainage ditch; The frequency domain replenishment motion model establishing module is configured to establish a groundwater motion model under the condition of upper boundary periodic replenishment, and includes: when the replenishment amount R fluctuates, that is, under the condition of periodic irrigation, R presents a periodic fluctuation in the form of a trigonometric function with time, at this time, the distribution of groundwater level fluctuation between the drainage ditches is: where h p (x, ω) represents the simulated fluctuating groundwater level, which is in complex form, |h p | is the amplitude of the fluctuating groundwater level, is the complex unit; R p (ω) is the amplitude of the fluctuating recharge, ω is the frequency of the fluctuation, which is assumed to be T is the fluctuation period, ω=2 π / T ; is the pressure conductivity of the phreatic aquifer, μ is the instantaneous saturation deficit of the groundwater level, i.e., the soil water yield; L is the spacing of the drainage ditches, x is the horizontal distance of the simulated point of the groundwater level from the drainage ditch, and sinh is the hyperbolic sine function; The frequency component obtaining module is configured to obtain frequency components of steady replenishment and fluctuating replenishment by performing frequency domain decomposition on time series replenishment data or rainfall data based on a discrete Fourier decomposition method. The drainage calculation module is configured to calculate the groundwater level under steady replenishment and fluctuating replenishment of different frequencies according to the steady replenishment and fluctuating replenishment, and the steady replenishment motion model and the frequency domain replenishment motion model, to obtain the groundwater level signals under different frequencies and superimpose them in the time domain.

Images