A calculation method for soil infiltration rate applicable to freeze-thaw environment in cold regions

Abstract

The present invention discloses a method for calculating the soil infiltration rate applicable to the freeze-thaw environment in cold regions. For the four freeze-thaw stages experienced by the soil, namely the initial melting period, the complete melting period, the initial freezing period, and the complete freezing period, different infiltration equations are respectively given to calculate the soil infiltration rate; the construction process of the formula of the present invention reflects the regional differences in soil water infiltration and the spatio-temporal distribution characteristics of the melting stage, which is more in line with the construction requirements of the distributed hydrological model and is applicable to the distributed hydrological model; by defining the slope influence coefficient, the slope is added as a variable affecting the infiltration process to the infiltration formula; taking the melting / freezing depth as a variable, the ratio of this variable to the maximum freezing depth of the active layer measured by the local hydrological station is used as a digital parameter of the freeze-thaw state to construct the infiltration equation. According to the calculation results of the embodiments, the Horton-RCCC formula constructed by the present invention can better reflect the infiltration process of water in the frozen soil environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrological calculations, and specifically relates to a method for calculating soil infiltration rate applicable to the freeze-thaw environment in cold regions. Background Art

[0002] The Horton formula is used to describe the variation law of soil infiltration rate with time, as shown in the following formula:

[0003] ;

[0004] Where: : Time t Infiltration rate at time; f 0: Initial infiltration rate; fc : Steady infiltration rate; k : Decay coefficient.

[0005] However, the initial infiltration rate f 0 and the steady infiltration rate f c These two infiltration parameters are easily affected by the underlying surface factors. The values obtained by simulating without considering the underlying surface factors cannot reflect the real infiltration process. In the frozen soil environment in cold regions, due to the significant influence of freeze-thaw action on soil structure and water movement characteristics, the calculation method using the Horton formula cannot accurately describe the water infiltration process in the frozen soil environment in cold regions. In addition, the initial infiltration rate f 0 and the steady infiltration rate f c These two parameters are generally obtained from experiments at a single point in the basin. During the use of the Horton formula, the initial infiltration rate, steady infiltration rate, and decay coefficient parameters are not associated with each point in the basin. Due to the large differences in the underlying surface conditions, it is difficult to achieve good simulation results when applying the Horton formula parameters at a single point to the entire basin, that is, the Horton formula is applicable to lumped hydrological models and cannot be used in distributed hydrological models.

[0006] Aiming at the above problems, it is urgent to propose a method for calculating soil infiltration rate for the freeze-thaw environment in cold regions, which is used to reflect the influence of the underlying surface conditions and freeze-thaw process on the infiltration process and is applicable to distributed hydrological models at the same time. Summary of the Invention

[0007] The purpose of the present invention is to consider the influence of freeze-thaw action on soil structure and water movement characteristics, establish the connection between the underlying surface factors and infiltration parameters, and propose a method for calculating soil infiltration rate applicable to the freeze-thaw environment in cold regions, which can be used to simulate hydrological processes in distributed hydrological models.

[0008] To achieve the above purpose, the technical solution of the present invention is specifically as follows:

[0009] A calculation method of soil infiltration rate applicable to freeze-thaw environment in cold regions. For the four freeze-thaw stages experienced by the soil, namely the initial melting period, the complete melting period, the initial freezing period, and the complete freezing period, the following infiltration equations are respectively used to calculate the soil infiltration rate:

[0010] Initial melting period:

[0011]

[0012] Complete melting period:

[0013]

[0014] Initial freezing period:

[0015]

[0016] Complete freezing period:

[0017]

[0018] In the formula, f p is t the maximum infiltration rate at time h m is the melting depth, is the maximum freezing depth of the active layer; is the freezing parameter, is the melting parameter, t is the time, k is the attenuation coefficient; h v is the freezing depth; is the slope influence coefficient, and the calculation method is: taking the infiltration amount of the flat slope as the reference value, and the ratio of the infiltration amounts of other slopes to the infiltration amount of the flat slope.

[0019] Furthermore, the calculation formula of the slope influence coefficient for different property soils is:

[0020] Sandy soil:

[0021]

[0022] Thin-layer soil:

[0023]

[0024] Black soil:

[0025]

[0026] Among them, i is the slope.

[0027] Furthermore, the initial infiltration ratef 0 The stable infiltration rate f c is calculated by the formula:

[0028]

[0029] In the formula, is the soil bulk density, FVC is the vegetation coverage rate.

[0030] In the embodiments of the present invention, the soil bulk density is measured by experiments. Among them, the soil bulk density is measured by the oven-drying method, the vegetation coverage is obtained by the visual estimation method, and is obtained from the slope infiltration experiment; the freezing parameters, melting parameters, and attenuation coefficient are obtained by fitting rainfall and runoff data.

[0031] In the model application stage, the soil bulk density can be obtained from the database. The soil bulk density can be obtained from the soil type parameter library, and the vegetation coverage is obtained from the NDVI database, all of which are open data. The slope influence coefficients corresponding to sandy soil, thin-layer soil, and black soil are calculated according to the formula proposed by the present invention. The acquisition method of is: if there is historical infiltration experiment data in the basin to be studied, check the freeze-thaw period of the infiltration experiment, calculate the slope influence coefficient according to the slope influence coefficient calculation formula of different property soils described in the present invention, calculate the initial infiltration rate and stable infiltration rate according to the initial infiltration rate and stable infiltration rate calculation formulas described in the present invention, and then fit with the infiltration experiment data to obtain the infiltration equation corresponding to different freeze-thaw periods described in the present invention.

[0032] Furthermore, if there is no infiltration experiment data in the basin to be studied, the freezing parameters, melting parameters, and attenuation coefficient are calibrated according to the historical rainfall and runoff data of the basin. According to the soil bulk density and vegetation coverage rate of the basin to be studied, use the initial infiltration rate and stable infiltration rate calculation formulas described in the present invention to calculate f 0 , f c , and calculate the slope influence coefficient according to the slope influence coefficient calculation formula of different property soils described in the present invention;

[0033] The initial melting period f 0 is corrected to , f c is corrected to ; The complete melting period f 0 is corrected to , f c is corrected to ; The initial freezing period f0 Modify to , f c Modify to ; Substitute the thawing depth during the initial thawing period of the study basin h m , the thawing depth during the initial freezing period h v , and the maximum freezing depth of the active layer values; Substitute the modified f 0 , f c and the corresponding rainfall intensities and runoff data for different periods into the basin runoff generation calculation model for fitting to obtain the values of the freezing parameter, thawing parameter, and attenuation coefficient; In the case of more rainfall data, through iterative calculation, take the set of data with the highest fitting accuracy of the runoff result as the calibration result of the parameters.

[0034] The specific explanations are as follows:

[0035] Without considering the change in rainfall intensity and the influence of initial soil water content on the process in the same rainfall event, the existing rainfall data: a certain basin The thawing depth during the initial thawing period h m , the thawing depth during the initial freezing period h v , and the maximum freezing depth of the active layer ; The rainfall during the initial thawing period P 1 , the rainfall during the complete thawing period P 2 , the rainfall during the initial freezing period P 3 ; The rainfall intensity during the initial thawing period i 1, the rainfall intensity during the complete thawing period i 2, the rainfall intensity during the initial freezing period i 3; The runoff during the initial thawing period R 1, the runoff during the complete thawing period R 2, the runoff during the initial freezing period R 3.

[0036] Obtained according to the initial infiltration rate and stable infiltration rate calculation formulas described in the present invention f 0 , f c ;

[0037] Because: , so modify the initial thawing period f 0 to , f c Modify to ; Fully melting period f 0 Revised to , f c Revised to ; Initial freezing period f 0 Revised to , f c Revised to .

[0038] Substitute the revised f 0 , f c and the rainfall intensity and runoff data corresponding to different periods into the basin runoff generation calculation model based on the Horton curve, that is, into the following three abbreviated equations:

[0039]

[0040] At this time, the calibration results of the freezing parameter, melting parameter, and attenuation coefficient can be directly obtained by solving the equation. In the case of more precipitation data, the computer will obtain a set of freezing parameters, melting parameters, and attenuation coefficients through an iterative method, with the highest fitting accuracy of the runoff result as the calibration target of the parameters.

[0041] The beneficial effects of the present invention are as follows:

[0042] The present invention fits the equations between the underlying surface parameters of soil bulk density and vegetation coverage rate and the infiltration parameters of initial infiltration rate and stable infiltration rate, constructs the relationship between the underlying surface factors and infiltration parameters, and the infiltration parameters of areas without infiltration data can be obtained through the soil type database; the construction process of the formula of the present invention reflects the regional differences in soil water infiltration and the spatio-temporal distribution characteristics of the melting stage, is more in line with the construction requirements of the distributed hydrological model, and is applicable to the distributed hydrological model; by defining the slope influence coefficient, the slope is added as a variable affecting the infiltration process to the infiltration formula; with the melting / freeze depth as the variable, the ratio of this variable to the maximum freeze depth of the active layer measured by the local hydrological station is used as the digital parameter of the freeze-thaw state, and an infiltration equation is constructed. According to the calculation results of the embodiments, the Horton-RCCC formula constructed by the present invention can better reflect the water infiltration process in the frozen soil environment. Description of the drawings

[0043] Figure 1 Is the curve of the influence coefficient of sandy soil changing with the slope;

[0044] Figure 2 Is the curve of the influence coefficient of thin-layer soil changing with the slope;

[0045] Figure 3 The variation curve of the influence coefficient of black soil with slope;

[0046] Figure 4 The comparison chart of the fitting results of the Horton formula and the Horton-RCCC formula during the complete melting period in Example 2;

[0047] Figure 5 The fitting result of the soil infiltration capacity of Fenghuoshan during the whole period using the Horton formula;

[0048] Figure 6 The fitting result of the soil infiltration capacity of Fenghuoshan during the whole period using the Horton-RCCC formula. Specific implementation mode

[0049] Example 1:

[0050] The present invention is developed on the basis of the Horton formula, and mainly makes three improvements to the Horton formula: the first is to construct the relationship between the underlying surface parameters and the infiltration parameters; the second is to reveal the influence of the terrain slope on the infiltration process; the third is to reflect the influence of the freeze-thaw process on the infiltration process in the infiltration equation. This example illustrates the improvement process.

[0051] The underlying surface factors include soil characteristics, surface cover, land use type, topography and geomorphology, etc. The surface cover includes vegetation, vegetation type, etc. The soil characteristics include soil texture, soil bulk density, soil structure, soil moisture content, etc. The topography and geomorphology include slope, aspect and altitude, etc.

[0052] The factors selected by the present invention when considering the influence of the underlying surface conditions take the following aspects into account:

[0053] 1. The influencing factors are easy to obtain. Data such as vegetation coverage and soil bulk density can be obtained through certain channels.

[0054] 2. The influencing factors can be parameterized. Influencing factors such as vegetation type are difficult to quantify and consider, and the results obtained by considering vegetation type according to root systems, leaves or average height are different.

[0055] 3. The influencing factors have strong independence. There is strong independence among soil bulk density, vegetation and slope. Variables such as soil texture and soil porosity have strong correlations with soil bulk density itself and can be converted through SPAW software.

[0056] 4. The underlying surface factors directly affect the infiltration process. Similar to aspect and altitude, they mainly affect the infiltration process by influencing vegetation growth conditions or rock development conditions. If such factors are considered, taking the soil unit into the laboratory for subsequent tests also changes the altitude, and the research results are not advisable.

[0057] In summary, the present invention selects soil bulk density and vegetation coverage rate as factors reflecting underlying surface factors, and only considers soil bulk density γ and vegetation coverage rate when calculating the initial infiltration rate and the stable infiltration rate. FVC The calculation formula of soil infiltration rate is as follows:

[0058]

[0059] Where: H is the freeze-thaw influence factor, related to the freezing / thawing depth h ; is the slope influence coefficient, related to the slope i ; f 1 , f 2 are functions of . Since the formula contains the surface unit attribute , this formula can be applied to distributed hydrological models.

[0060] The research object of the present invention is the hydrological process of frozen soil in alpine regions. The selected study areas are: the Fenghuoshan Basin (34°43′ N, 92°54′ E), a representative basin of permafrost; the Zoige Basin (33°56′ N, 102°5′ E) & the Jiuzhi Basin (33°23′ N, 101°35′ E), representative basins of seasonal frozen soil. For the representative basins, 5 test points were selected in the Fenghuoshan Basin, 2 test points in the Zoige Basin, and 1 test point in the Jiuzhi Basin under the condition that local conditions permit, and 1 sampling point was set in each of the three basins.

[0061] The specific implementation of this embodiment is as follows:

[0062] Step 1: Select soil bulk density and vegetation coverage rate as factors reflecting underlying surface factors, and obtain the corresponding initial infiltration rate f 0 and stable infiltration rate f c through in-situ double-ring infiltration tests, and construct equations accordingly.

[0063] Obtaining soil bulk density γ: In the detection of soil bulk density, considering that the surface soil is easily affected by roots and the deep soil is easily affected by gravels, the soil bulk density at a depth of 30 cm at the double-ring infiltration point is selected as the research parameter. A soil sampler with a diameter of 5 cm and a volume of 100 ml is used for sampling. After sampling, it is sealed and stored, and the bulk density of the soil sample in the sampler is obtained by the drying method. This method belongs to the prior art and will not be elaborated here.

[0064] Obtaining the vegetation coverage rate: It is obtained by visual estimation method at the test points.

[0065] In this embodiment, the soil bulk density and vegetation coverage rate of each test point are shown in Table 1 below.

[0066] Table 1 Information Table of Soil and Infiltration Parameters

[0067]

[0068] Initial infiltration rate f 0 and steady infiltration rate f c were obtained through the following specific process: An infiltrometer with double rings (model: GZH014) was used to conduct infiltration tests during the complete melting period at each test point. The double rings were approximately 50 cm high, with diameters of 0.25 m and 0.5 m respectively, and the material was a 2-mm steel plate. During the test, water was injected into both the inner and outer iron rings simultaneously, and the water columns in both rings were kept stable at the same height. After installing and debugging the Mariotte bottle, infiltration tests were carried out on the test plots. First, record the initial water level of the Mariotte bottle, open the drain valve. When the water flows into the inner infiltration ring, pull out the rubber plug of the organic ring, start the stopwatch, and when the free water surface in the infiltration ring touches the bottom surface of the plexiglass ring, quickly insert the rubber plug to block the small hole of the organic ring, and read the value according to the set time. Calculate the infiltration capacity t corresponding to each moment point f p (i.e., the maximum infiltration rate at that moment). In the Origin software, use the Horton formula to fit the data points to obtain f 0 and f c , and the results are shown in Table 1.

[0069] Using the plane formula to fit the data in Table 1, the plane equation obtained is:

[0070]

[0071] In the fitting results, the fitting accuracy f 0 is 0.89, R 2 and the fitting accuracy f c is 0.93. R 2

[0072] Step 2, when considering the influence of slope, put forward a basic assumption: the influence of slope on the infiltration process at any moment is constant.

[0073] Test steps:

[0074] 1. Select a device for measuring surface runoff and subsurface flow under a precipitation condition in the laboratory as the container for soil samples (with a length × width × height of 30 × 40 × 50 cm). Fill the soil box according to the depth of in-situ soil burial. Compare the restored soil core samples with the core samples at the sampling point. Appropriately compact or loosen the restored samples to keep the difference in soil wet density between the two within ±0.5 g / cm³.

[0075] 2. Place the soil box on a horizontal ground. Add 1800 ml (15 mm rainfall) of water into a pressure sprayer with a capacity of 2 L. When simulating rainfall above the restored samples, considering that the selected rainfall intensity reduces the error caused by rain erosion of the test samples on the basis of being higher than the stable infiltration rate, control the rainfall intensity at 1 mm / min.

[0076] 3. After the rainfall is completed, let it stand for a period of time until the surface runoff completely flows into the collection cup, measure the surface runoff volume and record the data. Repeat the experiment twice with an interval of more than 5 h and obtain the average value as the surface runoff volume under the flat slope condition The rainfall amount (1800 ml) minus the surface runoff volume gives the infiltration amount , and the infiltration amount = rainfall amount - runoff volume (without considering evaporation).

[0077] 4. Adjust the slope to 4°, 7°, 10°, 13°, 16°, 20°, 25° and 30° respectively by raising the sides, and repeat steps 2 - 3 to obtain the infiltration amounts under different slope conditions .

[0078] When the slope i increases, the infiltration amount will decrease significantly. To better reflect the change of infiltration amount under different slope conditions, taking the infiltration amount of the flat slope (0°) as the reference value, define the ratio of the infiltration amounts of the other slopes to the infiltration amount of the flat slope as the slope influence coefficient, that is:

[0079]

[0080] Among them, represents the slope influence coefficient when the slope is ; represents the infiltration amount when the slope is ; represents the infiltration amount when the slope is 0.

[0081] Therefore:

[0082]

[0083] Among them, represents the maximum infiltration rate of the soil at time t when the slope is ;​ It represents the maximum infiltration rate of the soil at time t when the slope is i.

[0084] Test results: The variation of the slope influence coefficient of sandy soil, thin-layer soil, and black soil with the slope is as shown in Figure 1 , 2 , and Figure 3. The exponential function is selected (the exponential function must pass through the point (0, 1), satisfying the prerequisite that the flat slope has no influence on the infiltration process, and at the same time satisfying , and fitting the change trend of the data points). The fitting curve formula and fitting accuracy R² are shown in Equation 8 - 10.

[0085] Sandy soil:

[0086]

[0087] Thin-layer soil:

[0088]

[0089] Black soil:

[0090]

[0091] Step 3: When considering the influence of the freeze-thaw state on the infiltration process, corresponding infiltration formulas are proposed according to the four freeze-thaw stages of frozen soil (initial melting period, complete melting period, initial freezing period, complete freezing period). Considering that during the complete melting period, the freeze-thaw process has no influence on the infiltration process, and at this time, only the combination with the underlying surface parameters and the influence of the slope are considered. Therefore, the infiltration equation for the complete melting period is:

[0092]

[0093] Among them, f p represents the maximum infiltration rate; t represents the time; k represents the attenuation coefficient, f 0 , f c are obtained from Equations 4 and 5 respectively.

[0094] During the complete freezing period, the soil is completely frozen, and the infiltration process is considered as 0. Therefore, the infiltration equation for the complete freezing period is:

[0095]

[0096] During the initial melting period, the water phase state of the active layer of frozen soil shows a phenomenon of melting from top to bottom. When the melting depth is 0 (the starting moment of the initial melting period, the melting depth h m= 0), the infiltration capacity f p (t) should be the same as that in the full freezing period (Equation 12), i.e., , at this time . When the thawing depth reaches the maximum freezing depth of the active layer , the entire active layer of frozen soil thaws, and the frozen soil is in the transition stage from the initial thawing period to the full thawing period. The infiltration capacity is the same as that in the full thawing period (Equation 11), i.e., , at this time , at this time . Select the thawing depth h m and the maximum freezing depth of the active layer (which can be obtained from the local hydrological station) to reflect the thawing state, i.e., . According to the above content, must pass through the fixed points (0, 0) and (1, 1), and during the thawing process of the active layer of frozen soil ( from 0 to 1), should satisfy monotonic increase. Among the functions that meet this condition, the power function fitting is the most appropriate. Therefore, the infiltration equation for the initial thawing period is:

[0097]

[0098] In the formula, represents the thawing parameter.

[0099] In the initial freezing period, the water phase state of the active layer of frozen soil shows a phenomenon of freezing from top to bottom. When the freezing depth h v is 0 (the start time of the initial freezing period, h v = 0), the infiltration capacity should be the same as that in the full thawing period, i.e.: , at this time . When the freezing depth reaches the maximum freezing depth of the active layer , the infiltration intensity is the same as that in the full freezing period, i.e.: , at this time . Select the freezing depth h v and the maximum freezing depth of the active layer to reflect the freezing state, i.e., . According to the above content, must pass through the fixed points (0, 1) and (1, 0), and during the freezing process of the active layer of frozen soil ( from 0 to 1), should satisfy monotonic decrease. Referring to the initial thawing period, the power function fitting is used. Therefore, the infiltration equation for the initial freezing period is:

[0100]

[0101] In the formula, represents the freezing parameter.

[0102] In summary, by aggregating Formulas 11 - 14, the Horton—RCCC formula is obtained:

[0103] Initial melting period:

[0104]

[0105] Full melting period:

[0106]

[0107] Initial freezing period:

[0108]

[0109] Full freezing period:

[0110]

[0111] Example 2:

[0112] In this example, undisturbed soil was collected and restored in a freeze-thaw laboratory. Then, calculations were performed using the Horton—RCCC formula and the Horton formula respectively to verify the effect of the Horton—RCCC formula.

[0113] Taking the undisturbed soil collected from the Fenghuoshan Basin as an example, after restoration in a freeze-thaw laboratory, a single-ring infiltration test was simulated for a flat slope ( ) under different freeze-thaw states. The Horton—RCCC formula and the Horton formula were fitted according to the test data at the same level.

[0114] 1. In the laboratory, a device for measuring surface runoff and subsurface flow under a certain precipitation condition was selected as the container for the soil sample. The length × width × height was 30 × 40 × 80 cm. The soil box was filled with soil according to the in-situ soil burial depth. The restored soil core sample was compared with the soil core sample at the sampling point, and the restored sample was appropriately compacted or loosened to make the difference in soil wet density between the two within ±0.5 g / cm³. During the process of restoring the soil sample, soil temperature and humidity sensors were buried at depths of 10 cm, 20 cm, 35 cm, 55 cm, and 75 cm in the soil column. The sensors were connected to the indoor soil moisture and temperature monitoring system, model: ZL—3000.

[0115] 2. The restored soil column was wrapped with two layers of 3-cm-thick thermal insulation cotton around its perimeter and at the bottom, so that the water in the soil column could freeze and melt from top to bottom.

[0116] 3. Hammer a single ring with a diameter of 25 cm and a height of 40 cm into the soil column, and the penetration depth is 5 - 10 cm.

[0117] 4. Adjust the indoor temperature to -25~-30 °C, observe the real-time monitoring data of the soil moisture and temperature monitoring system, and start the single-ring infiltration test when the freezing depth reaches 15 cm (observing that the soil temperature data at 10 cm and 20 cm depths are below and above zero respectively, that is, the zero-degree Celsius front is located at a depth of 15 cm).

[0118] 5. First, record the initial water level of the Mariotte bottle. Open the water release valve. When the water flows into the infiltration inner ring, pull out the rubber plug of the organic ring, start the stopwatch, and quickly plug the rubber plug and block the small hole of the organic ring when the free water surface in the infiltration ring touches the bottom surface of the plexiglass ring, and read according to the set time. Calculate the infiltration capacity corresponding to each moment point t from the test data f p , and use the Horton formula in Origin software to fit the data points to obtain f 0 、 f c .

[0119] The selected freeze-thaw states are the initial melting period (melting depths of 15, 35, 55 cm), the full melting period (fully melted), and the initial freezing period (freezing depth of 15 cm). Figure 4 is the fitting result during the full melting period, and the parameter f 0、 f c 、 k value data are shown in Table 2 below:

[0120] Table 2 Parameters during the full melting period f 0、 f c 、 k value fitting result

[0121]

[0122] During the above fitting process, the initial infiltration rate f 0 and the steady infiltration rate f c in the Horton formula are obtained by curve fitting, and the initial infiltration rate f 0 and the steady infiltration rate f c in the Horton - RCCC formula are obtained from Equations 4 and 5. Among them, the soil bulk density , and the vegetation coverage rate FVC= 0.3, thus the initial infiltration rate is obtained f 0 = 5.535 stable infiltration rate f c = 0.516, the fitting result with the Horton formula: initial infiltration rate f 0 = 5.974, stable infiltration rate f c = 0.523, which is similar. Therefore, under the flat slope condition, the Horton—RCCC formula has good applicability during the complete melting period. The fitting accuracy R² of the Horton formula before improvement is 0.979, and the accuracy of the Horton—RCCC formula is 0.976. It can be seen that the accuracies are quite comparable.

[0123] Example 3:

[0124] Using the data of rainfall runoff simulation tests on the flat slope and 10° slope of Fenghuoshan (obtained according to Equation 8 ), the rationality of the slope influence coefficient is tested. The sandy soil samples for slope runoff and the soil samples for single-ring infiltration are both the same batch of Fenghuoshan soil samples. The external conditions set for the slope runoff test are the complete melting period. Therefore, the parameters f 0, f c , k used for calculating the runoff of Fenghuoshan can refer to the fitting results of the single-ring infiltration test, that is Figure 2 .

[0125] When calculating runoff using the Horton formula and the Horton—RCCC formula, the two formulas should be calibrated first. Since the initial water content of the soil samples in the slope rainfall runoff simulation test is relatively large, the actual f 0 should be smaller than the fitting result of the single-ring infiltration test. Therefore, f 0 is selected as the calibration object. Using the rainfall runoff data under the flat slope condition to calibrate f 0 , and using the calibrated model to calculate the runoff of the 10° slope to verify the rationality of the slope influence coefficient.

[0126] Table 3 shows the infiltration and runoff parameters of the Horton formula and the Horton—RCCC formula during the complete melting period.

[0127] Table 3 Information table for calculating surface runoff at different slopes

[0128]

[0129] Among them, is the rainfall intensity, P is the precipitation, R1 is the measured surface runoff result of the slope rainfall runoff simulation experiment, R which is the calculation method in the basin runoff calculation model based on the Horton curve, that is, in the following formulas 15-16, and is the calculated surface runoff result.

[0130]

[0131] Among them, t r represents the rainfall duration; t a represents the moment when surface runoff is generated.

[0132] Under the flat slope state, the runoff volume of 15 mm of precipitation is 1.667 mm, and the f c of the Horton formula is 0.523 mm / min, k is 0.306, and according to formula 15-16, the calibrated f 0 is 2.272 mm / min. The f c of the Horton—RCCC formula is 0.516 mm / min, k is 0.279, and similarly, the calibrated result of the Horton—RCCC formula f 0 is 2.157 mm / min. Using the calibrated f 0 to calculate the runoff of the 10° slope respectively, the calculation results of the Horton formula and the Horton—RCCC formula are 1.667 mm and 7.478 mm respectively. When f 0 and f c in the Horton—RCCC formula will be modified according to formula 11 to and and substituted into the calculation.

[0133] According to the information in Table 3, the runoff results of the Horton formula under different slope conditions are the same as those on the flat slope. Under the condition of considering the influence of slope, the runoff result of 7.478 mm calculated by the Horton—RCCC formula is closer to the measured value of 8.3 mm. The main reason for the large deviation between the calculation result and the measured value is mainly the systematic error of the runoff simulation experiment itself, but the calculation result is sufficient to prove the superiority and rationality of the parameters.

[0134] During the entire initial melting (freezing) period, the Horton formula can only simulate the basin infiltration of the entire melting or freezing process using the infiltration parameters at a single moment and a single location, without reflecting the dynamics of the infiltration conditions of the underlying surface caused by the freeze-thaw process. The Horton-RCCC formula well solves this problem with the melting (freezing) depth as a parameter.

[0135] Figure 5 、 6 They are the fitting results of the Horton formula and the Horton-RCCC formula for the experimental data of the initial melting period (melting depths of 15, 35, and 55 cm), the complete melting period, and the initial freezing period (freezing depth of 15 cm) respectively. The data are shown in Tables 4 and 5.

[0136] Table 4 Fitting results of the Horton model

[0137]

[0138] Table 5 Fitting results of the Horton-RCCC model

[0139]

[0140] To better present the variation form of the soil infiltration process with the freeze-thaw depth and make a more practical comparative analysis, the day sequence number is used instead of the freeze-thaw depth. To simplify the calculation, the daily melting / freezing depth is set to 5 cm, and the freeze-thaw depth remains unchanged during the complete melting period. The specific comparison content is shown in Table 6.

[0141] Table 6 Freeze-thaw state - day sequence number comparison table

[0142]

[0143] The fitting surface of the Horton formula is a cylindrical surface, and this cylindrical surface is perpendicular to f p - t the plane, indicating that the infiltration process does not change during different time periods of the freeze-thaw process, which does not conform to the actual process; the infiltration processes of the Horton-RCCC formula are different during different time periods of the freeze-thaw process, manifested in: the infiltration capacity changes significantly with the increase of the melting depth within the first ten days, then the infiltration capacity converges to that of the complete melting period from the 10th day to the 35th day, enters the initial freezing period after the 55th day, and the infiltration capacity slowly becomes 0. The process of the infiltration capacity first increasing and then decreasing during the freeze-thaw change cycle is more in line with the actual situation. From the perspective of fitting accuracy, the fitting accuracy R² of the Horton formula is 0.740, and the fitting accuracy R² of the Horton-RCCC formula is 0.976. Thus, it can be seen that the Horton-RCCC formula has higher applicability in considering the influence of freeze-thaw changes on the infiltration process.

[0144] In summary, compared with the Horton formula, the Horton-RCCC formula can better reflect the infiltration process of water in the frozen soil environment.

Claims

1. A calculation method for soil infiltration rate applicable to freeze-thaw environments in cold regions, characterized in that, For the four freeze-thaw stages experienced by the soil, namely the initial melting period, the complete melting period, the initial freezing period, and the complete freezing period, the following infiltration equations are used to calculate the soil infiltration rate respectively: Initial melting period: ; Complete melting period: ; Initial freezing period: ; Complete freezing period: ; In the formula, f p is t the maximum infiltration rate at time f 0 is the initial infiltration rate, f c is the steady infiltration rate; h m is the thawing depth, is the maximum freezing depth of the active layer; is the freezing parameter, is the thawing parameter, t is the time, k is the attenuation coefficient; h v is the freezing depth; is the slope influence coefficient, and its calculation method is: taking the infiltration amount on a flat slope as the reference value, and the ratio of the infiltration amounts at other slopes to the infiltration amount on a flat slope.

2. The method for calculating soil infiltration rate applicable to freeze-thaw environment in cold regions according to claim 1, wherein The calculation formula for the slope influence coefficient of soils with different properties is: Sandy soil: ; Thin-layer soil: ; Black soil: ; Among them, i is the slope.

3. The method for calculating soil infiltration rate applicable to freeze-thaw environment in cold regions according to claim 2, characterized in that Initial infiltration rate f 0 , Steady infiltration rate f c The calculation formulas are as follows: ; In the formula, is the soil bulk density, FVC is the vegetation coverage rate.

4. The method for calculating soil infiltration rate applicable to freeze-thaw environment in cold regions according to claim 3, wherein The methods for obtaining the freezing parameters, melting parameters, and attenuation coefficients are as follows: If there are historical infiltration test data in the basin to be studied, check the freeze-thaw period of the infiltration test, calculate the slope influence coefficient according to formula (5), (6), or (7), calculate the initial infiltration rate and the stable infiltration rate according to formula (8), (9), and then substitute them together with the infiltration test data into the infiltration equation for the corresponding period for fitting.

5. The calculation method of soil infiltration rate applicable to freeze-thaw environment in cold regions according to claim 3, characterized in that, If there are no infiltration test data in the basin to be studied, the freezing parameters, melting parameters, and attenuation coefficients are calibrated based on the historical rainfall and runoff data of the basin. The method is: According to the soil bulk density and vegetation coverage rate of the basin to be studied, calculate the initial infiltration rate and the stable infiltration rate using formula (8), (9), and calculate the slope influence coefficient according to formula (5), (6), or (7); Modify the initial melting period f 0 to , f c to ; fully melting period f 0 to , f c to ; initial freezing period f 0 to , f c to ; Substitute the melting depth, freezing depth, and maximum freezing depth of the active layer in the initial melting period of the study basin h m , freezing depth h v , and maximum freezing depth of the active layer values; Substitute the corrected f 0 , f c and the rainfall intensity and runoff data corresponding to different periods into the basin runoff generation calculation model for fitting to obtain the values of freezing parameters, melting parameters, and attenuation coefficients; In the case of a large amount of rainfall data, the group of data with the highest fitting accuracy of the runoff result is taken as the calibration result of the parameters through iterative calculation.

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