Soil infiltration rate calculation method suitable for freezing and thawing environment in cold region

Abstract

The invention discloses a soil infiltration rate calculation method suitable for a freezing and thawing environment in a cold region, and the method comprises the steps: respectively giving different infiltration equations for calculating the soil infiltration rate according to four freezing and thawing stages of soil, namely an initial thawing stage, a complete thawing stage, an initial freezing stage and a complete freezing stage; the construction process of the formula reflects the regional difference of soil moisture infiltration and the spatial and temporal distribution characteristics of the melting stage, is more in line with the construction requirements of the distributed hydrological model, and is suitable for the distributed hydrological model; by defining a slope influence coefficient, adding the slope as a variable influencing the infiltration process into an infiltration formula; the infiltration equation is constructed by taking the thawing / freezing depth as a variable and taking the ratio of the variable to the maximum freezing depth of the active layer measured by the local hydrometric station as a digital parameter of the freezing and thawing state, and the calculation result of the embodiment shows that the constructed Horton-RCCC formula can better reflect the infiltration process of the moisture in the frozen soil environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrological calculation, and particularly relates to a method for calculating soil infiltration rate applicable to 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: ; Where: : time t Infiltration rate at time; f 0 : Initial infiltration rate; fc : Steady infiltration rate; k : Decay coefficient.

[0003] However, the initial infiltration rate f 0 and the steady infiltration rate f c in the Horton formula are easily affected by underlying surface factors. The numerical values obtained by simulating without considering the underlying surface factors cannot reflect the real infiltration process. In the frozen soil environment of 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 of 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 underlying surface conditions, it is difficult to obtain a good simulation effect 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.

[0004] In view of 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 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

[0005] 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 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.

[0006] To achieve the above purpose, the technical solution of the present invention is specifically as follows: A calculation method of 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, the following infiltration equations are respectively used to calculate the soil infiltration rate: Initial melting period:

[0007] Complete melting period:

[0008] Initial freezing period:

[0009] Complete freezing period:

[0010] 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 on a flat slope as the reference value, and the ratio of the infiltration amounts of other slopes to the infiltration amount on a flat slope.

[0011] Furthermore, the calculation formula for the slope influence coefficient of different property soils is: Sandy soil:

[0012] Thin-layer soil:

[0013] Black soil:

[0014] Among them, i is the slope.

[0015] Furthermore, the initial infiltration rate f 0 and the stable infiltration rate f c The calculation formulas are:

[0016] In the formula, is the soil bulk density, FVC is the vegetation coverage rate.

[0017] 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 visual estimation, and is obtained by the slope infiltration experiment; the freezing parameter, the melting parameter, and the attenuation coefficient are obtained by fitting rainfall and runoff data.

[0018] 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 as follows: 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 the 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.

[0019] Furthermore, if there is no infiltration experiment data in the basin to be studied, the freezing parameter, the melting parameter, and the 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, f 0 and f c are calculated according to the slope influence coefficient calculation formula of different property soils described in the present invention;

[0020] 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 f 0 is corrected to , f c is corrected to ; Substitute the melting depth of the initial melting period h m and the melting depth of the initial freezing period of the research basin intoh v , the maximum freezing depth of the active layer value; the corrected f 0 , f c and the corresponding rainfall intensities and runoff data for different periods are brought into the basin runoff generation calculation model for fitting to obtain the values of the freezing parameter, melting parameter, and attenuation coefficient; in the case of a large amount of rainfall data, a set of data with the highest fitting accuracy of the runoff result is taken as the calibration result of the parameters through iterative calculation.

[0021] The specific explanation is as follows: Without considering the change in rainfall intensity and the influence of the initial soil water content on the process in the same rainfall event, the existing rainfall data: a certain basin Melting depth in the initial melting period h m , melting depth in the initial freezing period h v , the maximum freezing depth of the active layer ; rainfall in the initial melting period P 1 , rainfall in the complete melting period P 2 , rainfall in the initial freezing period P 3 ; rainfall intensity in the initial melting period i 1 , rainfall intensity in the complete melting period i 2 , rainfall intensity in the initial freezing period i 3 ; runoff in the initial melting period R 1 , runoff in the complete melting period R 2 , runoff in the initial freezing period R 3 .

[0022] According to the initial infiltration rate and stable infiltration rate calculation formulas described in the present invention, f 0 , f c ; Because: , so the initial melting period f 0 is corrected to , f c is corrected to ; the complete melting period f 0 is corrected to , fc Revised to ; Initial freezing period f 0 Revised to , f c Revised to .

[0023] 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:

[0024] 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.

[0025] The beneficial effects of the present invention are as follows: 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 can obtain the infiltration parameters in areas without infiltration data 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 a 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

[0026] Figure 1 Is the change curve of the influence coefficient of sandy soil with slope; Figure 2 Is the change curve of the influence coefficient of thin-layer soil with slope; Figure 3 Is the change curve of the influence coefficient of black soil with slope; Figure 4 Is the comparison chart of the fitting results of the Horton formula and the Horton-RCCC formula during the full melting period in Embodiment 2; Figure 5is the fitting result of the soil infiltration capacity during the entire period of Fenghuoshan Mountain using the Horton formula; Figure 6 is the fitting result of the soil infiltration capacity during the entire period of Fenghuoshan Mountain using the Horton - RCCC formula. Detailed implementation mode

[0027] Example 1:

[0028] The present invention is developed on the basis of the Horton formula, and mainly makes three improvements to the Horton formula: First, it constructs the relationship between the underlying surface parameters and the infiltration parameters; second, it reveals the influence of the terrain slope on the infiltration process; third, it reflects the influence of the freeze - thaw process on the infiltration process in the infiltration equation. This example illustrates the improvement process.

[0029] 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.

[0030] When considering the influence of the underlying surface conditions, the factors selected by the present invention take into account the following aspects: 1. The influencing factors are easy to obtain. Data such as vegetation coverage and soil bulk density can be obtained through certain channels.

[0031] 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.

[0032] 3. The influencing factors have strong independence. The independence among soil bulk density, vegetation and slope is strong. Variables such as soil texture and soil porosity have strong correlations with soil bulk density itself and can be converted through SPAW software.

[0033] 4. The underlying surface factors directly affect the infiltration process. Factors such as aspect and altitude 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 experiments also changes the altitude, and the research results are not advisable.

[0034] In summary, the present invention selects soil bulk density and vegetation coverage rate as the factors reflecting the underlying surface factors. When calculating the initial infiltration rate and the stable infiltration rate, only the soil bulk density γ and the vegetation coverage rate are considered. FVC . The calculation formula of the soil infiltration rate is as follows:

[0035] Where: His the freeze-thaw influence factor, related to the freezing / thawing depth h and is the slope influence coefficient, related to the slope i and f 1 and f 2 is a function of . Since the formula contains the surface unit attribute , this formula can be applied to the distributed hydrological model

[0036] The research object of the present invention is the hydrological process of permafrost in alpine regions. The selected research 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, and 1 sampling point was set in each of the three basins under the condition of local permission

[0037] The specific implementation of this embodiment is as follows Step 1: Select the soil bulk density and vegetation coverage rate as the factors reflecting the underlying surface factors, and obtain the corresponding initial infiltration rate f 0 and stable infiltration rate f c through the in-situ double-ring infiltration test, and construct an equation based on this

[0038] Obtaining the soil bulk density γ: In the soil bulk density detection, 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 ring knife with a diameter of 5 cm and a capacity of 100 ml is used for sampling. After sampling, it is sealed and stored, and the bulk density of the soil sample in the ring knife is obtained by the drying method. This method belongs to the prior art and will not be elaborated here

[0039] Obtaining the vegetation coverage rate: Obtained by the visual estimation method at the test points

[0040] In this embodiment, the soil bulk density and vegetation coverage rate results of each test point are shown in Table 1 below

[0041] Table 1 Soil and infiltration parameter information table

[0042] Initial infiltration rate f 0 and stable infiltration rate f cThe specific process of obtaining it is as follows: An infiltration test is carried out using a double-ring infiltrometer (model: GZH014) during the fully melted period at each test point. The double-ring is about 50 cm high, with diameters of 0.25 m and 0.5 m respectively, and the material is a 2-mm steel plate. During the test, water is injected into both the inner and outer iron rings simultaneously, and the water columns in both the inner and outer rings are kept stable at the same height. After installing and debugging the Mariotte bottle, an infiltration test is carried out in the test plot. 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 stopper of the organic ring, start the stopwatch. When the free water surface in the infiltration ring touches the bottom surface of the plexiglass ring, quickly plug the rubber stopper to block the small hole of the organic ring, and read the value according to the set time. Calculate the infiltration capacity corresponding to each moment point t (i.e., the maximum infiltration rate at that moment), and obtain the fitting of data points using the Horton formula in the Origin software f p 0 f 0 , f c , and the results are shown in Table 1.

[0043] Using the plane formula to fit the data in Table 1, the plane equation obtained is:

[0044] In the fitting result f 0 The fitting accuracy R 2 is 0.89, f c The fitting accuracy R 2 is 0.93.

[0045] Step 2, when considering the influence of slope, a basic assumption is proposed: The influence of slope on the infiltration process at any moment is constant.

[0046] Test steps: 1. Select a device for measuring surface runoff and subsurface flow under a precipitation condition in the laboratory as the container for the soil sample (length × width × height is 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 points, and appropriately compact or loosen the restored samples to make the difference in soil wet density between the two within ±0.5 g / cm³.

[0047] 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 sample, considering that the selected rainfall intensity reduces the error caused by rainwater scouring of the test sample on the basis of being higher than the stable infiltration rate, the rainfall intensity is controlled at 1 mm / min.

[0048] 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 state , and the infiltration volume is obtained by subtracting the surface runoff volume from the rainfall amount (1800 ml). Infiltration volume = rainfall amount - runoff volume (evaporation not considered).

[0049] 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 volume under different slope conditions. .

[0050] When the slope i increases, the infiltration volume will decrease significantly. To better reflect the change of infiltration volume under different slope conditions, taking the infiltration volume of the flat slope (0°) as the reference value, the ratio of the infiltration volume of the other slopes to the infiltration volume of the flat slope is defined as the slope influence coefficient, that is:

[0051] Among them, represents the slope influence coefficient when the slope is ; represents the infiltration volume when the slope is ; represents the infiltration volume when the slope is 0.

[0052] Therefore:

[0053] Among them, represents the maximum infiltration rate of the soil at time t when the slope is ; represents the maximum infiltration rate of the soil at time t when the slope is.

[0054] 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 , 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 curve formula and fitting accuracy according to the change trend of data points R² See Equation 8-10.

[0055] Sandy soil:

[0056] Thin-layer soil:

[0057] Black soil:

[0058] Step 3, when considering the influence of 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 only the influence of combination with underlying surface parameters and slope is considered at this time. Therefore, the infiltration equation for the complete melting period is:

[0059] Among them, f p represents the maximum infiltration rate; t represents time; k represents the attenuation coefficient, f 0 、 f c are obtained from Equation 4 and Equation 5 respectively.

[0060] 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:

[0061] 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 complete freezing period (Equation 12), that is , and at this time . When the melting depth reaches the maximum freezing depth of the active layer, the entire active layer of frozen soil melts, and the frozen soil is in the transition stage from the initial melting period to the complete melting period. The infiltration capacity is the same as that in the complete melting period (Equation 11), that is when , and at this time . Select the melting depth hm The ratio with the maximum freezing depth of the active layer (which can be obtained from the local hydrological station) is used to reflect the melting state, that is . According to the above content, must pass through the fixed points (0,0) and (1,1), and during the melting 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 melting period is:

[0062] In the formula, represents the melting parameter.

[0063] During 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 starting moment of the initial freezing period, h v =0), the infiltration capacity should be the same as that in the fully melted period, that is: , 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 fully frozen period, that is: , at this time . Select the ratio of the freezing depth h v to the maximum freezing depth of the active layer to reflect the freezing state, that is . 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 power function fitting in the initial melting period. Therefore, the infiltration equation for the initial freezing period is:

[0064] In the formula, represents the freezing parameter.

[0065] In summary, by summarizing Equations 11 - 14, the Horton—RCCC formula is obtained: Initial melting period:

[0066] Fully melted period:

[0067] Initial freezing period:

[0068] Completely frozen period:

[0069] Example 2: In this example, undisturbed soil was collected and restored in the freeze-thaw laboratory. Then, the Horton-RCCC formula and the Horton formula were used for calculation respectively to verify the effect of the Horton-RCCC formula.

[0070] Taking the undisturbed soil collected from the Fenghuoshan Basin as an example, after restoration in the freeze-thaw laboratory, the single-ring infiltration test was simulated under flat slopes ( ) in different freeze-thaw states. The Horton-RCCC formula and the Horton formula were fitted at the same level according to the test data.

[0071] 1. Select a device for measuring surface runoff and subsurface flow under a certain precipitation condition in the laboratory as the container for the soil sample. The length × width × height is 30 × 40 × 80 cm. Fill the soil box according to the in-situ soil burial depth. Compare the restored soil core sample with the core sample at the sampling point. Appropriately compact or loosen the restored sample to make the difference in soil wet density between the two within ±0.5 g / cm³. During the process of restoring the soil sample, install soil temperature and humidity sensors at depths of 10 cm, 20 cm, 35 cm, 55 cm, and 75 cm in the soil column. The sensors are connected to the indoor soil moisture and temperature monitoring system, model: ZL-3000.

[0072] 2. Wrap two layers of thermal insulation cotton with a thickness of 3 cm around the restored soil column, so that the water in the soil column freezes from top to bottom and melts from top to bottom.

[0073] 3. Hammer a single ring with a diameter of 25 cm and a height of 40 cm into the soil column, and the hammering depth is 5 - 10 cm.

[0074] 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 depths of 10 cm and 20 cm are below and above zero respectively, that is, the zero-degree Celsius front is located at a depth of 15 cm).

[0075] 5. First, record the initial water level of the Mariotte bottle. Open the water discharge valve. When the water flows into the infiltration inner 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 plug 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 corresponding to each time point according to the test data t corresponding to fp , the data points were fitted using the Horton formula in Origin software to obtain f 0 、 f c 。

[0076] The selected freeze - thaw states were the initial melting period (melting depths of 15, 35, and 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: Table 2 Parameters during the full melting period f 0 、 f c 、 k value fitting results

[0077] During the above - mentioned fitting process, the initial infiltration rate f 0 and the stable infiltration rate f c in the Horton formula were obtained through curve fitting. The initial infiltration rate f 0 and the stable infiltration rate f c in the Horton - RCCC formula were obtained from Equations 4 and 5. Among them, the soil bulk density , and the vegetation coverage rate FVC = 0.3. Therefore, the initial infiltration rate f 0 = 5.535 and the stable infiltration rate f c = 0.516. It is similar to the fitting results of the Horton formula: the initial infiltration rate f 0 = 5.974 and the stable infiltration rate f c = 0.523. Therefore, under the flat slope state, the Horton - RCCC formula has good applicability during the full melting period. The fitting accuracy R² of the Horton formula before improvement was 0.979, and the accuracy of the Horton - RCCC formula was 0.976. It can be seen that the accuracies are quite comparable.

[0078] Example 3: Using the flat slope and 10° slope of Fenghuoshan (obtained according to Equation 8 )The rationality of the slope influence coefficient is tested with the data from the rainfall runoff simulation experiment. 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 experiment are the fully melted period. Therefore, the parameters used to calculate the runoff of Fenghuoshan f 0 、 f c 、 k can refer to the single-ring infiltration experiment, that is, Figure 2 the fitting results.

[0079] 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 experiment is relatively large, the actual f 0 is less than the fitting result of the single-ring infiltration experiment. Therefore, f 0 is selected as the calibration object. The rainfall runoff data under the flat slope condition is used to calibrate f 0 , and the calibrated model is used to calculate the runoff of the 10° slope to verify the rationality of the slope influence coefficient through comparison.

[0080] Table 3 shows the infiltration and runoff parameters of the Horton formula and the Horton-RCCC formula during the fully melted period.

[0081] Table 3 Information table for surface runoff calculation at different slopes

[0082] Among them, is the rainfall intensity, P is the precipitation, R 1 is the measured surface runoff result of the slope rainfall runoff simulation experiment, R is the calculation method in the basin runoff calculation model based on the Horton curve, that is, Equations 15-16 below, and the calculated surface runoff result.

[0083]

[0084] Among them, t r represents the rainfall duration; t a represents the moment when surface runoff occurs.

[0085] Under the flat slope condition, the runoff volume for 15 mm of precipitation is 1.667 mm, and the f c of the Horton formula is 0.523 mm / min, kis 0.306, calibrated according to Equation 15 - 16 f 0 is 2.272 mm / min. For the Horton—RCCC formula f c is 0.516 mm / min, k is 0.279. Similarly, the calibration result of the Horton—RCCC formula f 0 is 2.157 mm / min. Using the calibrated f 0 respectively calculate the runoff of the 10° slope surface, and 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 will be modified according to Equation 11 respectively to and Substitute into the calculation.

[0086] 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.

[0087] During the entire initial melting (freezing) period, the Horton formula can only use the infiltration parameters at a single moment and a single position to simulate the basin infiltration during the entire melting or freezing process, without reflecting the dynamic change of the underlying surface infiltration conditions caused by the freeze-thaw process. The Horton—RCCC formula solves this problem well with the melting (freezing) depth as a parameter.

[0088] Figure 5 、 6 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.

[0089] Table 4 Fitting Results of the Horton Model

[0090] Table 5 Fitting Results of the Horton-RCCC Model

[0091] To better present the variation form of the soil infiltration process with the freeze-thaw depth and make a comparative analysis more in line with the actual situation, the day sequence number is used instead of the freeze-thaw depth. To simplify the calculation, the depth of daily melting / freezing 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.

[0092] Table 6 Comparison table of freeze-thaw state - day sequence number

[0093] The fitted 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 Horton-RCCC formula has certain differences in the infiltration process during different time periods of the freeze-thaw process, manifested as follows: the infiltration capacity changes significantly with the increase of the melting depth within the first ten days, and then the infiltration capacity converges to the complete melting period from the 10th day to the 35th day. After the 55th day, it enters the initial freezing period, 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.

[0094] 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 soil infiltration rate calculation method suitable for freeze-thaw environment in cold regions, characterized in that: According to 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 soil infiltration rate is calculated using the following infiltration equations: Initial melting period: ; Complete melting period: ; Initial freeze period: ; Complete freeze period: ; In the formula, f p for t The maximum infiltration rate at time f 0 is the initial infiltration rate, f c To stabilize the infiltration rate; h m is the melting depth, is the maximum freezing depth of the active layer; To freeze the parameters, is the melting parameter, t For time, k is the attenuation coefficient; h v is the freezing depth; is the slope influence coefficient, which is calculated as follows: taking the infiltration of the flat slope as the reference value, the ratio of the infiltration of other slopes to the infiltration of the flat slope.

2. The soil infiltration rate calculation method suitable for freeze-thaw environment in cold regions according to claim 1 is characterized in that: The calculation formula of slope influence coefficient of soil with different properties is: Sandy soil: ; Thin layer of soil: ; Black soil: ; in, i For the slope.

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

4. The soil infiltration rate calculation method suitable for freeze-thaw environment in cold regions according to claim 3 is characterized in that: The method for obtaining the freezing parameter, melting parameter and attenuation coefficient is as follows: if there is historical infiltration test data for the watershed 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 stable infiltration rate according to formula (8) and (9), and then substitute them together with the infiltration test data into the infiltration equation of the corresponding period to obtain the fitting result.

5. The soil infiltration rate calculation method suitable for freeze-thaw environment in cold regions according to claim 3 is characterized in that: If there is no infiltration test data in the watershed to be studied, the freezing parameter, melting parameter and attenuation coefficient are calibrated according to the historical rainfall and runoff data of the watershed. The method is as follows: according to the soil bulk density and vegetation coverage of the watershed to be studied, the initial infiltration rate and stable infiltration rate are calculated using formulas (8) and (9), and the slope influence coefficient is calculated according to formulas (5), (6) or (7); Initial melting period f 0 Corrected to , f c Corrected to Complete melting period f 0 Corrected to , f c Corrected to ; Initial freeze period f 0 Corrected to , f c Corrected to ;Substitute the melting depth of the initial melting period of the study basin into h m , initial freezing period melting depth h v , Maximum freezing depth of active layer Value; the corrected f 0 , f c The corresponding rainfall intensity and runoff data of different periods are substituted into the basin runoff calculation model for fitting to obtain the values ​​of freezing parameter, melting parameter and attenuation coefficient; When there is a lot of rainfall data, the set of data with the highest runoff fitting accuracy is taken as the parameter calibration result through iterative calculation.

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