Method for calculating rainfall infiltration replenishment phreatic water volume under variable burial depth scene

Abstract

The invention discloses a method for calculating rainfall infiltration recharge groundwater under a variable burial depth scene, which comprises the following steps of: analyzing the comprehensive influence of rainfall and pre-rainfall groundwater burial depth on groundwater recharge groundwater, and constructing a corresponding segmented scene; constructing a rainfall infiltration phreatic water supply total amount model under a variable burial depth scene; constructing a distribution model of the total rainfall infiltration phreatic water replenishment amount; calibration of distribution model parameters; and the total amount model parameters are calibrated and substituted into a rainfall infiltration phreatic water replenishment total amount model for simulation, and the rainfall infiltration replenishment phreatic water amount is obtained. According to the method, the phreatic water supply amount is calculated by using the underground water burial depth and the rainfall data, the dynamic influence of the change of the underground water burial depth on the rainfall infiltration supply effect and the lag distribution effect of the rainfall infiltration supply phreatic water process are considered, and the problem that the after-rain infiltration supply amount is underestimated is effectively solved; and the method has a considerable practical application value for simulation of the phreatic water replenishment amount in a short period of time.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrology and water resources, and particularly relates to a calculation method for the rainfall infiltration recharge amount of phreatic water under the condition of variable buried depth. Background Technique

[0002] Rainfall infiltration is the main recharge source of groundwater in plain areas. Especially for areas with relatively shallow groundwater burial depths, accurately estimating the rainfall infiltration recharge amount under the condition of changing burial depths is crucial for evaluating the groundwater resource quantity.

[0003] Phreatic water is the shallow groundwater. When the groundwater burial depth changes, the path of rainfall infiltration recharge to phreatic water changes, resulting in changes in the rainfall redistribution process and increasing the estimation difficulty of the rainfall infiltration recharge amount of phreatic water. In the prior art, the rainfall infiltration recharge amount of phreatic water is often calculated in the form of the infiltration recharge coefficient method and the groundwater burial depth change method. Both of these methods are carried out for the condition of changing groundwater burial depths, but there are still the following deficiencies: In the infiltration recharge coefficient method, the piecewise coefficient method is used for processing. This processing method needs to segment the regional groundwater burial depth to determine the empirical values of the infiltration recharge coefficients within each groundwater burial depth interval, and multiply the two to obtain the rainfall infiltration recharge amount of phreatic water. This processing method ignores the dynamic relationship between the groundwater burial depth and the infiltration recharge coefficient, only focuses on the recharge effect of rainfall on phreatic water on the day of rainfall, and ignores the comprehensive influence of the groundwater burial depth and rainfall on the lag distribution process after rainfall.

[0004] In the groundwater burial depth change method, the dynamic analysis method is used for processing. This processing method first divides the rainfall events, and gives the change range of the groundwater burial depth and the specific yield within the rainfall event period, and multiplies the two to obtain the rainfall infiltration recharge amount of phreatic water. The application premise of this processing method is to know the change range of the groundwater burial depth within the period, which is mostly applicable to the estimation on an annual scale or a larger time scale and is difficult to meet the dynamic estimation requirements within a short period, resulting in poor estimation accuracy of the infiltration recharge amount within a short period. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the prior art does not consider the dynamic relationship between the groundwater burial depth and the infiltration recharge coefficient, nor does it consider the lag distribution process of the groundwater burial depth and rainfall on the recharge amount of phreatic water, resulting in poor estimation accuracy of the infiltration recharge amount within a short period. Therefore, a calculation method for the rainfall infiltration recharge amount of phreatic water under the condition of variable buried depth is proposed.

[0006] The technical solution of the present invention is as follows: A calculation method for the rainfall infiltration recharge amount of phreatic water under the condition of variable buried depth, comprising the following steps: Step 1, segmented influence discrimination: Select the event of rainfall infiltration recharge to the phreatic water, analyze the comprehensive influence of rainfall amount and groundwater depth before rain on the total phreatic water recharge, determine whether there is segmentation, and construct corresponding segmented scenarios.

[0007] Step 2, total amount model construction: Establish a model for the total amount of rainfall infiltration recharge to the phreatic water under the scenario of fixed groundwater depth, so that the parameters of the model for the total amount of rainfall infiltration recharge to the phreatic water under the scenario of fixed groundwater depth change dynamically with the groundwater depth, and construct a model for the total amount of rainfall infiltration recharge to the phreatic water under the scenario of variable groundwater depth.

[0008] Step 3, allocation model construction: Based on the lag distribution effect of the rainfall infiltration recharge process to the phreatic water, construct a characteristic function of the lag distribution weight for the total amount of rainfall infiltration recharge to the phreatic water, and construct an allocation model according to the superposition property of the phreatic water recharge process.

[0009] Step 4, calibration of allocation model parameters: Select the event of rainfall infiltration recharge where there is rainfall only at the 0th time step, and use the allocation weight at the 0th time step to calibrate the parameters of the characteristic function of the lag distribution weight.

[0010] Step 5, calibration of total amount model parameters: Substitute the calibrated parameter values of the characteristic function of the lag distribution weight into the allocation model, and according to the segmented scenarios in Step 1, calibrate the remaining parameters of the total phreatic water recharge model, and simulate the amount of rainfall infiltration recharge to the phreatic water.

[0011] Furthermore, Step 1 includes: Step 11, to avoid the overlap between the previous rainfall infiltration recharge process and the current event process, the event of rainfall infiltration recharge to the phreatic water selected should meet the following conditions: there is no rainfall in the five days before the start and the five days after the end of the current event, and both the soil moisture content and the groundwater depth are in a non-recharge state.

[0012] Step 12, use the classification algorithm to divide different segmented categories according to the influence of rainfall amount and groundwater depth before rain on the total phreatic water recharge, and obtain the segmented values of rainfall amount and groundwater depth before rain. According to the segmented values of rainfall amount and groundwater depth before rain, construct different segmented scenarios by pairwise combination.

[0013] For example, if the segmented value of rainfall amount is Pt 1 , and the segmented values of groundwater depth before rain are Ht 1 and Ht 2 , then there are 6 combined scenarios: 1) rainfall amount ≤ Pt 1 , 0 < groundwater depth before rain ≤ Ht 1 ; 2) rainfall amount ≤ Pt 1 ,Ht 1 <The groundwater depth before rainfall ≤ Ht 2 ; 3) The rainfall ≤ Pt 1 , and the groundwater depth before rainfall > Ht 2 ; 4) The rainfall > Pt 1 , 0 < the groundwater depth before rainfall ≤ Ht 1 ; 5) The rainfall > Pt 1 , Ht 1 <The groundwater depth before rainfall ≤ Ht 2 ; 6) The rainfall > Pt 1 , and the groundwater depth before rainfall > Ht 2 .

[0014] Furthermore, when the groundwater depth remains fixed in step 2, the amount of water that the vadose zone can accommodate is limited. Based on the premise of the limited amount of water that can be accommodated, the total phreatic recharge is limited by the amount of water that can be accommodated and has a limit value. Therefore, the rainfall infiltration phreatic recharge total model under the fixed groundwater depth scenario (abbreviated as the fixed-depth model) is:

[0015] Wherein, R g is the total rainfall infiltration phreatic recharge, mm; P is the rainfall, mm; R max is the limit value of the total rainfall infiltration phreatic recharge, mm, R max > 0; η is the maximum rate of increase of the total phreatic recharge with the rainfall, 0 < η < 1.

[0016] Derivation process of the fixed-depth model: In the shallow groundwater area, the variation range of the groundwater depth is limited. Under a specific groundwater depth, the amount of water that the vadose zone can accommodate is certain. Based on the premise of the limited amount of water that can be accommodated, the phreatic recharge does not increase infinitely with the rainfall, but is limited by the amount of water that can be accommodated. Therefore, as the rainfall increases, the phreatic water volume will continuously increase and then tend to a stable value, and its growth rate with respect to the rainfall will also gradually decrease from the initial relatively large growth rate and tend to 0.

[0017] Based on the above total rainfall infiltration phreatic recharge R g with respect to the rainfallP The change process R g and P The relationship between them should satisfy the following conditions:

[0018] To meet the requirements of C3 and C4 for in Equation (S2-1), assume according to the derivative principle:

[0019] In the formula, η , a and b are constant coefficients; represents the change rate of P when R g tends to 0.0 mm P with the change of

[0020] From Equation (S2-2), we can get:

[0021] To meet the requirements of C3 and C4 for R g in Equation (S2-1), it should be such that . Substitute this equation into the above formula, and we can get:

[0022] If Equation (S2-4) is to meet C1 in Equation (S2-1), it should be such that b = 0, then:

[0023] Combining the above formula and Equation (S2-2), based on the derivative principle, since is always less than 0, then is always not more than η . Therefore, η is the maximum rate of the total phreatic water recharge with the increase of rainfall. Considering that η is also the phreatic water recharge rate when P tends to 0.0 mm, if it is to meet C2 in Equation (S2-1) and make P always exceed the generated R g , it should be such that . Therefore, R g The final relationship between P is as follows:

[0024] Based on the above analysis and the physical meaning of the parameters, it is necessary to ensure that the parameter R max > 0, 0 < η < 1.

[0025] Furthermore, set the groundwater depth threshold H 0s and correct it based on the water-holding capacity of the vadose zone, the degree of water deficit, and the influence of evaporation during the infiltration process R max so that the parameter R max of the fixed-depth model changes dynamically with the groundwater depth, and thus obtain the total rainfall infiltration and phreatic water recharge amount when the groundwater depth changes R g That is, the total rainfall infiltration and phreatic water recharge amount model under the fixed-depth scenario (abbreviated as the variable-depth model) is:

[0026] Where H 0s is the optimal groundwater depth, m; R gm is H 0s the corresponding maximum phreatic water recharge amount, mm; R gm and H 0s are both greater than 0; H is the groundwater depth, m.

[0027] Derivation process of the variable-depth model: When P takes a specific value, R g is not fixed but changes with the groundwater depth H The depth not only affects the water-holding capacity of the vadose zone but also affects the degree of water deficit in the vadose zone and the infiltration recharge duration. If the change of R g with H is hidden in R max , then the water-holding capacity of the vadose zone, the degree of water deficit in the pre-rain vadose zone, and the influence of evaporation during the infiltration process on H 0s are divided by the depth threshold R max : When the depth is 0.0 m, the water-holding capacity of the vadose zone and the vertical hydraulic gradient are both zero, that is, R max is 0.

[0028] When the depth is less thanH 0s When the infiltration path is short, the duration of rainfall infiltration recharge is short and the vadose zone quickly reaches saturation. In this case, R max The value of mainly depends on the water-holding capacity of the vadose zone, thus R max will increase with H the increase of.

[0029] When the burial depth exceeds H 0s After that, due to the increase of the infiltration path, both the duration of rainfall infiltration recharge and the degree of water deficit in the vadose zone before rainfall will increase. Although the influence depth of evapotranspiration is limited, the consumption of the infiltrated water volume in the vadose zone by long-term evaporation cannot be underestimated. In this case, R max The value of depends on the degree of water deficit in the vadose zone before rainfall and the evaporation during the infiltration process, thus R max will decrease with H the increase of.

[0030] When the burial depth approaches infinity, due to the evaporation during the infiltration process, R max tends to 0.

[0031] Based on the above R max change process with H The relationship between the two should satisfy the following conditions:

[0032] To meet the requirements of C2 and C4 for in Equation (S2-7), assume according to the derivative principle:

[0033] Let and , then:

[0034] From this, we can get:

[0035] In Equations (S2-8) to (S2-11), a, b, c are all constant coefficients.

[0036] When , . According to the derivative principle, to meet C3 in Equation (S2-7), it is necessary to make a＞0 .

[0037] To satisfy C1 and C4 in Equation (S2-7), it is necessary to make c=0 and , that is, Equation (S2-11) should be:

[0038] According to the above equation, it can be obtained that:

[0039] If it is necessary to ensure that the above equation is consistent with the assumption in Equation (S2-8) and satisfy all conditions in Equation (S2-7), further obtain and . Thus, substituting these two equations into Equation (S2-12), R max and H The final relationship between them is as follows:

[0040] Through the above analysis and the physical meaning of the parameters, it is necessary to ensure that the parameters R gm and H 0s are both greater than 0.

[0041] Combining Equation (S2-6) and Equation (S2-14), the variable buried depth model is as follows:

[0042] Furthermore, Step 3 includes the following sub-steps: Step 31, determine the time step according to the application requirements, and divide the rainfall infiltration recharge to the phreatic water process into time steps.

[0043] Step 32, use the 0th step to represent the time when rainfall starts. Then the total phreatic water recharge generated by the rainfall in the i th step is distributed to the t th step, and the weight calculation formula is as follows:

[0044] Among them, i is the ordinal number of the time step, i = 0, 1... t ; w ( t - i ) is the weight of the total phreatic water recharge generated by the rainfall in the i th step lagged and distributed to the t th step; H ( i ) is thei The depth of the phreatic water, m; P ( i ) is the i step rainfall, mm; B 0 is the depth coefficient, related to the lithology of the vadose zone, m; B 1 is the rainfall coefficient, mm; P 0S is the optimal rainfall, mm.

[0045] Step 33, based on the superposition of the phreatic water recharge process, the phreatic water recharge in the current time step is the sum of the infiltration recharge amounts caused by the previous rainfall lagged and distributed to the current step. Then, the phreatic water recharge in the t step is the total phreatic water recharge caused by all rainfall from step 0 to step t lagged and distributed to the phreatic water recharge in step t The sum of the phreatic water recharge, that is, the distribution model is:

[0046] Among them, r g ( t ) represents the phreatic water recharge in the t step, mm.

[0047] Derivation process of the weight calculation formula and the distribution model: The duration of rainfall recharge to the phreatic water is relatively slow. If the start and end times of a certain rainfall are called the time length of the rainfall, and the start and end times of the phreatic water recharge process generated by this rainfall are called the time length of rainfall recharge to the phreatic water. In the shallow phreatic water area, the time lengths of the two are inconsistent, and the time length of phreatic water recharge is greater than the time length of rainfall, that is, there is a lagged distribution effect in rainfall recharge to the phreatic water. Equation (S2-15) gives the total amount of rainfall P generated by the rainfall infiltration phreatic water recharge R g . However, when the daily scale is used as the simulation scale, the lagged distribution process of the total rainfall phreatic water recharge should be considered, otherwise the phreatic water recharge amount on the day of rainfall will be overestimated.

[0048] The basic idea of existing research to characterize this lagged distribution effect is to identify the changing characteristics of the weight distribution of the total phreatic water recharge in time and construct the corresponding characteristic function. This characteristic function should satisfy that the area enclosed by its change curve and the coordinate axes in the first quadrant is 1, that is, the sum of the weights of the lagged distribution of the total phreatic water recharge should be 1. Based on the superposition of the phreatic water recharge process, taking the start day of rainfall as the start day of the phreatic water recharge process ( t=0 ), then the phreatic water recharge on the t day is from the start day of rainfall to thet The total amount of phreatic recharge caused by all rainfall within a day is lagged and distributed to the sum of the phreatic recharge amounts on the t day, that is:

[0049] In the formula, r g ( t ) represents the phreatic recharge amount on the t day, in mm; R g ( i ) is the total amount of phreatic recharge generated by the rainfall on the i day, in mm; i is the day ordinal number, i = 0, 1... t ; w ( t - i ) is the weight of the total amount of phreatic recharge generated by the rainfall on the i day lagged and distributed to the phreatic recharge amount on the t day, t ≥ i .

[0050] Most of the current research on the characteristic function of weight distribution only considers the influence of lag time on recharge weight, and rarely considers the influence of environmental factors on recharge weight. In the shallow groundwater area, the weight of phreatic infiltration recharge is affected not only by lag time, but also by rainfall and groundwater depth. These three factors jointly determine the shape of the phreatic recharge distribution weight curve and the time when the maximum recharge weight appears. The distribution weight curve of the total phreatic recharge in the shallow groundwater area presents two shapes: one is a monotonically decreasing change, and the other is a unimodal change. Which curve form it is is determined by the time when the maximum weight appears in the distribution curve, and the time when the maximum recharge weight appears also reflects the flatness of the distribution curve. When the time when the maximum weight appears is more delayed, the weight distribution curve is also flatter. Within a specific rainfall range, as the depth increases, the maximum recharge weight in the daily-scale distribution curve gradually delays, so that the distribution curve changes from monotonically decreasing to unimodal. However, when the rainfall increases or decreases more, the maximum recharge weight always appears on the day of rainfall, that is, the curve always shows a decreasing change. Therefore, there is a rainfall threshold that controls the time when the maximum recharge weight appears and the influence degree of groundwater depth on the curve shape.

[0051] Among the existing weight assignment characteristic functions, Chen Chongxi's formula (Literature: Chen Chongxi. Delayed recharge weight function - Method for dealing with the hysteresis of rainfall recharge to phreatic water [J]. Hydrogeology & Engineering Geology, 1998, 6(07): 24 - 26.) takes into account the influence of both the lag time and the groundwater depth on the weight assignment curve, and the formula has shown good application effects in many regions. Chen Chongxi's formula is applicable to the simulation of discrete phreatic water recharge processes, and its basic form is:

[0052] In the formula, B is called the depth interval coefficient, which is related to factors such as the lithology of the vadose zone, m. The meanings of the remaining parts of the formula are the same as above.

[0053] In the shallow groundwater area, as the depth increases, the weight assignment process curve of rainfall infiltration recharge to the phreatic water should gradually become flatter. Equation (S3 - 2) can already well reflect the change of the weight assignment process curve with the depth. However, Equation (S3 - 2) does not reflect the influence of rainfall amount on the assignment curve. Based on the changes in the lagged distribution process of phreatic water volume in the shallow groundwater area described above, w (0) is the research focus during modeling. When t = 0, . As H becomes larger, w (0) gradually becomes smaller, that is, the assignment curve gradually becomes flatter. Under a specific groundwater depth, there should exist a rainfall threshold P 0S such that w (0) changes its monotonicity. When 0 < P < P 0S , as P increases, w (0) gradually decreases. When P ≥ P 0S , as P increases, w (0) then increases again. Therefore, modifying B in Equation (S3 - 2) to , the weight assignment characteristic function applicable to the shallow groundwater area is:

[0054] In the formula, H ( i ) is the groundwater depth on the i th day, m; P ( i ) is the rainfall amount on the i th day, mm; B 0 is the depth coefficient, related to the lithology of the vadose zone, m;B 1 is the rainfall coefficient, in mm; P 0S is the optimal rainfall, in mm. The meanings of the other formulas are the same as above.

[0055] Further, the said step 4 includes: Step 41, when there is rainfall in multiple time steps, it is difficult to divide the distribution process of the groundwater recharge amount caused by rainfall within a single time step. Select the rainfall infiltration recharge event with rainfall only in the 0th time step, and calculate when t = i = 0 at this time w(0) the actual value, that is, the calculation formula for the distribution weight of the 0th time step is as follows:

[0056] where, T r is the total number of time steps of this rainfall infiltration recharge event.

[0057] Step 42, the parameters of the lagged distribution weight characteristic function B 0 , B 1 and P 0S , set the following constraints according to their physical meanings:

[0058] Use the optimization algorithm to calibrate and obtain the optimal solutions of B w(0) through the actual value, the rainfall of the 0th step and the groundwater depth data. 0 B 1 and P 0S

[0059] Further, the said step 5 includes: Step 51, substitute the optimal solutions of the parameters B 0 , B 1 and P 0S of the lagged distribution weight characteristic function into the distribution model.

[0060] Step 52, for the parameters R gm , H 0s and η of the total groundwater recharge amount calculation model, set the following constraints according to their physical meanings:

[0061] Based on the segmented scenarios constructed in Step 12, through the rainfall and groundwater depth data at each time step in the rainfall infiltration recharge event, the parameters are calibrated for each scenario using an optimization algorithm. R gm , H 0s and η optimal solutions.

[0062] Step 53: Substitute the optimal solutions of the lag distribution weight characteristic function parameters B 0 , B 1 and P 0S , and the optimal solutions of the parameters R gm , H 0s and η of the total phreatic water recharge calculation model into the total phreatic water recharge model under the variable groundwater depth scenario to calculate the daily rainfall infiltration recharge phreatic water volume in the rainfall event.

[0063] The beneficial effects of the present invention are as follows: The method proposed by the present invention calculates the phreatic water recharge using groundwater depth and rainfall data, considering the dynamic influence of groundwater depth changes on the rainfall infiltration recharge effect and the lag distribution effect in the process of rainfall infiltration recharge to the phreatic water, effectively solving the problem of underestimation of the infiltration recharge volume after rainfall, and having considerable practical application value for simulating the phreatic water recharge volume in a short time period. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is a schematic diagram of the lag distribution weight characteristic function in Step 3 of the present invention; Figure 2 is a schematic diagram of the superposition property of the phreatic water recharge process in Step 3 of the present invention; Figure 3 is the classification result of the decision tree in Example 1; Figure 4 is the effect of simulating the daily rainfall infiltration recharge phreatic water volume using the method proposed by the present invention in Example 1; Figure 5 is the comparison effect of simulating the phreatic water recharge volume between the present invention and the existing Method 1 in Example 2. DETAILED DESCRIPTION OF THE INVENTION

[0065] The following further describes in detail the specific embodiments of the present invention with reference to the drawings and examples: The following examples are only used to explain the present invention and are not intended to limit the scope of the present invention.

[0066] Example 1: In this embodiment, the field data around the Wudaogou Experimental Station is used, and the measured field data from 2010 to 2021 is selected to verify the feasibility and effectiveness of the calculation method of the present invention. The field soil is lime concretion black soil, and the planted crops include wheat and corn. The measured data of the experimental station includes the groundwater depth, soil moisture content (including depths of 5, 15, 25, 35, 45, 55, 70, and 90 cm), and the measured data of the meteorological station includes rainfall and average temperature. The above monitoring frequency is once a day for all.

[0067] The specific calculation steps are as follows: Step 1, select the events of rainfall infiltration replenishing phreatic water. Use the decision tree to classify rainfall and groundwater depth before rain according to the total phreatic water recharge in the field, and establish segmented scenarios, which specifically include the following sub-steps: Step 11, use the meteorological data of the field from 2010 to 2021, the measured groundwater depth and soil moisture content data of the experimental station to select the events of rainfall infiltration replenishing phreatic water. The selected events need to meet the following conditions: the rainfall monitored in the five days before the start and the five days after the end of the current event are both 0, the soil moisture content (including depths of 5, 15, 25, 35, 45, 55, 70, and 90 cm) shows an unchanged or decreasing trend, and the groundwater depth shows an unchanged or increasing trend.

[0068] According to this requirement, a total of 207 events of rainfall infiltration replenishing phreatic water are selected. Table 1 shows the key information such as rainfall characteristics, phreatic water recharge characteristics, and soil layer humidity before rain in the selected events.

[0069] Table 1 Key information of 207 events of rainfall infiltration replenishing phreatic water

[0070] Calculate the total phreatic water recharge using the measured groundwater depth. Assume that during rainfall, the influence of phreatic water evaporation on the change of the groundwater level is small, then the decrease in depth is caused by rainfall infiltration. The phreatic water recharge during the period is calculated by the following formula:

[0071] Where, R g is the total rainfall infiltration phreatic water recharge, mm; is the decrease in groundwater depth caused by rainfall infiltration during the period, mm; h is the average groundwater depth during the period, m; is the specific yield varying with h . For the specific yield of lime concretion black soil, when h is between 0.0 m and 1.0 m, a constant value of 0.035 is taken, and when h exceeds 1.0 m, a constant value of 0.045 is taken.

[0072] When calculating the total phreatic water recharge in the selected event, with a day as the unit time period, the total phreatic water recharge in the event is the sum of the phreatic water recharge in each time period.

[0073] Step 12: Based on the information of the selected 207 events, use decision tree analysis to analyze the influence degree of rainfall and the pre-rain groundwater depth (i.e., the pre-rain depth in Table 1) on the total phreatic water recharge. The decision result shows that the influence degree of rainfall on the total phreatic water recharge exceeds that of the pre-rain depth. Due to the great disparity in the influence degree between the two, the decision tree ignores the pre-rain groundwater depth and only represents the stage of the total phreatic water recharge based on the numerical size of a single factor of rainfall. Figure 3 The classification result of the decision tree is shown, and the sample quantity is represented by n The total sample size is 207. The decision tree takes 32.5 mm of rainfall as the boundary and divides the total phreatic water recharge into two categories: one is that the rainfall is less than 32.5 mm, which contains 106 samples and accounts for 51.2% of the total sample size, and the average value of the total phreatic water recharge is 5.822 mm with a standard deviation of 5.790 mm; the other is that the rainfall is greater than or equal to 32.5 mm, which contains 101 samples and accounts for 48.8% of the total sample size, and the average value of the total phreatic water recharge is 28.823 mm with a standard deviation of 33.593 mm. Therefore, according to the decision result, two segmented scenarios are constructed, namely the scenario with rainfall ≤ 32.5 mm and the scenario with rainfall > 32.5 mm.

[0074] Step 2: Establish a variable-depth model, and the calculation formula is as follows:

[0075] Among them, R g is the total phreatic water recharge by rainfall infiltration, in mm; R gm is H 0s the corresponding maximum total phreatic water recharge, in mm; H 0s is the optimal groundwater depth, in m; H is the groundwater depth, in m; P is the rainfall, in mm; η is the maximum rate of increase of the total phreatic water recharge with the increase of rainfall; the parameters η and H 0s and R gm are determined in the following step 5 according to the rainfall scenario.

[0076] Step 3: Determine the time step according to the application requirements, establish a lagged distribution weight characteristic function, and distribute the total phreatic water recharge at this time step, which specifically includes the following sub-steps: Step 31. Based on the actual application requirements, obtaining the daily-scale phreatic water recharge can meet the simulation requirements. Therefore, taking the day as the time step, the time scale of the phreatic water recharge process caused by rainfall events is divided.

[0077] Step 32. Establish a lag distribution weight characteristic function for the total phreatic water recharge caused by rainfall infiltration, as Figure 1 shown. Then, the 0th day is the starting day of rainfall, and the formula for calculating the weight of the total phreatic water recharge generated by the rainfall on the i th day allocated to the phreatic water recharge on the t th day is as follows:

[0078] where, i is the ordinal number of the time step, which is the daily ordinal number in this embodiment, i = 0, 1... t ; w ( t - i ) is the weight of the total phreatic water recharge generated by the rainfall on the i th day lagged and allocated to the phreatic water recharge on the t th day; H ( i ) is the groundwater depth on the i th day, m; P ( i ) is the rainfall on the i th day, mm; B 0 is the depth coefficient, m; B 1 is the rainfall coefficient, mm; P 0S is the optimal rainfall, mm.

[0079] Step 33. The phreatic water recharge on the current day is the sum of the lagged allocations of the infiltration recharge caused by the previous rainfall to the current day. As Figure 2 shown, the phreatic water recharge on the t th day is the sum of the phreatic water recharge on the t th day lagged and allocated from all the rainfall-induced phreatic water recharge from the 0th day to the t th day. The calculation formula is as follows:

[0080] where, r g ( t ) represents the phreatic water recharge on the t th day, mm.

[0081] Step 4: Select the event with rainfall only on the 0th day in Table 1, identify the weight value of the total phreatic water recharge allocated on the rainfall day, and calibrate the parameters of the lag-allocation weight characteristic function using the least squares method. Specifically, it includes the following sub-steps: Step 41: Select the events with a rainfall duration of 1 day in Table 1, a total of 45 events. According to the following formula, calculate the allocation weight of the total phreatic water recharge on the first day in the 45 events w (0), and the calculation formula is as follows:

[0082] To simplify the calibration difficulty and improve the calibration efficiency, take the logarithm of both sides of the above formula, and the result is as follows:

[0083] Step 42: The parameters of the lag-allocation weight characteristic function B 0 、 B 1 and P 0S , set the following constraints according to their physical meanings:

[0084] Using the non-linear least squares method, through the actual values, rainfall amounts, and pre-rain groundwater depths in the 45 events , calibrate to obtain the optimal solutions of B 0 、 B 1 and P 0S are 1.12, 8.56, and 33.12 respectively. w The goodness of fit between the actual value and the simulated value of (0) is 0.74. Table 2 gives the input and output information of the lag-allocation weight characteristic function in the 45 events.

[0085] Table 2 Input and output information of the lag-allocation weight characteristic function in the selected 45 events

[0086] Step 5: Substitute the optimal solutions of the parameters B 0 、 B 1 and P 0S , calibrate the total phreatic water recharge according to the scenario segmentation obtained in Step 12, and calculate the remaining parameters of the total phreatic water recharge model. Specifically, it includes the following sub-steps: Step 51: Substitute the B 0 、B 1 and P 0S The optimal solutions are substituted into the allocation model. Among them, B 0 , B 1 and P 0S The optimal solutions are 1.12, 8.56, and 33.12 in sequence.

[0087] Step 52, for the parameters R gm , H 0s and η of the total phreatic recharge calculation model, set the following constraints according to their physical meanings:

[0088] Using the daily groundwater table depth, rainfall, and phreatic recharge data in 207 events, for the two types of scenarios obtained in step 12: one type is that the rainfall is less than 32.5 mm; the other type is that the rainfall is greater than or equal to 32.5 mm, the optimal solutions of R gm , H 0s and η are obtained by calibrating in different scenarios using the non - linear least - squares method, as shown in Table 3.

[0089] Table 3 Optimal solutions of the parameters of the total phreatic recharge calculation model

[0090] Using the optimal solutions of the parameters of the total phreatic recharge model and the lagged allocation weight characteristic function estimated above, the daily rainfall infiltration recharge to the phreatic water in 207 events is simulated. As Figure 4 shown, the goodness of fit between the measured value and the simulated value of the recharge to the phreatic water is 0.96, the mean absolute error is 0.56 mm, and the root - mean - square error is 1.11 mm. The results show that the simulation effect between the two is good.

[0091] Example 2:

[0092] To further illustrate the simulation effect of this method, two existing phreatic recharge calculation methods are compared, and typical event scenarios are selected to conduct a comparison of the simulation effects. The serial number of the selected typical event scenario is 19, the occurrence period of the event scenario is from June 22, 2020 to July 10, 2020, the groundwater table depth before rainfall is 2.01 m, the rainfall is 141.3 mm, and the total rainfall infiltration recharge to the phreatic water is 50.89 mm.

[0093] The existing method 1 is the infiltration recharge coefficient method. Based on the influence of the groundwater depth on the infiltration recharge coefficient in 207 events in Table 1, the recharge coefficient is segmented according to the groundwater depth: when the groundwater depth ≤ 1.0 m, the infiltration recharge coefficient is 0.31; when 1.0 m < groundwater depth ≤ 2.0 m, the infiltration recharge coefficient is 0.25; when the groundwater depth > 2.0 m, the infiltration recharge coefficient is 0.14. Figure 5 The effects of Method 1 and this method on simulating the rainfall infiltration recharge amount of groundwater in typical events were compared. The results show that the correlation coefficient between this method and the measured value is as high as 0.96, while the correlation coefficient between Method 1 and the measured value is 0.88. At the same time, Method 1 can only predict the groundwater recharge amount on the day of rainfall and is difficult to capture the groundwater recharge amount with a lag distribution after rainfall, resulting in an underestimation of the groundwater recharge amount after rainfall.

[0094] The existing method 2 is the groundwater depth change method. According to the characteristics of lime concretion black soil, when the groundwater depth is between 0.0 m and 1.0 m, the specific yield is taken as 0.035, and when the groundwater depth exceeds 1.0 m, the specific yield is taken as 0.045. There are 4 rainfall events in the event, and the rainfall amounts are 17.3, 89.8, 1.0, and 33.2 mm in sequence. The decreases in the groundwater depth during the rainfall periods are 49, 578, 2, and 576 mm in sequence. Thus, the estimated groundwater recharge amounts for the 4 rainfall events are 1.72, 20.23, 0.10, and 20.20 mm respectively, with a total of 42.25 mm. The total estimated groundwater recharge amount by this method is 51.51 mm. Comparing this method with Method 2, the estimated value of this method is closer to the actual value. In addition, when the duration of the rainfall event is long, Method 2 is difficult to further distribute the total groundwater recharge amount to a shorter time scale.

[0095] The above are the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art of this technology, without departing from the premise of the present invention, several improvements can still be made, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A method for calculating the amount of water recharged by rainfall infiltration under varying burial depth scenarios, characterized in that: The following steps are involved: Step 1: Segmental impact determination: Select rainfall infiltration recharge events, analyze the comprehensive impact of rainfall and pre-rain groundwater depth on the total amount of groundwater recharge, and determine whether there is segmentation and construct corresponding segmented scenarios; Step 2, total amount model construction: establish a total amount model of rainfall infiltration phreatic water recharge under a fixed burial depth scenario, make the parameters of the total amount model of rainfall infiltration phreatic water recharge under a fixed burial depth scenario change dynamically with the groundwater burial depth, and construct a total amount model of rainfall infiltration phreatic water recharge under a variable burial depth scenario; Step 3, allocation model construction: Based on the lagged allocation effect of the rainfall infiltration phreatic water recharge process, the lagged allocation weight characteristic function of the total rainfall infiltration phreatic water recharge is constructed, and the allocation model is constructed according to the superposition of the phreatic water recharge process; Step 4, calibration of allocation model parameters: select rainfall infiltration recharge events with rainfall only in the 0th time step, use the 0th time step to allocate weights, and calibrate the parameters of the lagged allocation weight characteristic function; Step 5, calibrate the total amount model parameters: substitute the calibrated parameter values ​​of the lagged allocation weight characteristic function into the allocation model, calibrate the parameters of the phreatic recharge total amount model according to the segmented scenario of step 1, and simulate the rainfall infiltration recharge phreatic water volume.

2. The method for calculating the amount of rainfall infiltration recharge in a changing burial depth scenario according to claim 1 is characterized in that: Step 1 includes: Step 11, select the rainfall infiltration recharge diving event that meets the following requirements: no rainfall occurs in the five days before and after the current event, and the soil moisture content and groundwater depth are both in a non-recharge state; Step 12, using a classification algorithm to divide different segmentation categories according to the impact of rainfall and groundwater depth before rain on the total amount of groundwater recharge, obtain the segmentation values ​​of rainfall and groundwater depth before rain, and construct different segmentation scenarios based on the segmentation values ​​of rainfall and groundwater depth before rain.

3. The method for calculating the amount of rainfall infiltration recharge in a changing burial depth scenario according to claim 2 is characterized in that: The total amount of recharge from rainfall infiltration into groundwater under the fixed burial depth scenario described in step 2 is: ； in, R g is the total amount of rainfall infiltration phreatic recharge, mm; P is the rainfall, mm; R max is the limit value of the total amount of rainfall infiltration and phreatic recharge, mm, R max >0; η is the maximum rate at which the total amount of phreatic water recharge increases with rainfall, 0< η <1.

4. The method for calculating the amount of rainfall infiltration recharge in a changing burial depth scenario according to claim 3 is characterized in that: The total amount of recharge from rainfall infiltration into groundwater under the changing burial depth scenario described in step 2 is: ； in, H 0s is the optimum groundwater depth, m; R gm for H 0s The corresponding maximum diving recharge volume, mm; R gm and H 0s All are greater than 0; H is the groundwater depth, m.

5. The method for calculating the amount of rainfall infiltration recharge in a changing burial depth scenario according to claim 4 is characterized in that: Step 3 specifically includes: Step 31, determining the time step according to the application requirements, and dividing the rainfall infiltration recharge diving process into time steps; Step 32, with step 0 representing the time when rainfall starts, then step i The total amount of phreatic water recharge generated by the first rainfall is allocated to the t The weight calculation formula of the step is as follows: ； in, i is the ordinal number of the time step, i =0, 1... t ; w ( t - i ) is the i The total amount of phreatic water recharge generated by the first rainfall is distributed to the second rainfall with a delay. t The weight of the diving recharge volume in the first step; H ( i ) is the i Groundwater depth, m; P ( i ) is the i Step rainfall, mm; B 0 is the burial depth coefficient, which is related to the lithology of the aeration zone, m; B 1 is the rainfall coefficient, mm; P 0S is the optimum rainfall, mm; Step 33: According to the superposition of the phreatic water recharge process, the phreatic water recharge in the current time step is the sum of the infiltration recharge caused by the previous rainfall and the current step. t The diving supply for the step is from step 0 to step t The total amount of phreatic water recharge caused by all rainfall within the step is allocated to the t The sum of the diving recharge in the first step, that is, the distribution model is: ； in, r g ( t ) indicates the t Diving supply volume for each step, mm.

6. The method for calculating the amount of water recharged by rainfall infiltration under a changing burial depth scenario according to claim 5 is characterized in that: Step 4 specifically includes: Step 41, select the rainfall infiltration recharge event with only rainfall in the 0th time step, and calculate the t=i=0 hour w The actual value of (0), that is, the weight calculation formula for the 0th time step is as follows: ； Step 42, Parameters of the hysteresis distribution weight characteristic function B 0. B 1 and P 0S , according to its physical meaning, the constraints are set as follows: ； Using optimization algorithms w(0) The actual value of , the rainfall in step 0 and the groundwater depth data are used to calibrate B 0. B 1 and P 0S The optimal solution of .

7. The method for calculating the amount of rainfall infiltration recharge in a changing burial depth scenario according to claim 6 is characterized in that: Step 5 specifically includes: Step 51: assign the parameters of the hysteresis weight characteristic function B 0. B 1 and P 0S Substitute the optimal solution into the allocation model; Step 52, the parameters of the diving recharge total amount calculation model R gm , H 0s and η , according to its physical meaning, the constraints are set as follows: ； Based on the segmented scenarios constructed in step 12, the rainfall and groundwater depth data of each time step in the rainfall infiltration recharge event are used to calibrate the scenario by using the optimization algorithm. R gm , H 0s and η The optimal solution of Step 53: assign the hysteresis weight characteristic function parameter B 0. B 1 and P 0S The optimal solution for the total amount of diving supply calculation model parameters R gm , H 0s and η The optimal solution is substituted into the total amount of phreatic water recharge model under the changing burial depth scenario, and the daily rainfall infiltration recharge to phreatic water in the rainfall event is calculated.

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