A method for calculating phreatic evaporation

Abstract

The present invention discloses a method for calculating phreatic evaporation, which belongs to the hydrological science category of the geophysical science category. The present invention establishes a calculation formula that reflects phreatic evaporation at different burial depths by considering the hysteresis effect between air temperature and soil temperature at different depths, and can simulate phreatic evaporation processes at various time scales based on water surface evaporation, air temperature, soil temperature and phreatic burial depth. The technical solution provided by the present invention can improve the simulation accuracy of phreatic evaporation, provide a scientific basis for decision-making on groundwater resource utilization, and also fill the gap in the description of energy-driven evaporation process in the current phreatic evaporation empirical model.

Description

Technical Field

[0001] The invention relates to a method for calculating phreatic evaporation, and belongs to the technical field of hydrology under geophysics. Background Art

[0002] Phreatic evaporation is an important part of the water cycle and the main vertical consumption pathway of shallow groundwater. Improving the simulation accuracy of phreatic evaporation is of great significance to the rational development and utilization of groundwater resources and ecological environmental protection. The methods for determining phreatic evaporation include direct observation, numerical simulation and empirical formula calculation. Among them, the empirical formula has simple data requirements and high ease of use, and is the main method used in production practice. The empirical phreatic evaporation calculation formulas currently used include Averyanov formula, Ye Shuiting formula, Shen Lichang formula, Zhang Chaoxin formula, Tsinghua University formula, etc., but these formulas only consider variables related to meteorological factors and soil water transport capacity, ignoring the energy drive in the evaporation process, and not considering the characteristics that the amplitude of the temperature wave in the soil decreases with increasing soil depth, and the peak and valley time of the highest and lowest temperatures lags with increasing depth, resulting in the simulation results being different from the actual phreatic evaporation process under the influence of the vertical distribution of soil temperature. Summary of the invention

[0003] The invention provides a method for calculating submerged evaporation, which can reflect the influence of temperature variables on submerged evaporation and improve simulation accuracy.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] (A) Obtain water surface evaporation, groundwater depth, air temperature and soil temperature at groundwater depth on a uniform time scale during the study period;

[0006] (B) Calculation of soil temperature coefficient K at submerged depth Tg ;

[0007]

[0008] In the formula, α is the fitting parameter, T a and T g are air temperature and soil temperature at burial depth, respectively;

[0009] (C) Calculate the phreatic evaporation of soil temperature by multiplying the soil temperature coefficient with the existing phreatic evaporation empirical formula; the calculation formula is as follows:

[0010]

[0011] E g =E0×e -bH ×K Tg

[0012] Where, E0 is the evaporation from the water surface; H is the burial depth of the groundwater, H max is the ultimate evaporation depth of groundwater, n and b are fitting parameters; E g Evaporation for diving.

[0013] The fitting parameter H in steps B and C max , n, b and α are determined by an optimization algorithm.

[0014] Fitting parameter H max It is a parameter related to the physical properties of soil, which is related to soil type and physical characteristics. The constraint range that conforms to the actual situation should be determined in combination with existing literature results, changes in groundwater depth and soil properties in the study area to ensure the rationality of the calculation formula.

[0015] The optimization algorithm is to calculate the E g Compared with the measured E g The objective function is to minimize the sum of squares of the errors between them. A global search is performed within the reasonable range of the parameters to obtain a set of optimal H max , n, b and α, so that the result calculated by using this set of parameters satisfies the minimum sum of squares of errors between the calculated value and the measured value;

[0016] Furthermore, after step C, the method of the present invention can also be applied to explore and quantify the influence of rainfall on the measurement error of phreatic evaporation, comprising the following steps:

[0017] (D) Based on the measured precipitation and infiltration recharge data, the full series of phreatic water evaporation data during the study period is divided into a rainy day series affected by rainfall and a rainless day series not affected by rainfall;

[0018] The division method is generally applicable to the daily calculation period. The actual process of whether the water table is affected by rainfall infiltration is used as the basis for division. The measured data of water table evaporation without rainfall and infiltration recharge on that day are classified as the series of rainless days, and the remaining data are classified as the series of rainy days.

[0019] (E) using the rainless day sequence, according to steps (A) to (C), obtain the quadratic fitting parameter combination of rainless days;

[0020] The quadratic fitting parameter combination of rainless days is calculated from part of the data in the study period, that is, the rainless day sequence that is not affected by rainfall. Compared with the original parameters calculated using the full sequence data in the study period, it can reflect the actual phreatic evaporation process excluding the influence of rainfall.

[0021] (F) The phreatic water evaporation during the entire study period is calculated using the rainless day sequence parameters, and the phreatic water evaporation sequence that is not affected by rainfall during the study period is reconstructed. The results are compared with the calculation results of step (C) using the original parameters of the full sequence, the differences are analyzed, and the phreatic water evaporation error under the influence of rainfall is quantified.

[0022] Beneficial effects:

[0023] The present invention takes into account the characteristics that the amplitude of the temperature wave in the soil decreases with increasing soil depth, and the peak and valley appearance time of the highest and lowest temperatures lags with increasing depth. By introducing the description of the energy-driven evaporation process into the existing empirical formula, the calculation results of the present invention are more consistent with the actual groundwater evaporation under the vertical distribution of soil temperature; it has higher simulation accuracy; the required parameters are easy to obtain, the time scale can be adjusted as needed, and the applicability is strong; it is further applied to the analysis of the impact of rainfall on the groundwater evaporation process, and can provide a scientific reference basis for basin water cycle research and groundwater resource utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a flow chart of the method for calculating phreatic evaporation based on soil temperature according to the present invention;

[0025] Figure 2 is the fitting parameter H in the embodiment of the present invention max A diagram illustrating the reasonable constraints range;

[0026] Figure 3 This is a comparison chart of the accuracy of the basic formula results and the calculation method results of the present invention in the embodiment of the present invention;

[0027] Figure 4 It is a relationship diagram between the basic formula in the embodiment of the present invention and the simulation results and the actual measurement results of the calculation method of the present invention;

[0028] Figure 5 It is a relationship diagram between the simulation results and the measured results of the calculation method of the present invention using all the sequence parameters and the rainless day sequence parameters in the embodiment of the present invention;

[0029] Figure 6 This is a comparison chart between the diving evaporation simulation results and the measured results at various depths in the embodiment of the present invention. DETAILED DESCRIPTION

[0030] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. Specifically, the following steps are included:

[0031] Step 1: Define the research period and time scale, and obtain the water surface evaporation (E0), groundwater burial depth (H), and temperature (T a ) and the soil temperature at the subsurface depth (T g )material;

[0032] The time scale refers to the fact that the phreatic evaporation to be studied is the phreatic evaporation on a daily / monthly / yearly basis. When it is daily phreatic evaporation, the water surface evaporation (E0) is the total daily evaporation, and the temperature (T a ) and the soil temperature at the subsurface depth (T g ) is the daily average temperature; when the evaporation is monthly, the surface evaporation (E0) is the monthly total evaporation, and the air temperature (T a ) and the soil temperature at the subsurface depth (T g ) is the monthly average temperature; other arbitrary calculation time scales are deduced in the same way;

[0033] Step 2: Select the applicable basic formula according to the research area and research purpose;

[0034] The applicable basic formula is an existing empirical formula for phreatic evaporation, such as Avilyanov's formula, Ye Shuiting's formula, Shen Lichang's formula, etc.; such as formula (1) and formula (2):

[0035]

[0036] E g =E0×e -bH (2)

[0037] Where, E0 is the evaporation from the water surface, mm; H is the burial depth, m, H max is the ultimate evaporation depth of groundwater, m, n and b are fitting parameters; E g is the phreatic evaporation, mm;

[0038] Step 3: Calculate the soil temperature coefficient K at the submerged depth Tg ;

[0039]

[0040] In the formula, α is the fitting parameter, T a and T g are air temperature and soil temperature at burial depth, ℃;

[0041] Step 4: Combine the soil temperature coefficient with the basic formula to establish the calculation formula of groundwater evaporation based on soil temperature by multiplication; such as formula (4) and formula (5):

[0042]

[0043] E g =E0×e -bH ×K Tg (5)

[0044] Step 5: Determine the corresponding parameters and calculate the phreatic evaporation of the study area during the study period;

[0045] The corresponding parameters include the basic formula and the soil temperature coefficient K Tg The fitting parameters in the paper are combined with the existing literature results, the change of groundwater depth and soil properties in the study area to determine the parameter constraint range that conforms to the actual situation. The fitting parameters are solved by the optimization problem with the minimum fitting error as the objective function to ensure the rationality of the calculation formula.

[0046] Step 6: Divide rainy days and rainless days based on precipitation data and infiltration recharge data;

[0047] The classification method is based on the actual process of whether the water table is affected by rainfall infiltration, and is generally applicable to daily calculation periods. The daily scale data without rainfall and infiltration recharge are classified as rainless days, and the remaining periods are classified as rainy days.

[0048] Step 7: Use the fitting parameters obtained from the rainless day data to calculate the actual phreatic evaporation process that is not affected by rainfall, and further analyze the impact of rainfall on the phreatic evaporation process.

[0049] Embodiment 1:

[0050] This example takes the Shajiang black soil of the Wudaogou Hydrological Experiment Station in the Huaibei Plain as an example, selects the Aviryanov formula and the Ye Shuiting formula as the basic formula, and determines the fitting parameter H according to the measured data results of the station and the soil physical properties of the Shajiang black soil. max The reasonable constraint range is [1.40, +∞]( Figure 2 ), and then all fitting coefficients are determined by the least square method, and the method of the present invention is used to calculate the daily groundwater evaporation at groundwater depths of 0.2m, 0.4m, 0.6m, 0.8m, and 1.0m in 2019-2020. The specific expression of the groundwater evaporation calculation formula based on soil temperature based on the Averyanov formula is obtained as formula (2), and the specific expression of the Ye Shuiting formula as the basic formula is obtained as formula (3):

[0051]

[0052]

[0053] Among them, E g is the evaporation of groundwater, mm; E0 is the evaporation of water surface, mm; H is the burial depth of groundwater, m; T a is the air temperature, ℃; T g is the soil temperature at H, ℃.

[0054] From the perspective of accuracy, the Nash coefficient NSE of formula (2) and formula (3) is 0.70, and the certainty coefficient R 2=0.71, the relative errors RE of the total amount are 2.43% and 1.06% respectively, which are 4.7% and 6.1% higher than the fitting accuracy of the original basic formula ( Figure 3 ); From the relationship between the simulated value and the measured value, the simulated value sequence obtained by the calculation method considering the temperature variable of the present invention is closer to the measured sequence than the result directly calculated using the basic formula ( Figure 4 ).

[0055] Based on the actual process of whether the water table is affected by rainfall infiltration, the specific calculation formula obtained after classifying the daily data without rainfall and infiltration recharge as rainless days is:

[0056]

[0057]

[0058] The root mean square error of formula (4) and formula (5) is RMSE = 0.39, the Nash coefficient is NSE = 0.82, and the certainty coefficient R 2 =0.83, the total relative error RE is 3.32% and 1.85% respectively, and the accuracy is further improved ( Figure 5 ); from the perspective of the phreatic evaporation process at each depth, compared with the results calculated using only the basic formula, the results of the calculation formula of the present invention can better reflect and be close to the characteristics of the rapid change of phreatic evaporation with depth. At the same time, the phreatic evaporation data on rainless days that are not affected by precipitation infiltration are more concentrated and show more consistent regularity, which can better reflect the phreatic evaporation process under actual conditions ( Figure 6 ).

[0059] It can be seen from this embodiment that the simulation result obtained by using the phreatic evaporation calculation method based on soil temperature provided by the present invention is more consistent with the actual phreatic evaporation situation, has higher simulation accuracy, flexible time scale and strong applicability.

Claims

1. A method for calculating diving evaporation, characterized in that: The following steps are involved: Obtain water surface evaporation, groundwater depth, air temperature and soil temperature at groundwater depth on a uniform time scale during the study period; Calculate the soil temperature coefficient K at the submerged depth Tg ; In the formula, α is the fitting parameter, T a and T g are air temperature and soil temperature at burial depth, respectively; The soil temperature coefficient is multiplied by the existing empirical formula for phreatic evaporation to calculate phreatic evaporation based on soil temperature: AND g =And g ′×K Tg In the formula, E g is the phreatic evaporation based on soil temperature; E g ' is the phreatic evaporation calculated using the existing phreatic evaporation empirical formula.

2. The method for calculating diving evaporation according to claim 1, characterized in that: Existing empirical formulas for diving evaporation include: AND g ′=E0×e -bH Where, E0 is the evaporation from the water surface; H is the burial depth of the groundwater, H max is the ultimate evaporation depth of groundwater, n and b are fitting parameters; E g ' is the phreatic evaporation calculated by the existing phreatic evaporation empirical formula; The soil temperature coefficient is calculated by multiplying the above two empirical formulas for phreatic evaporation to obtain the phreatic evaporation based on soil temperature: AND g =E0×e -bH ×K Tg In the formula, E g Evaporation for diving.

3. The method for calculating diving evaporation according to claim 2, characterized in that: Fitting parameter H max , n, b and α are determined by: Search H by global optimization algorithm max , n, b and α, and find the best matching H max , n, b and α, so that H max The calculation results obtained by using , n, b and α satisfy the objective function of minimizing the sum of squares of errors between the calculated values ​​and the measured values.

4. The method for calculating diving evaporation according to claim 1, characterized in that: In the step of obtaining the water surface evaporation, groundwater burial depth, air temperature and soil temperature at the groundwater burial depth on a unified time scale within the studied period, the studied period is the time series span for which groundwater evaporation needs to be calculated; the time scale is the groundwater evaporation to be studied, which is the daily / monthly / yearly groundwater evaporation; when it is daily groundwater evaporation, the water surface evaporation is the daily total evaporation, and the air temperature and soil temperature at the groundwater burial depth are the daily average temperature; when it is monthly groundwater evaporation, the water surface evaporation is the monthly total evaporation, and the air temperature and soil temperature at the groundwater burial depth are the monthly average temperature.

5. The method for calculating diving evaporation according to claim 1, characterized in that: An optimization step is also included for optimizing the calculated groundwater evaporation based on the soil temperature, including: Based on precipitation data and infiltration recharge data, the whole series data in the research period are divided into rainy day series and non-rainy day series; The quadratic fitting parameters that can reflect the actual phreatic evaporation process not affected by rainfall are obtained by using the rainless day series. The quadratic fitting parameters obtained from the rainless day series were used to calculate the phreatic evaporation excluding the influence of precipitation.

6. The method for calculating diving evaporation according to claim 5, characterized in that: The optimization steps also include: The calculated phreatic water evaporation excluding the influence of precipitation is compared with the original parameter calculation results of the whole sequence to obtain the difference; the phreatic water evaporation error under the influence of rainfall is quantified by the calculated difference.

Images