A method for calculating evaporation of water under varying depth of burial scenarios

Abstract

The application discloses a kind of calculation methods of phreatic evaporation under the scenario of varying buried depth, comprising: collecting groundwater depth, weather information;Build the conceptual model of phreatic evaporation under fixed buried depth;Establish the calculation model of phreatic evaporation under variable buried depth;Select the measured value of phreatic evaporation by calculating the historical data of period not affected by rainfall, utilize optimization algorithm, calibrate the parameter of calculation model of phreatic evaporation under variable buried depth in different crop growth stages, and simulate to obtain phreatic evaporation.The method for calculating phreatic evaporation by using groundwater depth and weather data considers the influence of groundwater depth change on capillary fracture mechanism, effectively solves the problem that phreatic evaporation is overestimated when atmospheric evaporation capacity increases, and has practical application value for simulating phreatic evaporation in drought period.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrology and water resources, and in particular relates to a method for calculating phreatic water evaporation under a varying burial depth scenario. Background Art

[0002] Phreatic water refers to shallow groundwater. Phreatic water evaporation is the main way of groundwater discharge in plain areas. The depth of groundwater is a key factor affecting phreatic water evaporation, which determines the distance of water transportation during phreatic water evaporation. Accurately estimating the amount of phreatic water evaporation under the scenario of changing groundwater depth is crucial for evaluating groundwater resources.

[0003] In the existing technology, there are many quantitative studies on phreatic water evaporation under different scenarios. A series of empirical formulas for phreatic water evaporation have been established by correlating phreatic water evaporation with groundwater depth and atmospheric evaporation capacity. At present, the more classic phreatic water evaporation formulas include Averyanov's empirical formula (Averyanov. Horizontal drainage facilities for preventing and controlling salinization of irrigated land [M]. Lou Puli, trans. Beijing: China Industrial Press, 1963), Ye Shuiting's formula (Ye Shuiting et al. Analysis of the problem of calculating water supply using the empirical formula for phreatic water evaporation [J]. Hydrogeology and Engineering Geology, 1982, (04): 45-48+6), inverse logistic formula (Shang Songhao et al. Inverse logistic formula for calculating phreatic water evaporation coefficient [J]. Irrigation and Drainage, 1999, (02): 18-21), and Shen Lichang's formula (Shen Lichang. Discussion on the empirical formula for phreatic water evaporation [J]. Journal of Hydraulic Engineering, 1985, (07): 34-40).

[0004] The basic principle behind the above formulas assumes a monotonic relationship between groundwater evaporation and atmospheric evaporation capacity, meaning that as atmospheric evaporation capacity increases, groundwater evaporation increases accordingly. In reality, as both groundwater depth and atmospheric evaporation capacity increase, the distance water is transported increases, weakening the water transport capacity of capillaries in the unsaturated zone. Consequently, groundwater evaporation decreases due to capillary rupture. However, most existing technologies only consider the monotonic relationship between atmospheric evaporation capacity and groundwater evaporation, ignoring the impact of capillary rupture on groundwater evaporation when groundwater depth increases. This leads to an overestimation of groundwater evaporation when atmospheric evaporation capacity increases in this scenario, which contradicts reality. Summary of the Invention

[0005] The present invention aims to solve the problem that the existing technology does not consider the influence of groundwater depth and atmospheric evaporation capacity on the mechanism of capillary fracture, resulting in poor estimation accuracy of groundwater evaporation when the groundwater depth and atmospheric evaporation capacity increase, and proposes a method for calculating groundwater evaporation under a changing groundwater depth scenario.

[0006] The technical solutions of the present invention are as follows:

[0007] A method for calculating the evaporation of phreatic water in a variable buried depth scenario, comprising the following steps:

[0008] Step 1: Collecting the information of groundwater depth, meteorology, soil water supply degree and crop growth and development, estimating the atmospheric evaporation capacity according to the meteorological information, and dividing the crop growth stages according to the crop growth and development information.

[0009] Step 2: Considering the influence of atmospheric evaporation capacity on capillary fracture mechanism, reflecting the threshold value of capillary fracture through the optimum atmospheric evaporation capacity, and constructing the conceptual model of phreatic water evaporation under fixed buried depth.

[0010] The conceptual model of phreatic water evaporation under fixed buried depth is:

[0011]

[0012] Wherein, E g is the phreatic water evaporation, mm; E 0 is the atmospheric evaporation capacity, mm; E 0s is the optimum atmospheric evaporation capacity, mm; E max is E 0s the maximum phreatic water evaporation corresponding to, mm; E 0s and E max are greater than 0.

[0013] Step 3: Considering the influence of groundwater depth on the parameters of the conceptual model of phreatic water evaporation under fixed buried depth, making the parameters of the conceptual model of phreatic water evaporation under fixed buried depth change dynamically with the groundwater depth, and establishing the calculation model of phreatic water evaporation under variable buried depth.

[0014] The calculation model of phreatic water evaporation under variable buried depth is:

[0015]

[0016] Wherein, E 0m is the maximum phreatic water evaporation under 0.0 m buried depth, mm; m is E g is the decreasing rate with the increase, m-1; H is the groundwater depth, m; E 0m and m are greater than 0.

[0017] Step 4: Select historical data from periods not affected by rainfall to calculate the measured values ​​of groundwater evaporation. Use the optimization algorithm to calibrate the parameters of the groundwater evaporation calculation model under variable burial depths during different crop growth stages to simulate the groundwater evaporation.

[0018] The derivation process of the conceptual model of groundwater evaporation at a fixed burial depth is as follows:

[0019] There is a capillary break phenomenon in the process of phreatic evaporation. According to the atmospheric evaporation capacity and the water supply capacity of the capillary, the phreatic evaporation process can be roughly divided into four stages:

[0020] 1) When the atmospheric evaporation capacity is 0.0 mm, the diving evaporation is 0.0 mm;

[0021] 2) When the atmospheric evaporation capacity is small and the soil moisture content has not reached the capillary breaking point, the capillaries are fully supplied with water, and the phreatic evaporation increases with the increase of atmospheric evaporation capacity;

[0022] 3) When the atmospheric evaporation capacity increases and the soil moisture content reaches the capillary breaking point, some capillary tubes with suspended water will break due to insufficient water supply capacity, and the phreatic evaporation will decrease as the atmospheric evaporation capacity increases;

[0023] 4) When the soil moisture content is extremely low and the capillary water supply capacity is extremely weak, the groundwater evaporation tends to 0.0 mm as the atmospheric evaporation capacity increases.

[0024] In the aforementioned process of phreatic water evaporation varying with atmospheric evaporation capacity, there is a critical threshold point, the capillary break point. When the capillary break point is reached, phreatic water evaporation reaches its maximum. However, once this break point is exceeded, the monotonic relationship between phreatic water evaporation and atmospheric evaporation capacity changes. Therefore, determining the capillary break point is extremely important for describing the phreatic water evaporation process. Atmospheric evaporation capacity can, to a certain extent, reflect this phenomenon of capillary break, so the capillary break point is characterized by the optimal atmospheric evaporation capacity.

[0025] According to the above-mentioned diving evaporation ( E g ) with atmospheric evaporation capacity ( E 0) the process of change, E g and E The relationship between 0 should satisfy the following conditions:

[0026]

[0027] To satisfy the relationship between C2 and C4 in formula (S1-1), According to the derivative principle, we assume that:

[0028]

[0029] Let and , then:

[0030]

[0031] Thus, we have:

[0032]

[0033] In formula (S1-2) to formula (S1-5), a, b and c are constant coefficients.

[0034] When , . According to the derivative principle, in order to meet C3 in formula (S1-1), it is necessary to make a > 0.

[0035] In order to meet and in formula (S1-1), it is necessary to make c= 0 and , that is, formula (S1-5) should be:

[0036]

[0037] According to the above formula, we have:

[0038]

[0039] In order to ensure that the above formula is consistent with the assumption in formula (S1-2) and meets all conditions in formula (S1-1), we further obtain and . Thus, substituting these two equations into formula (S1-6), the conceptual model of evaporation of subsurface water is as follows:

[0040]

[0041] wherein, E max and E 0s The parameter meanings have been described in formula (S1-1) and will not be repeated here. Through the above analysis and the physical meaning of the parameters, it is necessary to ensure that the parameters E max and E 0s are greater than 0.

[0042] The derivation process of the calculation model of the evaporation of subsurface water under different buried depths is as follows:

[0043] In formula (S1-8), there are two key parameters E max and E 0s . E maxand E 0s It is not fixed, but changes with the depth of groundwater. The depth of groundwater determines the distance of water transport during evaporation. As the depth increases, the water transport distance increases, which weakens the ability of the unsaturated zone capillary to transport water, resulting in a decrease in the maximum amount of evaporation that can be achieved. At different depths, the water transport distance increases. E max and E 0s Also changed. E max The change with burial depth is more obvious. E 0s The change with the burial depth is slight. The maximum evaporation under the burial depth of 0.0m is set. E 0m When the groundwater depth reaches a certain range, E g Tends to 0.0mm, so theoretically E max It also tends to be a smaller value, which is corrected based on the influence of capillary water transport capacity and water transport distance. E max , that is, the parameters of the fixed depth model E max It changes dynamically with the depth of groundwater. H right E g The impact of E max In the formula (S1-8) E max Follow H Based on the above H right E max The influence of the two is described in exponential form and calculated by the following formula:

[0044]

[0045] In summary, the calculation model of groundwater evaporation under variable burial depth is as follows:

[0046]

[0047] Furthermore, step 4 specifically includes:

[0048] Step 41: To avoid the influence of rainfall on the calculation of the measured value of phreatic water evaporation, the data on the day of rainfall and the day after the rain when the groundwater is in a replenishing state are eliminated, and the data on the remaining days without rainfall are retained. The measured value of phreatic water evaporation is calculated using the groundwater depth data;

[0049] Step 42, based on the data of atmospheric evaporation capacity, groundwater depth, and groundwater evaporation, and based on the crop growth stages divided in step 12, the optimization algorithm is used to calibrate the parameters E max 、 E 0s and m The optimal solution of

[0050] Step 43, set the parameters E max 、 E 0s and m The optimal solution is substituted into the calculation model of phreatic water evaporation under variable burial depth to calculate the phreatic water evaporation.

[0051] Furthermore, the method for estimating the atmospheric evaporation capacity based on the collected meteorological information in step 1 is:

[0052] If the meteorological information includes rainfall and water surface evaporation, water surface evaporation is used to represent the atmospheric evaporation capacity; if the meteorological information does not include water surface evaporation, it is necessary to additionally collect soil heat flux, solar radiation, net radiation, air temperature, wind speed and air humidity information, and use the Penman-Monteith formula recommended by the Food and Agriculture Organization of the United Nations to calculate the reference crop evaporation, and use the reference crop evaporation to represent the atmospheric evaporation capacity.

[0053] Furthermore, the Penman-Monteith formula is:

[0054]

[0055] in, ET 0 is the reference crop evapotranspiration, mm; R n is the net radiation, MJ m -2 ; G is the soil heat flux, MJ m -2 ; T is the air temperature, ℃; u 2 is the wind speed at a height of 2m, ms -1 ; e s is the saturated vapor pressure, kPa; e a is the actual vapor pressure, kPa; Δ is the slope of the water vapor pressure curve, kPa ℃ -1 ; γ is the psychrometer constant, kPa ℃ -1 .

[0056] Furthermore, the crop growth and development information in step 1 includes crop types and phenological characteristics.

[0057] Crop growth stages are divided based on crop types and phenological characteristics, and the bare soil cover period is listed as a separate growth stage.

[0058] The beneficial effects of the present invention are:

[0059] The method of calculating phreatic water evaporation using groundwater depth and meteorological data takes into account the impact of groundwater depth changes on the capillary fracture mechanism, effectively solving the problem of overestimation of phreatic water evaporation when the atmospheric evaporation capacity increases. It has practical application value for simulating phreatic water evaporation during drought periods. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a schematic diagram of the change of submerged water evaporation at a fixed burial depth with atmospheric evaporation capacity in step 2 of the present invention;

[0061] Figure 2 This is the effect of simulating diving evaporation using the method proposed by the present invention in Example 1;

[0062] Figure 3 This is a comparison of the effects of simulating submerged evaporation in Example 2 between the present invention and the Averyanov formula and the Ye Shuiting formula;

[0063] Figure 4 This is a comparison of the effects of simulating diving evaporation using the present invention, the inverse logistic formula, and the Shen Lichang formula in Example 2. DETAILED DESCRIPTION

[0064] The following embodiments of the present invention are further described in detail with reference to the accompanying drawings and examples. The following embodiments are only used to explain the present invention and are not intended to limit the scope of the present invention.

[0065] Example 1:

[0066] This example uses field data from Xinmaqiao Town, Bengbu City, Anhui Province, and selects field measured data from 2020 to 2021 to verify the feasibility and effectiveness of the calculation method of the present invention. The field soil is sand ginger black soil, and the crops grown include wheat and corn. The measured data include groundwater depth and meteorological data, and the monitoring frequency is once a day. Among them, the monitored meteorological factors include rainfall, solar radiation, net radiation, temperature, wind speed at 2.0m, and air humidity, and the monitoring frequency is once every 10 minutes.

[0067] The specific calculation steps are as follows:

[0068] Step 1: Collect information on groundwater depth, weather conditions, soil water availability, and crop growth and development in the field. Estimate atmospheric evaporation capacity based on weather information and classify crop growth stages based on crop growth and development information. This includes the following sub-steps:

[0069] Step 11: Data on measured groundwater depth in the field, meteorological station data, manually observed crop growth and development, and manually measured soil water availability were collected from 2020 to 2021. For sandy black soil, the water availability was constant at 0.035 when the groundwater depth was between 0.0 m and 1.0 m; and at 0.045 when the groundwater depth exceeded 1.0 m.

[0070] Because the collected meteorological information does not include water surface evaporation elements, the Penman-Monteith formula recommended by the Food and Agriculture Organization of the United Nations is used to calculate the reference crop evaporation, and the reference crop evaporation is used to represent the atmospheric evaporation capacity.

[0071] Step 12. Based on the crop growth and development information from manual observations, the crops planted in the field are wheat and corn. From 2020 to 2021, wheat was sown on October 21 each year and harvested on May 31. Its phenological characteristics include emergence, tillering, greening, jointing, and maturity. Corn was sown on June 21 each year and harvested on September 30. Its phenological characteristics include emergence, tasting, grain filling, milky maturity, and yellow maturity. Based on phenological characteristics, the entire growth period of wheat can be divided into two growth stages: the early stage is from emergence to greening, when wheat develops relatively slowly; the middle and late stages are from greening to maturity. As the temperature rises, wheat development accelerates and gradually matures. The entire growth period of corn can be divided into two growth stages: the early stage is from emergence to tasting, when corn develops relatively slowly; the middle and late stages are from tasting to yellow maturity, when corn leaves are fully stretched and develop rapidly until they turn yellow and mature. The remaining periods are all bare soil, from June 1 to June 20 and October 1 to October 20 each year. The bare soil cover period is listed as a separate growth stage. The specific period divisions of the growth stages of wheat and corn are shown in Table 1.

[0072] Table 1 Growth stages of wheat and corn

[0073]

[0074] Table 2 shows the key information needed to estimate groundwater evaporation from 2020 to 2021, including cover type, time period, groundwater depth, rainfall, and atmospheric evaporation capacity. The atmospheric evaporation capacity is the reference crop evapotranspiration calculated using the Penman-Monteith formula in step 11.

[0075] Table 2 Information required for estimating some groundwater evaporation from 2020 to 2021

[0076]

[0077] Step 2: Figure 1 As shown, according to the above diving evaporation ( E g ) with atmospheric evaporation capacity (E 0) changes, and a conceptual model of groundwater evaporation at a fixed burial depth is constructed, where E 0 is represented by the reference crop evapotranspiration obtained in step 11.

[0078] Step 3: Set the parameters of the depth model E max As the groundwater depth changes dynamically, a calculation model for groundwater evaporation at variable depths is obtained.

[0079] Step 4: Select historical data from Table 2 for periods not affected by rainfall, use the optimization algorithm to calibrate the parameters of the phreatic water evaporation calculation model for different crop growth stages at varying depths, and simulate phreatic water evaporation. This includes the following sub-steps:

[0080] Step 41: Define the following two scenarios as rain-affected days: the first is the day of rainfall, indicating a direct rainfall impact; the second is the day when groundwater depth decreases after rainfall, indicating a groundwater recharge effect. Table 2 includes 256 rain-affected days, and data from the remaining 475 rain-free days are retained for parameter calibration.

[0081] The measured groundwater depth data of the field were used to calculate the measured value of phreatic evaporation. Assuming that the increase in groundwater depth during the period without rainfall is only caused by phreatic evaporation, the phreatic evaporation per unit area during the period was calculated using the following formula:

[0082]

[0083] in, E g is the phreatic evaporation, mm; is the increase in groundwater depth caused by evaporation during the period, mm; h is the average groundwater depth during the period, m; Follow h And the changing water supply degree.

[0084] Step 42: Calibrate the crop growth stages according to Table 1. Parameters are obtained by calibrating the crop growth stages using the nonlinear least squares method using atmospheric evaporation capacity and groundwater depth data. E max 、 E 0s and m The optimal solution of .

[0085] The parameters were calibrated using the groundwater depth and meteorological data for the 475 rain-free days in Table 2. The optimal solution is shown in Table 3.

[0086] Table 3 Optimal parameter solutions at different crop growth stages

[0087]

[0088] Step 43: Set the parameters in Table 3 E max 、 E 0s and m The optimal solution is substituted into the calculation model of phreatic evaporation under variable burial depth, and the phreatic evaporation is simulated, as shown in the following example: Figure 2 As shown in the figure, the correlation coefficient between the measured and simulated values ​​of phreatic evaporation is 0.89, the mean absolute error is 0.27 mm, and the root mean square error is 0.39 mm. The results show that the simulation accuracy between the two is high.

[0089] Example 2:

[0090] To further illustrate the simulation effect of the method in Example 1, the present invention is compared with four typical current phreatic evaporation calculation models. The rainless days selected in Example 1 are selected to carry out simulation effect comparison. The selected model structures and parameter meanings are shown in Table 4.

[0091] Table 4 Typical phreatic evaporation calculation model

[0092]

[0093] Figure 3 、 Figure 4 The simulation results of four phreatic water evaporation calculation models were compared. The correlation coefficients between the estimated values ​​and the measured values ​​using the EF1, EF2, EF3, and EF4 methods were 0.66, 0.62, 0.66, and 0.69, respectively. The mean absolute errors were 0.49, 0.49, 0.47, and 0.49 mm, and the root mean square errors were 0.69, 0.68, 0.65, and 0.62 mm. The simulation accuracy of the four currently used phreatic water evaporation calculation models was lower than that of this method.

[0094] When the groundwater depth is greater than 1.5 m and the atmospheric evaporation capacity is greater than 5 mm, the average measured phreatic evaporation is 0.71 mm, while the average estimated by this method is 0.71 mm. The averages estimated by the EF1, EF2, EF3, and EF4 methods are 0.89, 0.95, 0.84, and 0.82 mm, respectively. The average estimated by this method is closest to the measured average. This indicates that as the groundwater depth and atmospheric evaporation capacity increase, this method effectively captures the impact of capillary breakage on phreatic evaporation, while the other four methods tend to overestimate phreatic evaporation.

[0095] 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 method for calculating groundwater evaporation under varying burial depth scenarios, characterized in that: The following steps are involved: Step 1: Collect information on groundwater depth, weather conditions, soil water availability, and crop growth and development. Estimate atmospheric evaporation capacity based on weather information and divide crop growth stages based on crop growth and development information. Step 2: Considering the influence of atmospheric evaporation capacity on the capillary break mechanism, the optimal atmospheric evaporation capacity is used to reflect the occurrence threshold of capillary break, and a conceptual model of groundwater evaporation at a certain burial depth is constructed; The conceptual model of groundwater evaporation at a fixed burial depth is: ； in, E g is the diving evaporation; E 0 is the atmospheric evaporation capacity; E 0s is the optimum atmospheric evaporation capacity; E max for E 0s The corresponding maximum diving evaporation; E 0s and E max All greater than 0; Step 3: Considering the influence of groundwater depth on the parameters of the conceptual model of phreatic water evaporation at a fixed depth, the parameters of the conceptual model of phreatic water evaporation at a fixed depth are dynamically changed with the groundwater depth, and a calculation model of phreatic water evaporation at a variable depth is established; The calculation model of groundwater evaporation under variable burial depth is: ； in, E 0m The maximum evaporation at a burial depth of 0.0m; m for E g Decreasing rate with growth; H The depth of groundwater; E 0m and m All greater than 0; Step 4: Select historical data from periods not affected by rainfall to calculate the measured values ​​of groundwater evaporation. Use the optimization algorithm to calibrate the parameters of the groundwater evaporation calculation model under variable burial depths during different crop growth stages to simulate the groundwater evaporation.

2. The method for calculating phreatic evaporation under varying burial depth scenarios according to claim 1 is characterized in that: Step 4 specifically includes: Step 41: Eliminate the data on the day of rainfall and the day when groundwater is in a replenishment state after the rain, retain the data on the remaining days without rain, and calculate the measured value of phreatic evaporation using the groundwater depth data; Step 42, based on the data of atmospheric evaporation capacity, groundwater depth, and measured evaporation capacity, and the crop growth stages divided in step 1, the optimization algorithm is used to calibrate the parameters E max 、 E 0s and m The optimal solution of Step 43, set the parameters E max 、 E 0s and m The optimal solution is substituted into the calculation model of phreatic water evaporation under variable burial depth to calculate the phreatic water evaporation.

3. The method for calculating phreatic evaporation under varying burial depth scenarios according to any one of claims 1 to 2, characterized in that: The method for estimating the atmospheric evaporation capacity based on the collected meteorological information in step 1 is: If the meteorological information includes rainfall and water surface evaporation, water surface evaporation is used to represent the atmospheric evaporation capacity; if the meteorological information does not include water surface evaporation, it is necessary to additionally collect soil heat flux, solar radiation, net radiation, air temperature, wind speed and air humidity information, and use the Penman-Monteith formula recommended by the Food and Agriculture Organization of the United Nations to calculate the reference crop evaporation, and use the reference crop evaporation to represent the atmospheric evaporation capacity.

4. The method for calculating phreatic evaporation under varying burial depths according to claim 3 is characterized in that: The crop growth and development information in step 1 includes crop types and phenological characteristics.

5. The method for calculating phreatic evaporation under varying burial depth scenarios according to claim 3 is characterized in that: The Penman-Monteith formula is: ； in, ET 0 is the reference crop evapotranspiration; R n is the net radiation; G is the soil heat flux; T is the temperature; u 2 The wind speed at a height of 2m; e s is the saturated vapor pressure; e a is the actual vapor pressure; Δ is the slope of the water vapor pressure curve; γ is the psychrometer constant.

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