A calculation method for the recharge amount of rainfall infiltration into the phreatic water under the condition of variable buried depth

Abstract

The present invention discloses a calculation method for the rainfall infiltration recharge amount of phreatic water under the condition of variable buried depth, including: analyzing the comprehensive influence of rainfall amount and the pre-rain groundwater buried depth on the total phreatic water recharge amount, and constructing corresponding segmented scenarios; constructing a model for the total rainfall infiltration phreatic water recharge amount under the condition of variable buried depth; constructing a distribution model for the total rainfall infiltration phreatic water recharge amount; calibrating the parameters of the distribution model; calibrating the parameters of the total amount model, and substituting them into the rainfall infiltration phreatic water recharge amount model to simulate the rainfall infiltration recharge amount of phreatic water. This method calculates the phreatic water recharge amount by using the groundwater buried depth and rainfall data, considers the dynamic influence of the change in groundwater buried depth on the rainfall infiltration recharge effect and the lag distribution effect of the rainfall infiltration recharge process of phreatic water, effectively solves the problem of underestimation of the post-rain infiltration recharge amount, and has quite practical application value for the simulation of the phreatic water recharge amount in a short time period.

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 rainfall infiltration recharge to 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 variable burial depth is crucial for evaluating the groundwater resource quantity.

[0003] Phreatic water is shallow groundwater. When the groundwater burial depth changes, the path of rainfall infiltration recharge to phreatic water changes, resulting in a change in the rainfall redistribution process and increasing the difficulty of estimating the rainfall infiltration recharge amount to phreatic water. In the prior art, the rainfall infiltration recharge amount to phreatic water is often calculated in the form of the infiltration recharge coefficient method and the groundwater burial depth change method. Although both methods are used to deal with the situation of groundwater burial depth change, the following deficiencies still exist:

[0004] In the infiltration recharge coefficient method, the sectional coefficient method is used for processing. This processing method requires dividing the regional groundwater burial depth into sections and determining the empirical values of the infiltration recharge coefficients within each groundwater burial depth interval, and multiplying the two to obtain the rainfall infiltration recharge amount to 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 groundwater burial depth and rainfall on the lag distribution process after rainfall.

[0005] In the groundwater burial depth change method, dynamic analysis is used for processing. This processing method first divides the rainfall events, gives the change amplitude 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 to phreatic water. The application premise of this processing method is to know the change amplitude of the groundwater burial depth within the period, and it is mostly applicable to the estimation on an annual scale or a larger time scale, and it 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

[0006] 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 the lag distribution process of groundwater burial depth and rainfall on the recharge amount to phreatic water, resulting in poor estimation accuracy of the infiltration recharge amount within a short period. Therefore, a calculation method for rainfall infiltration recharge to phreatic water under the condition of variable buried depth is proposed.

[0007] The technical solution of the present invention is as follows:

[0008] A calculation method for rainfall infiltration recharge to phreatic water under the condition of variable buried depth includes the following steps:

[0009] 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.

[0010] Step 2, total amount model construction: Establish a model for the total amount of rainfall infiltration recharge to the phreatic water under a fixed groundwater depth scenario, such that the parameters of the model for the total amount of rainfall infiltration recharge to the phreatic water under the fixed groundwater depth scenario change dynamically with the groundwater depth, and construct a model for the total amount of rainfall infiltration recharge to the phreatic water under a variable groundwater depth scenario.

[0011] Step 3, distribution 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 a distribution model according to the superposition property of the phreatic water recharge process.

[0012] Step 4, calibration of distribution model parameters: Select the event of rainfall infiltration recharge where rainfall occurs only at the 0th time step, and use the distribution weight at the 0th time step to calibrate the parameters of the characteristic function of the lag distribution weight.

[0013] Step 5, calibration of total amount model parameters: Substitute the calibrated parameter values of the characteristic function of the lag distribution weight into the distribution 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.

[0014] Furthermore, Step 1 includes:

[0015] 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 satisfy: there is no rainfall in the five days before the start and the five days after the end of the current event, and the soil moisture content and the groundwater depth are in a non-recharge state.

[0016] Step 12, use a classification algorithm to divide different segmented categories based on 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.

[0017] For example, 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 < groundwater depth before rain ≤ Ht 2; 3) rainfall amount ≤ Pt 1, groundwater depth before rain >Ht 2; 4) rainfall > Pt 1, 0 < pre-raingroundwater depth ≤ Ht 1; 5) rainfall > Pt 1, Ht 1 < pre-raingroundwater depth ≤ Ht 2; 6) rainfall > Pt 1, pre-raingroundwater depth > Ht 2.

[0018] Furthermore, when the groundwater depth remains constant in Step 2, the amount of water that the vadose zone can accommodate is limited. On the premise of the limited water capacity, the total phreatic recharge is limited by the water capacity and has a limit value. Therefore, the rainfall infiltration phreatic recharge total model under the constant depth scenario (abbreviated as the constant depth model) is:

[0019]

[0020] where, 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 rainfall, 0 < η < 1.

[0021] Derivation process of the constant depth model:

[0022] In the shallow groundwater area, the change range of the groundwater depth is limited. Under a specific groundwater depth, the amount of water that the vadose zone can accommodate is certain. On the premise of the limited water capacity, the phreatic recharge does not increase infinitely with the rainfall, but is limited by the water capacity. Therefore, as the rainfall increases, the phreatic water volume will increase continuously and then tend to a stable value, and its growth rate with respect to the rainfall will gradually decrease from the initial large growth rate and tend to 0.

[0023] Based on the above total rainfall infiltration phreatic recharge R g with rainfall P the change process of, R g and P The relationship between should satisfy the following conditions:

[0024]

[0025] To satisfy C3 and C4 in Equation (S2-1) for According to the derivative principle, assume that:

[0026]

[0027] In the formula, η 、 a and b are constant coefficients; represents the rate of change of P when R g changes with P as

[0028] tends to 0.0 mm. From equation (S2-2), we can get:

[0029]

[0030] To meet the requirements of C3 and C4 in equation (S2-1) for R g should satisfy . Substituting this equation into the above formula, we can get:

[0031]

[0032] For equation (S2-4) to meet C1 in equation (S2-1), it is necessary to make b = 0, then:

[0033]

[0034] 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 increase in the total phreatic recharge with rainfall. Considering that η is also the phreatic recharge rate when P tends to 0.0 mm, to meet C2 in equation (S2-1) such that P always exceeds the generated R g , it should satisfy . Therefore, R g The final relationship between P is as follows:

[0035]

[0036] 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.

[0037] Furthermore, a groundwater depth threshold is set. H 0s , based on the water holding capacity of the vadose zone, the degree of water deficit, and the influence of evaporation during infiltration R max , even if the parameters of the depth model are fixed R max The total amount of rainfall infiltration and phreatic water recharge when the groundwater depth changes is obtained. R g , that is, the total amount of recharge from rainfall infiltration into phreatic water under a fixed burial depth scenario (referred to as the variable burial depth model) is:

[0038]

[0039] in, H 0s is the optimum groundwater depth, m; R gm for H 0s The corresponding maximum diving supply volume, mm; R gm and H 0s Both are greater than 0; H is the groundwater depth, m.

[0040] Derivation process of variable burial depth model:

[0041] when P When taking a specific value, R g It is not fixed, but changes with the depth of groundwater. H The burial 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 duration of infiltration recharge. R g Follow H The changes implied by R max Among them, the burial depth threshold H 0s The water holding capacity of the vadose zone, the degree of water deficit in the vadose zone before rain, and the evaporation effect during infiltration have an impact on the water content of the vadose zone. R max Impact:

[0042] When the burial depth is 0.0m, the water holding capacity of the vadose zone and the vertical hydraulic gradient are both zero, that is, R max is 0.

[0043] When the burial depth is less than H 0sWhen 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 numerical value mainly depends on the water storage capacity of the vadose zone, thus R max will increase with H the increase of

[0044] When the burial depth exceeds H 0s After that, due to the increase in 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 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 numerical value depends on the degree of water deficit in the vadose zone before rainfall and the evaporation during infiltration, thus R max will decrease with H the increase of

[0045] When the burial depth approaches infinity, due to the evaporation during infiltration, R max tends to 0.

[0046] According to the above R max change process of with H the relationship between the two should satisfy the following conditions:

[0047]

[0048] To meet the requirements of C2 and C4 for in Equation (S2-7), assume according to the derivative principle:

[0049]

[0050] Let and , then:

[0051]

[0052] From this, we can get:

[0053]

[0054] In Equations (S2-8) to (S2-11), a, b, c are all constant coefficients.

[0055] When , According to the derivative principle, to satisfy C3 in Equation (S2-7), it is necessary to make a＞0 .

[0056] To satisfy C1 and C4 in Equation (S2-7), it is necessary to make c=0 and , that is, Equation (S2-11) should be:

[0057]

[0058] According to the above equation, it can be obtained that:

[0059]

[0060] 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:

[0061]

[0062] 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.

[0063] Combining Equation (S2-6) and Equation (S2-14), the variable buried depth model is as follows:

[0064]

[0065] Furthermore, Step 3 includes the following sub-steps:

[0066] 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.

[0067] Step 32, represent the time when rainfall starts as the 0th step, then the total phreatic water recharge generated by the rainfall at the i th step is distributed to the t th step, and the weight calculation formula is as follows:

[0068]

[0069] Among them, i is the ordinal number of the time step, i = 0, 1... t ; w ( t-[[]]END i ) is the weight of the total phreatic water recharge generated by the rainfall in the i th step, which is lagged and distributed to the phreatic water recharge in the t th step; H ( i ) is the phreatic water depth in the i th step, in m; P ( i ) is the rainfall in the i th step, in mm; B 0 is the depth coefficient, related to the lithology of the vadose zone, in m; B 1 is the rainfall coefficient, in mm; P 0S is the optimal rainfall, in mm.

[0070] Step 33: Based on the superposition property of the phreatic water recharge process, the phreatic water recharge in the current time step is the sum of the lagged distribution of the infiltration recharge caused by the previous rainfall to the current step. Then, the phreatic water recharge in the t th step is the sum of the total phreatic water recharge caused by all rainfall from step 0 to step t lagged and distributed to the phreatic water recharge in the t th step. That is, the distribution model is:

[0071]

[0072] Among them, r g ( t ) represents the phreatic water recharge in the t th step, in mm.

[0073] Derivation process of the weight calculation formula and the distribution model:

[0074] 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, 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 rainfall infiltration phreatic water recharge P generated by the rainfall 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 on the day of rainfall will be overestimated.

[0075] The basic idea of the existing research to characterize this lagged allocation effect is to identify the change characteristics of the weighted allocation of the total phreatic water recharge over time and construct a 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 allocation of the total phreatic water recharge should be 1. According to the superposition property of the phreatic water recharge process, taking the rainfall start date as the start date of the rainfall recharge process of the phreatic water ( t=0 ) then the phreatic water recharge on the t th day is the sum of the phreatic water recharge amounts laggedly allocated to the t th day from all the rainfall-induced phreatic water recharge amounts from the rainfall start date to the t th day, that is:

[0076]

[0077] In the formula, r g ( t ) represents the phreatic water recharge amount on the t th day, in mm; R g ( i ) is the total phreatic water recharge amount generated by the rainfall on the i th day, in mm; i is the day ordinal number, i = 0, 1... t ; w ( t - i ) is the weight of the phreatic water recharge amount generated by the rainfall on the i th day laggedly allocated to the t th day, t ≥ i .

[0078] Most of the current research on the weight distribution characteristic function only considers the influence of lag time on the recharge weight, and rarely considers the influence of environmental factors on the recharge weight. In the shallow groundwater area, the weight of phreatic infiltration recharge is affected not only by the lag time, but also by the rainfall and the 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 shows 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 degree of influence of the groundwater depth on the curve shape.

[0079] Among the existing weight distribution characteristic functions, the Chen Chongxi formula (Literature: Chen Chongxi. Lag recharge weight function - a method for dealing with the lag of rainfall recharge to phreatic water [J]. Hydrogeology & Engineering Geology, 1998, 6(07):24-26.) considers the influence of both lag time and groundwater depth on the weight distribution curve, and the application effect of this formula is good in many regions. The Chen Chongxi formula is applicable to the simulation of discrete phreatic recharge processes, and its basic form is:

[0080]

[0081] 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 other formulas are the same as above.

[0082] In the shallow groundwater area, as the depth increases, the weight distribution process line of rainfall infiltration recharge to phreatic water should gradually become flatter. Equation (S3-2) can already well reflect the change of the weight distribution process line with the depth. However, Equation (S3-2) does not reflect the influence of rainfall on the distribution curve. Based on the changes in the lag 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 distribution curve gradually becomes flatter. Under a specific groundwater depth, there should be a rainfall threshold P 0S such that w(0) changes in 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, in equation (S3-2), B is improved to , that is, the weight distribution characteristic function applicable to the shallow groundwater area is:

[0083]

[0084] In the formula, 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, related to the lithology of the vadose zone, m; B 1 is the rainfall coefficient, mm; P 0S is the optimal rainfall, mm. The meanings of the remaining formulas are the same as above.

[0085] Further, step 4 includes:

[0086] Step 41, since it is difficult to divide the distribution process of the phreatic recharge caused by rainfall within a single time step when there is rainfall in multiple time steps. Select the rainfall infiltration recharge event with rainfall only in the 0th time step, and calculate the actual value of t = i = 0 when w(0) . That is, the weight calculation formula for the 0th time step is as follows:

[0087]

[0088] Among them, T r is the total number of time steps of this rainfall infiltration recharge event.

[0089] Step 42, the parameters B 0, B 1, and P 0S of the lagged distribution weight characteristic function are set with the following constraints according to their physical meanings:

[0090]

[0091] Using an optimization algorithm through w(0) actual values, rainfall and groundwater depth data at step 0, the optimal solutions of B0, B1 and P 0S are calibrated.

[0092] Furthermore, step 5 includes:

[0093] Step 51, substituting the optimal solutions of the lagged distribution weight characteristic function parameters B 0, B 1 and P 0S into the distribution model.

[0094] Step 52, for the parameters R gm , H 0s and η of the total phreatic water recharge calculation model, according to their physical meanings, the following constraints are set:

[0095]

[0096] Based on the segmented scenarios constructed in step 12, through the rainfall and groundwater depth data of each time step in the rainfall infiltration recharge event, the optimal solutions of the parameters R gm , H 0s and η are calibrated by scenario using the optimization algorithm.

[0097] Step 53, substituting the optimal solutions of the lagged distribution weight characteristic function parameters B 0, B 1 and P 0S , 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 changing groundwater depth scenario, and calculating the daily rainfall infiltration recharge phreatic water volume in the rainfall event.

[0098] The beneficial effects of the present invention are as follows:

[0099] The method proposed by the present invention calculates the phreatic water recharge using groundwater depth and rainfall data, considers the dynamic influence of groundwater depth changes on the rainfall infiltration recharge effect and the lagged distribution effect of the rainfall infiltration recharge phreatic water process, effectively solves the problem of underestimation of the infiltration recharge volume after rain, and has considerable practical application value for the simulation of phreatic water recharge volume in a short time period. Description of the Drawings

[0100] Figure 1 It is a schematic diagram of the lagging allocation weight feature function in step 3 of the present invention;

[0101] Figure 2 It is a schematic diagram of the superposability of the phreatic recharge process in step 3 of the present invention;

[0102] Figure 3 It is the classification result of the decision tree in Example 1;

[0103] Figure 4 It is the effect of simulating the daily rainfall infiltration recharge phreatic water volume by using the method proposed by the present invention in Example 1;

[0104] Figure 5 It is the comparison effect of simulating the phreatic recharge volume between the present invention and the existing method 1 in Example 2. Specific implementation manners

[0105] The following further elaborates on the specific implementation manners of the present invention in conjunction with the accompanying 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.

[0106] Example 1:

[0107] In this example, the field data around the Wudaogou Experimental Station is used, and the field measured 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 sandy black soil, and the planted crops include wheat and corn. The measured data of the experimental station includes the groundwater depth and 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 frequencies are all once a day.

[0108] The specific calculation steps are as follows:

[0109] Step 1, select the rainfall infiltration recharge phreatic water events, use the decision tree to classify the rainfall and the groundwater depth before rain according to the total phreatic recharge volume in the field, and establish segmented scenarios, which specifically include the following sub-steps:

[0110] Step 11, use the meteorological data from 2010 to 2021 in the field, the measured groundwater depth and soil moisture content data of the experimental station to select the rainfall infiltration recharge phreatic water events. 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.

[0111] A total of 207 rainfall infiltration recharge to the phreatic water events were selected according to this requirement. Table 1 shows the key information such as rainfall characteristics, phreatic water recharge characteristics, and soil moisture before rainfall in the selected events.

[0112] Table 1 Key information of 207 rainfall infiltration recharge to the phreatic water events

[0113]

[0114] The total phreatic water recharge is calculated using the measured groundwater depth. Assuming that the influence of phreatic water evaporation on the groundwater level change during rainfall is small, the decrease in groundwater depth is caused by rainfall infiltration. The phreatic water recharge during the time period is calculated by the following formula:

[0115]

[0116] where, R g is the total rainfall infiltration recharge to the phreatic water, mm; is the decrease in groundwater depth caused by rainfall infiltration during the time period, mm; h is the average groundwater depth during the time 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; when h exceeds 1.0 m, a constant value of 0.045 is taken.

[0117] When calculating the total phreatic water recharge in the selected events, 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.

[0118] Step 12: Based on the information of the selected 207 events, use decision tree analysis to analyze the influence degree of rainfall amount and groundwater depth before rainfall (i.e., the pre-rainfall depth in Table 1) on the total phreatic water recharge. The decision result shows that the influence degree of rainfall amount on the total phreatic water recharge exceeds that of the groundwater depth before rainfall. Due to the significant difference in the influence degree between the two, the decision tree ignores the groundwater depth before rainfall and only represents the stage of the total phreatic water recharge based on the numerical size of the single factor of rainfall amount. Figure 3 shows the classification result of the decision tree, and the sample quantity is in nIt is shown that the total sample size is 207. The decision tree takes 32.5 mm of rainfall as the boundary and divides the total amount of phreatic water recharge into two categories: one is when the rainfall is less than 32.5 mm, which contains 106 samples and accounts for 51.2% of the total sample size. The average value of the total amount of phreatic water recharge is 5.822 mm and the standard deviation is 5.790 mm; the other is when 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. The average value of the total amount of phreatic water recharge is 28.823 mm and the standard deviation is 33.593 mm. Therefore, according to the decision results, two segmented scenarios are constructed, namely the scenario with rainfall ≤ 32.5 mm and the scenario with rainfall > 32.5 mm.

[0119] Step 2, establish a variable burial depth model, and the calculation formula is as follows:

[0120]

[0121] Where R g is the total amount of phreatic water recharge by rainfall infiltration, in mm; R gm is H 0s the corresponding maximum total amount of phreatic water recharge, in mm; H 0s is the optimal groundwater burial depth, in m; H is the groundwater burial depth, in m; P is the rainfall, in mm; η is the maximum rate of increase of the total amount of phreatic water recharge with rainfall; the parameters η and H 0s and R gm are determined in the following step 5 for different rainfall scenarios.

[0122] Step 3, determine the time step according to the application requirements, establish a lagged distribution weight characteristic function, and distribute the total amount of phreatic water recharge at this time step, which specifically includes the following sub-steps:

[0123] Step 31, based on the actual application requirements, obtaining the daily 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 by rainfall infiltration for each rainfall event is divided.

[0124] Step 32, establish a lagged distribution weight characteristic function for the total amount of phreatic water recharge by rainfall infiltration. As Figure 1 shown, the 0th day is the start day of rainfall. The calculation formula for the weight of the total amount of phreatic water recharge generated by rainfall on the i th day distributed to the phreatic water recharge on the t th day is as follows:

[0125]

[0126] Among them, i is the ordinal number of the time step, which is the day ordinal number in this embodiment, i = 0, 1... t ; w ( t - i ) is the weight of the total phreatic recharge generated by the rainfall on the i th day lagged and distributed to the phreatic recharge on the t th day; H ( i ) is the phreatic water 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.

[0127] Step 33, the phreatic recharge on the current day is the sum of the infiltration recharge caused by the previous rainfall lagged and distributed to the current day. As shown in Figure 2 , the phreatic recharge on the t th day is the sum of the phreatic recharge on the t th day lagged and distributed to the t th day caused by all rainfall from the 0th day to the

[0128]

[0129] Among them, r g ( t ) represents the phreatic recharge on the t th day, mm.

[0130] Step 4, select the event with rainfall only on the 0th day in Table 1, identify the weight value of the total phreatic recharge distributed on the rainfall day, and calibrate the parameters of the lagged distribution weight characteristic function using the least squares method. Specifically, it includes the following sub-steps:

[0131] 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 distribution weight w (0) of the total phreatic recharge on the first day in the 45 events. The calculation formula is as follows:

[0132]

[0133] To simplify the calibration difficulty and improve the calibration efficiency, take the logarithm of both sides of the above formula. The result is as follows:

[0134]

[0135] Step 42: Determine the parameters of the lagged distribution weight characteristic function B 0, B 1, and P 0S , and set the following constraints according to their physical meanings:

[0136]

[0137] Using the non - linear least - squares method, through the actual values, rainfall, and pre - rainfall groundwater depth data in 45 events , the optimal solutions of B 0, B 1, and P 0S are calibrated and obtained as 1.12, 8.56, and 33.12 in sequence. 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 lagged distribution weight characteristic function in 45 events.

[0138] Table 2 Input and output information of the lagged distribution weight characteristic function in the selected 45 events

[0139]

[0140] Step 5: Substitute the parameters of the lagged distribution weight characteristic function B 0, B 1, and P 0S 's optimal solutions, and calibrate the total phreatic recharge according to the scenario segmentation obtained in Step 12, and calculate the remaining parameters of the total phreatic recharge model. The specific sub - steps are as follows:

[0141] Step 51: Substitute the optimal solutions ofthe B 0, B 1, and P 0S obtained in Step 42 into the distribution model. Among them, B 0, B 1, and P 0S 's optimal solutions are 1.12, 8.56, and 33.12 in sequence.

[0142] 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:

[0143]

[0144] Using the data of daily groundwater depth, rainfall, and phreatic water recharge volume in 207 events, for the two types of scenarios obtained in step 12: one is that the rainfall is less than 32.5 mm; the other 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 nonlinear least squares method, as shown in Table 3.

[0145] Table 3 Optimal solutions of parameters of the total phreatic water recharge calculation model

[0146]

[0147] Using the optimal solutions of the parameters of the total phreatic water recharge model and the lag distribution weight characteristic function estimated above, the daily rainfall infiltration recharge to the phreatic water volume in 207 events is simulated, as Figure 4 shown. The goodness of fit between the measured value and the simulated value of the recharge phreatic water volume 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.

[0148] Example 2:

[0149] To further illustrate the simulation effect of this method, two existing calculation methods for phreatic water recharge are compared, and typical event scenarios are selected to carry out a comparison of 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 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.

[0150] The first existing method is the infiltration recharge coefficient method. According to the influence of groundwater depth on the infiltration recharge coefficient in 207 events in Table 1, the recharge coefficient is segmented according to 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 in simulating the rainfall infiltration recharge to the phreatic water volume in typical event scenarios are 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 phreatic water recharge on the day of rainfall and is difficult to capture the lagged distribution of phreatic water recharge after rainfall, resulting in an underestimation of the phreatic water recharge after rainfall.

[0151] The second existing method is the groundwater depth change method. Based on the characteristics of sandy black soil, the water supply degree is 0.035 when the groundwater depth is between 0.0m and 1.0m, and 0.045 when the groundwater depth exceeds 1.0m. The event included four rainfall events, with rainfall amounts of 17.3, 89.8, 1.0, and 33.2mm, respectively. The groundwater depth decreases during these rainfall periods were 49, 578, 2, and 576mm, respectively. Based on this, the estimated phreatic water recharge for the four rainfall events was 1.72, 20.23, 0.10, and 20.20mm, respectively, for a total of 42.25mm. The total phreatic water recharge estimated by this method is 51.51mm. Compared with Method 2, this method's estimate is closer to the actual value. Furthermore, when rainfall events last for a long time, Method 2 has difficulty distributing the total phreatic water recharge to a shorter timescale.

[0152] The above is a preferred embodiment of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements without departing from the scope of the present invention. These improvements should also be regarded as within the scope of protection of the present invention.

Claims

1. A calculation method for the recharge amount of rainfall infiltration into the phreatic water under the condition of variable buried depth, characterized in that, It includes the following steps: Step 1, segmented influence discrimination: Select the events of rainfall infiltration recharge to the phreatic water, analyze the comprehensive influence of rainfall amount and pre-rain groundwater depth on the total phreatic water recharge, determine whether there is segmentation and construct the corresponding segmented scenarios; Step 2, total amount model construction: Establish the model of rainfall infiltration phreatic water recharge total amount under the fixed depth scenario, make the parameters of the rainfall infiltration phreatic water recharge total amount model under the fixed depth scenario change dynamically with the groundwater depth, and construct the model of rainfall infiltration phreatic water recharge total amount under the variable depth scenario; The model of rainfall infiltration phreatic water recharge total amount under the variable depth scenario is: Among them, H 0s is the optimal groundwater depth, m; R gm is the maximum total phreatic water recharge corresponding to H 0s , mm; R gm and H 0s are both greater than 0; H is the groundwater depth, m; R g is the total phreatic water recharge by rainfall infiltration, mm; P is the rainfall, mm; η is the maximum rate of increase of the total phreatic water recharge with rainfall, 0 < η < 1; Step 3, distribution model construction: Based on the lag distribution effect of the rainfall infiltration phreatic water recharge process, construct the lag distribution weight characteristic function of the rainfall infiltration phreatic water recharge total amount, and construct the distribution model according to the superposition property of the phreatic water recharge process; Specifically including: Step 31, Determine the time step according to the application requirements and divide the rainfall infiltration recharge phreatic water process into time steps; Step 32, Taking the 0th step as the time when rainfall starts, the calculation formula for the weight of the total phreatic water recharge generated by the rainfall in the ith step distributed to the tth step is as follows: where \(i\) is the ordinal number of the time step, \(i = 0, 1,\cdots,t\); \(w(t - i)\) is the weight of the total phreatic water recharge generated by the rainfall in the \(i\)-th step lagged and allocated to the phreatic water recharge at the \(t\)-th step; \(H(i)\) is the phreatic water depth at the \(i\)-th step, \(m\); \(P(i)\) is the rainfall at the \(i\)-th step, \(mm\); \(B_0\) 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, \(mm\); Step 4, calibration of distribution model parameters: Select the rainfall infiltration recharge events where there is rainfall only in the 0th time step, and use the distribution weight in the 0th time step to calibrate the parameters of the lag distribution weight characteristic function; Step 5, calibration of total amount model parameters: Substitute the calibrated parameter values of the lag distribution weight characteristic function into the distribution model, and according to the segmented scenarios in Step 1, calibrate the parameters of the phreatic water recharge total amount model to simulate the rainfall infiltration recharge phreatic water volume.

2. The calculation method of rainfall infiltration recharge to phreatic water volume under the condition of variable buried depth according to claim 1, characterized in that Step 1 includes: Step 11, The selected rainfall infiltration recharge phreatic water events should meet the following conditions: There is no rainfall in the five days before the start and five days after the end of the current event, and the soil moisture content and groundwater depth are in a non-recharge state; Step 12, Use the classification algorithm to divide different segmented categories according to the influence of rainfall amount and pre-rain groundwater depth on the total phreatic water recharge, obtain the segmented values of rainfall amount and pre-rain groundwater depth, and construct different segmented scenarios by combining them in pairs.

3. The calculation method of rainfall infiltration recharge to phreatic water under the condition of variable buried depth according to claim 2, characterized in that The model of rainfall infiltration phreatic water recharge total amount under the fixed depth scenario in Step 2 is: Among them, R max is the limit value of the total recharge of rainfall infiltration into the phreatic water, in mm, and R max > 0.

4. The calculation method for rainfall infiltration recharge to phreatic water volume under the condition of variable buried depth as claimed in claim 1, characterized in that, Step 3 also includes: Step 33, According to the superposition property of the phreatic water recharge process, the phreatic water recharge amount in the current time step is the sum of the lagged distribution of the infiltration recharge amount caused by the previous rainfall to the current step. Then the phreatic water recharge amount in the tth step is the sum of the phreatic water recharge amounts lagged and distributed to the tth step caused by all rainfall from the 0th step to the tth step, that is, the distribution model is: Among them, r g (t) represents the diving recharge amount at the t-th step, in mm.

5. The calculation method of rainfall infiltration recharge potential groundwater volume under the scenario of variable buried depth according to claim 4, characterized in that Step 4 specifically includes: Step 41, Select the rainfall infiltration recharge events where there is rainfall only in the 0th time step, calculate the actual value of w(0) when t = i = 0, that is, the calculation formula for the distribution weight in the 0th time step is as follows: Step 42, assign parameters B0, B1, and P of the lag weight feature function 0S , and set the following constraints according to their physical meanings: Using an optimization algorithm, the optimal solutions of B0, B1, and P are calibrated through the actual value of w(0), rainfall, and groundwater depth data at the 0th step. 0S ​ 6. The calculation method of rainfall infiltration recharge groundwater volume under the condition of variable buried depth according to claim 5, characterized in that, Step 5 specifically includes: Step 51, substitute the optimal solutions of the parameters B0, B1, and P of the lagged allocation weight feature function into the allocation model; 0S ​ Step 52: For the parameters R gm , H 0s and η of the diving recharge total amount calculation model, set the following constraints according to their physical meanings: Based on the piecewise scenarios constructed in step 12, through the rainfall and groundwater depth data at each time step in the event of infiltration recharge by storm rainfall, the optimal solutions of R gm , H 0s and η are obtained by calibrating the scenarios using the optimization algorithm; Step 53, assign the optimal solutions of the lagged allocation weight characteristic function parameters B0, B1, and P 0S to the calculation model parameter R of the total phreatic water recharge gm , H 0s and the optimal solution of η into the total phreatic water recharge model under the scenario of variable buried depth, and calculate the daily rainfall infiltration recharge of phreatic water in each rainfall event.

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