Method for calculating negative temperature soil water infiltration and monitoring device

Abstract

This invention relates to the field of hydrological monitoring technology, specifically to a method and monitoring device for calculating soil moisture infiltration at sub-zero temperatures. The method includes: acquiring rainfall intensity and soil temperature of the area to be measured; determining the freeze-thaw state of the soil in the area based on the soil temperature; when the soil is determined to be in a frozen state, calculating the actual unfrozen soil moisture content, actual saturated soil moisture content, actual soil water potential, and actual soil permeability coefficient of the area to be measured; the formula for calculating the soil permeability coefficient is constructed based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature; when the rainfall intensity is less than or equal to the actual soil permeability coefficient, the cumulative soil moisture infiltration is equal to the product of rainfall intensity and time; when the rainfall intensity is greater than the actual soil permeability coefficient, calculating the cumulative soil moisture infiltration based on the actual soil permeability coefficient, time, the difference between the actual saturated soil moisture content and the actual unfrozen soil moisture content, and the actual soil water potential.

Description

Technical Field

[0001] This invention relates to the field of hydrological monitoring technology, specifically to a method for calculating and a monitoring device for soil moisture infiltration at sub-zero temperatures. Background Technology

[0002] In high-altitude and cold regions, soils are constantly exposed to sub-zero temperatures or freeze-thaw cycles. The water infiltration process exhibits significant nonlinear characteristics due to the formation of ice crystals within the pores and the dynamic changes in unfrozen water. Accurately calculating the water infiltration rate in sub-zero temperature soils is fundamental for hydrological simulation and water resource allocation in cold regions.

[0003] Currently, soil moisture infiltration calculations mainly rely on classical methods. Model or Equations. This type of model assumes a stable soil pore structure and that water exists in a continuous liquid state, without considering the blocking effect of ice on pores at sub-zero temperatures or the temperature dependence of unfrozen water content.

[0004] While some studies have incorporated ice content to correct for saturated water content in related schemes, the determination of the permeability coefficient still relies on macroscopic empirical parameters, making it difficult to reflect the physical mechanisms of water transport at sub-zero temperatures. Furthermore, traditional infiltration models require iterative solutions, resulting in low computational efficiency, and lack integration with real-time monitoring data, making it difficult to meet the continuous monitoring needs of high-altitude and cold regions. Summary of the Invention

[0005] This invention provides a method and device for calculating soil moisture infiltration at sub-zero temperatures, in order to solve the problems of low accuracy in calculating soil moisture infiltration under sub-zero conditions and difficulty in real-time monitoring.

[0006] The first aspect of this invention provides a method for calculating soil moisture infiltration at sub-zero temperatures, comprising: acquiring rainfall intensity and soil temperature of the area to be tested; determining the freeze-thaw state of the soil in the area to be tested based on the soil temperature; when the state is determined to be frozen, calculating the actual unfrozen soil moisture content, actual saturated soil moisture content, actual soil water potential, and actual soil permeability coefficient of the area to be tested based on calculation formulas for unfrozen soil moisture content, saturated soil moisture content, soil water potential, and soil permeability coefficient; wherein the calculation formula for soil permeability coefficient is constructed based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature; when the rainfall intensity is less than or equal to the actual soil permeability coefficient, the cumulative soil moisture infiltration is equal to the product of the rainfall intensity and time; when the rainfall intensity is greater than the actual soil permeability coefficient, calculating the cumulative soil moisture infiltration based on the actual soil permeability coefficient, time, the difference between the actual saturated soil moisture content and the actual unfrozen soil moisture content, and the actual soil water potential.

[0007] Optionally, when the rainfall intensity is less than or equal to the actual soil permeability coefficient, the formula for calculating the cumulative soil moisture infiltration F(t) is:

[0008] When the rainfall intensity is greater than the actual soil permeability coefficient, the formula for calculating the cumulative soil moisture infiltration F(t) is as follows:

[0009] Where R is the rainfall intensity, K is the actual soil permeability coefficient, and t is time. This refers to the saturated water content of the soil at sub-zero temperatures. This refers to the unfrozen soil moisture content at sub-zero temperatures. This represents the actual soil water potential.

[0010] Optionally, the formula for calculating the actual unfrozen soil moisture content is:

[0011] in, This refers to the unfrozen soil moisture content at sub-zero temperatures. denoted as residual soil moisture content, a and N are fitting parameters, and T is soil temperature.

[0012] Optionally, the formula for calculating the actual soil saturated water content is:

[0013] in, This refers to the saturated water content of the soil at sub-zero temperatures. This represents the saturated soil moisture content at 0℃. This refers to the unfrozen soil moisture content at 0℃. This refers to the unfrozen soil moisture content at sub-zero temperatures. This represents the volume ratio of ice to water.

[0014] Optionally, the formula for calculating the actual soil water potential is:

[0015] in, This represents the actual soil water potential. This refers to the saturated water content of the soil at sub-zero temperatures. This refers to the unfrozen soil moisture content at sub-zero temperatures. denoted as residual soil moisture content, and α and β are fitting parameters.

[0016] Optionally, the formula for calculating the actual soil permeability coefficient K is:

[0017] Where K is the actual soil permeability coefficient. Let ρ be the density of supercooled water, g be the acceleration due to gravity, D be the capillary fractal dimension, and n be the porosity, which is the saturated water content of the soil at sub-zero temperatures. τ is the maximum pore diameter as a function of temperature, μ is the dynamic viscosity of the subcooled water, and τ is the tortuosity.

[0018] Optionally, the formula for calculating the dynamic viscosity μ of the subcooled water is:

[0019] The density of the supercooled water The calculation formula is:

[0020] Where T represents soil temperature.

[0021] Optionally, the temperature-related maximum pore diameter The calculation formula is:

[0022] in, For the free energy of ice water, This is the freezing point of water. To melt latent heat, Where is the density of ice, and T is the soil temperature, both in K.

[0023] Optionally, the formulas for calculating the tortuosity τ and the capillary fractal dimension D are as follows:

[0024]

[0025] Where n is the porosity and its value is the soil saturation water content at negative temperatures. Minimum pore diameter, This represents the maximum pore diameter in relation to temperature.

[0026] A second aspect of the present invention provides a monitoring device for soil moisture infiltration at negative temperatures, comprising: a calculation module for executing the calculation method for soil moisture infiltration at negative temperatures as described in any of the preceding claims; a rainfall intensity monitoring module connected to the calculation module for acquiring the rainfall intensity of the area to be measured; and a soil temperature monitoring module connected to the calculation module for acquiring the soil temperature of the area to be measured.

[0027] Beneficial effects: This invention employs a model based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature in the calculation of soil permeability coefficient, replacing the traditional empirical parameter correction method. This model can describe the impact of negative temperatures on permeability from two perspectives: the fractal characteristics of pore structure and the changes in fluid properties with temperature. This helps improve the rationality of permeability coefficient calculations and reduces reliance on empirical fitting.

[0028] This invention calculates cumulative infiltration using a piecewise explicit analytical formula based on the relationship between rainfall intensity and permeability coefficient. When the rainfall intensity does not exceed the permeability coefficient, the calculation is directly based on the rainfall amount; when it exceeds the permeability coefficient, the solution is obtained directly through a closed analytical expression without iteration. This scheme ensures the rationality of infiltration calculation under sub-zero temperatures while reducing computational complexity, facilitating real-time operation in embedded devices.

[0029] This invention integrates the aforementioned calculation method with a rainfall intensity monitoring module and a soil temperature monitoring module into a unified monitoring device. This device can automatically acquire field data and output infiltration calculation results in real time. Compared to traditional methods relying on manual observation or offline calculation, this device facilitates continuous monitoring of soil moisture infiltration processes at sub-zero temperatures, providing data support for hydrological simulation and early warning in cold regions. Attached Figure Description

[0030] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0031] Figure 1 A flowchart of a method for calculating soil moisture infiltration at negative temperatures provided in an embodiment of the present invention; Figure 2 A comparison chart of the traditional infiltration simulation curve at -0.1℃, the negative temperature infiltration simulation curve, and the measured values ​​provided in the embodiments of the present invention; Figure 3 A comparison chart of the traditional infiltration simulation curve, the negative temperature infiltration simulation curve, and the measured values ​​at -0.2℃ provided in the embodiments of the present invention; Figure 4 A graph showing the change of soil permeability coefficient with temperature, provided for an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of the negative temperature soil moisture infiltration monitoring device provided in an embodiment of the present invention.

[0032] Explanation of reference numerals in the attached figures: 1. Rainfall intensity monitoring module; 2. Soil temperature monitoring module; 3. Buttons; 4. Electrical control box; 5. Display. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] The first aspect of this invention provides a method for calculating the infiltration of soil moisture at negative temperatures, comprising: Obtain rainfall intensity and soil temperature in the area to be tested; Determine the freeze-thaw state of the soil in the test area based on soil temperature; When the soil is determined to be in a frozen state, the actual soil unfrozen moisture content, actual soil saturated moisture content, actual soil water potential, and actual soil permeability coefficient of the area to be tested are calculated based on the calculation formulas for soil unfrozen moisture content, soil saturated moisture content, soil water potential, and actual soil permeability coefficient. The formula for calculating the soil permeability coefficient is based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature. When the rainfall intensity is less than or equal to the actual soil permeability coefficient, the cumulative soil moisture infiltration is equal to the product of the rainfall intensity and the time. When the rainfall intensity is greater than the actual soil permeability coefficient, the cumulative soil moisture infiltration is calculated based on the actual soil permeability coefficient, time, the difference between the actual soil saturated moisture content and the actual unfrozen soil moisture content, and the actual soil water potential.

[0035] This invention employs a model based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature in the calculation of soil permeability coefficient, replacing the traditional empirical parameter correction method. This model can describe the impact of negative temperatures on permeability from two perspectives: the fractal characteristics of pore structure and the changes in fluid properties with temperature. This helps improve the rationality of permeability coefficient calculations and reduces reliance on empirical fitting.

[0036] This invention calculates cumulative infiltration using a piecewise explicit analytical formula based on the relationship between rainfall intensity and permeability coefficient. When the rainfall intensity does not exceed the permeability coefficient, the calculation is directly based on the rainfall amount; when it exceeds the permeability coefficient, the solution is obtained directly through a closed analytical expression without iteration. This scheme ensures the rationality of infiltration calculation under sub-zero temperatures while reducing computational complexity, facilitating real-time operation in embedded devices.

[0037] This invention integrates the aforementioned calculation method with rainfall intensity monitoring module 1 and soil temperature monitoring module 2 into a unified monitoring device, which can automatically acquire field data and output infiltration calculation results in real time. Compared with traditional methods that rely on manual observation or offline calculation, this device helps to achieve continuous monitoring of soil moisture infiltration process in sub-zero temperatures, providing data support for hydrological simulation and early warning in cold regions.

[0038] Reference Figure 1 As shown, the method for calculating soil moisture infiltration at negative temperatures according to the present invention specifically includes the following steps: Step S101: Obtain the rainfall intensity and soil temperature of the area to be tested.

[0039] Step S102: Determine the freeze-thaw state of the soil in the area to be tested based on the soil temperature.

[0040] Step S103: When the area is determined to be frozen, calculate the soil infiltration parameters of the area to be tested.

[0041] The calculation of various soil infiltration parameters in the test area specifically includes: calculating the actual unfrozen soil moisture content, actual saturated soil moisture content, actual soil water potential, and actual soil permeability coefficient. The formula for calculating the soil permeability coefficient is based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature.

[0042] Step S104: Determine whether the rainfall intensity is greater than the actual soil permeability coefficient.

[0043] If not, proceed to step S105a; if yes, proceed to step S105b.

[0044] Step S105a: The cumulative soil moisture infiltration is equal to the product of rainfall intensity and time.

[0045] Step S105b: Calculate the cumulative soil moisture infiltration.

[0046] The calculation of cumulative soil moisture infiltration includes: calculating the cumulative soil moisture infiltration based on the actual soil permeability coefficient, time, the difference between the actual soil saturated moisture content and the actual unfrozen soil moisture content, and the actual soil water potential.

[0047] In one alternative implementation, a sandy loam slope on the edge of the permafrost region of the Qinghai-Tibet Plateau is selected as the area to be tested, and the rainfall intensity and soil temperature of the area are first obtained.

[0048] Rainfall intensity is acquired in real time, with a pulse signal generated for every 0.1 mm of accumulated rainfall. This signal is transmitted to the computing module via wired or wireless means. Soil temperature is measured at three depths below the surface: 5 cm, 10 cm, and 20 cm, with a measurement accuracy of ±0.1℃. Samples are taken every 10 minutes. The measurement points are protected with stainless steel and waterproofed to withstand the freeze-thaw environment of high-altitude and cold regions.

[0049] Freeze-thaw conditions are determined based on soil temperature: when the temperature measured at a depth of 10cm is below 0℃, the area is considered frozen; if the temperature is 0℃ or above, it is considered thawed. When the area is determined to be frozen, the actual unfrozen soil moisture content, actual saturated soil moisture content, actual soil water potential, and actual soil permeability coefficient of the tested area are calculated using the formulas for calculating unfrozen soil moisture content, saturated soil moisture content, soil water potential, and actual soil permeability coefficient.

[0050] The formula for calculating the soil permeability coefficient is based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature. After obtaining the actual soil permeability coefficient, it is compared with the rainfall intensity.

[0051] When the rainfall intensity is less than or equal to the actual soil permeability coefficient, the cumulative soil moisture infiltration is equal to the product of the rainfall intensity and the time. When the rainfall intensity is greater than the actual soil permeability coefficient, the cumulative soil moisture infiltration is calculated based on the actual soil permeability coefficient, the time, the difference between the actual soil saturated moisture content and the actual unfrozen soil moisture content, and the actual soil water potential.

[0052] This approach first obtains rainfall intensity and soil temperature to determine the freeze-thaw state, then initiates subsequent calculations only under frozen conditions, avoiding unnecessary calculations under non-frozen conditions. This method limits infiltration calculations to actual freezing conditions, helping to reduce the waste of computational resources while ensuring that the specific infiltration calculation formula is only used under sub-zero temperature conditions.

[0053] In some implementations, when the rainfall intensity is less than or equal to the actual soil permeability coefficient, the formula for calculating the cumulative soil moisture infiltration F(t) is as follows:

[0054] When the rainfall intensity is greater than the actual soil permeability coefficient, the formula for calculating the cumulative soil moisture infiltration F(t) is:

[0055] Where F(t) is the cumulative soil moisture infiltration at time t (mm), R is the rainfall intensity (mm / h), K is the actual soil permeability coefficient (mm / d), and t is the time (h). Soil saturation water content at sub-zero temperatures ( ), The unfrozen soil moisture content at sub-zero temperatures ( ), The actual soil water potential is shown in mm.

[0056] Specifically, in the above formula, the unit of rainfall intensity R is mm / h, the unit of time t is h, and the unit of actual soil permeability coefficient K, calculated using the aforementioned fractal formula, is mm / d. When substituting these values ​​into the infiltration formula, the unit of K needs to be converted from mm / d to mm / h, i.e., divided by 24. The experimental verifications below and the data in Table 1 have all been calculated using this conversion relationship and with standardized units.

[0057] To verify the accuracy of this formula, two negative temperature conditions, -0.1℃ and -0.2℃, were set in sandy loam soil, with initial moisture contents of 0.16 cm³ / cm³ and 0.12 cm³ / cm³, respectively, and saturated moisture contents at 0℃ of 0.23 cm³ / cm³ and 0.19 cm³ / cm³, respectively. Surface water was accumulated using rainfall intensity exceeding the soil infiltration capacity, and measured values ​​were obtained through a double-ring infiltration test. The results calculated by this formula were then compared with traditional methods. The improved formula was compared.

[0058] Table 1 - Formula for infiltration at negative temperatures of 0.1℃ and traditional methods Comparison of calculation results of the improved formula

[0059] Table 2 - Formula for infiltration at negative temperatures of 0.2℃ and traditional methods Comparison of calculation results of the improved formula

[0060] The above data are based on the following experimental conditions: soil type: sandy loam; soil temperatures: -0.1℃ and -0.2℃; initial soil moisture content: 0.16 cm³ / cm³ and 0.12 cm³ / cm³; saturated soil moisture content: 0.23 cm³ / cm³ and 0.19 cm³ / cm³; and rainfall intensity exceeding soil infiltration capacity leading to surface water accumulation was used for simulation. Traditional comparative methods were selected. The improved formula for the model is in the form of:

[0061] The measured values ​​were obtained through a field double-ring infiltration test under waterlogged conditions.

[0062] The comparison results are shown in Table 1 and Table 2. Figure 2 and Figure 3 As shown. Figure 2This compares the changes in the simulated infiltration curves at -0.1℃ and negative temperature infiltration curves over infiltration time. Figure 3 A comparison of the changes in infiltration simulation curves at -0.2℃ and negative temperature infiltration simulation curves with infiltration time is shown. It can be seen that the error of the traditional formula increases rapidly with infiltration time, while the error of the formula of this invention is always controlled within a small range.

[0063] Specifically, at -0.1℃, the deviation between the simulated value and the measured value of the traditional formula continued to widen as the infiltration time increased, and the error exceeded 900% at 226 minutes; at -0.2℃, the error of the traditional formula increased even more significantly, reaching a maximum of more than 1300%.

[0064] In contrast, the formula of this invention maintains an error of less than 4% between the simulated and measured values ​​at each time point under both temperature conditions.

[0065] In the initial stage of infiltration (the first 30 minutes), the error difference between the two formulas is not very obvious. However, as the infiltration time increases, the cumulative error of the traditional formula increases rapidly. The formula of this invention, because it introduces the permeability coefficient based on fractal theory and the temperature-dependent physical property parameters of supercooled water in the calculation process, can more accurately reflect the actual impact of ice crystal blockage of pores on the infiltration process at negative temperatures. Therefore, its simulated value and measured value always maintain good consistency.

[0066] The above comparison results show that the method for calculating soil moisture infiltration at sub-zero temperatures proposed in this invention has higher calculation accuracy under sub-zero conditions. The piecewise explicit analytical formula used in this invention does not require iterative solutions, the calculation steps are simple, and it is suitable for real-time operation in low-power embedded devices. Furthermore, since the formula directly incorporates the actual soil permeability coefficient, the difference between saturated and unfrozen water content at sub-zero temperatures, and soil water potential, it can reflect the comprehensive influence of ice relative on the infiltration process under sub-zero conditions. Therefore, the calculated cumulative infiltration is closer to the measured value.

[0067] In one alternative implementation, the formula for calculating the actual unfrozen soil moisture content is:

[0068] in, The unfrozen soil moisture content at sub-zero temperatures ( ), Soil residual moisture content ( ), where a and N are the fitting parameters, and T is the soil temperature (°C). The above fitting parameters a, N, and residual water content... The test should be conducted using an indoor low-temperature freezing experiment on the soil to be tested.

[0069] Specifically, undisturbed soil samples were tested for unfrozen water content at different sub-zero temperatures in a temperature-controlled low-temperature chamber. The liquid water content was measured using time-domain reflectometry or nuclear magnetic resonance (NMR). The obtained data were then fitted using the formula described above to obtain a, N, and... .

[0070] These parameters differ for different types of soil (such as sandy soil, loam, and clay), so actual measurements should be taken for the specific area to be measured to ensure the accuracy of the calculation.

[0071] This formula allows for the direct calculation of unfrozen water content at sub-zero temperatures based on measured soil temperature. The formula is simple in form, requires few parameters, and can be quickly retrieved from monitoring equipment, providing fundamental data for subsequent calculations of soil saturation water content, soil water potential, and permeability coefficient.

[0072] It should be noted that the above fitting parameters a, N, And the α, β, and α involved in subsequent formulas , All parameters must be obtained through field measurements of the soil in the test area. For a specific test area, the above parameters only need to be measured once through indoor experiments during the initial application, and can then be directly used for subsequent calculations in that area. If the test area is changed or the soil type changes significantly, resampling and corresponding measurements are required. Soil residual moisture content It can be obtained by extrapolation from the soil moisture characteristic curve.

[0073] In some implementation methods, the formula for calculating the actual soil saturation water content is:

[0074] in, Soil saturation water content at sub-zero temperatures ( ), Soil saturation water content at 0℃ ), The unfrozen soil moisture content at 0℃ ( ), The unfrozen soil moisture content at sub-zero temperatures ( ), that is, the initial total water content of the soil before it freezes ( ), The volume ratio of ice to water is taken as 1.09.

[0075] and Indoor experiments were conducted to determine the saturated water content of soil samples prepared from the test soil and saturated under constant temperature conditions of 0℃. Meanwhile, its initial volumetric water content was measured in the unfrozen state as... It should be noted that, It is related to the initial moisture content of the soil. In practical applications, the value should be determined based on the actual initial moisture content of the area to be tested.

[0076] This formula can quantitatively describe the extent to which ice crystals occupy pore space, leading to a decrease in saturated water content, at sub-zero temperatures. Based on the relationship between the ice-to-water volume ratio and the unfrozen water content, the formula incorporates the direct impact of ice phase change on pore structure, avoiding the common practice of simply approximating the saturated water content at sub-zero temperatures to the value at 0°C.

[0077] In one alternative implementation, the formula for calculating the actual soil water potential is:

[0078] in, The actual soil water potential is shown in mm. Soil saturation water content at sub-zero temperatures ( ), The unfrozen soil moisture content at sub-zero temperatures ( ), Soil residual moisture content ( ), where α and β are fitting parameters, determined through soil moisture characteristic curve experiments.

[0079] α and β can be determined through soil moisture characteristic curve experiments: under positive temperature conditions, soil moisture content at different matrix potentials is measured using a pressure membrane apparatus or centrifuge method, and α and β are obtained by fitting the data. For negative temperature conditions, this formula assumes that the relationship between unfrozen water content and matrix potential remains in the same functional form, only replacing the saturated water content with the value under negative temperature conditions. .

[0080] This formula establishes a quantitative relationship between the unfrozen water content and soil water potential at sub-zero temperatures. Soil water potential is a key parameter for determining the direction and rate of water transport; incorporating it into the infiltration calculation formula helps improve the accuracy of infiltration calculations under sub-zero conditions.

[0081] Alternatively, the formula for calculating the actual soil permeability coefficient K is:

[0082] Where K is the actual soil permeability coefficient (unit: mm / d). Where is the density of supercooled water (kg / m³), g is the acceleration due to gravity (taken as 9.8 N / kg), D is the capillary fractal dimension, and n is the porosity, which is taken as the saturated water content of the soil at sub-zero temperatures. τ is the temperature-dependent maximum pore diameter (nm), μ is the dynamic viscosity of the subcooled water (Pa·s), and τ is the tortuosity.

[0083] Among the above sub-parameters, , , To be calculated according to the formulas in the subsequent embodiments, D and τ are calculated according to the above formulas.

[0084] This formula treats soil pores as curved capillary bundles with fractal characteristics, and fully considers the combined effects of ice crystal blockage of pores at sub-zero temperatures and changes in the physical properties of supercooled water on permeability.

[0085] In this formula, the capillary fractal dimension D is used to describe the fractal characteristics of soil pore size distribution, the tortuosity τ reflects the ratio of the actual flow path length of the pore channel to the straight-line distance, and the maximum pore diameter... Temperature-dependent, representing the maximum pore size that allows unfrozen water to flow at a given sub-zero temperature. These parameters collectively determine the soil's permeability at sub-zero temperatures.

[0086] When calculating the actual soil permeability coefficient K, the sub-parameters can be calculated in the following order: First, calculate the dynamic viscosity μ of the supercooled water based on the soil temperature T, and then calculate the density of the supercooled water. Then calculate the temperature-dependent maximum pore diameter. Based on this, the calculated soil saturation water content at sub-zero temperatures was used. Then, calculate the tortuosity τ and capillary fractal dimension D in sequence. Substitute these sub-parameters into the main formula for permeability coefficient to obtain the actual soil permeability coefficient K.

[0087] Compared to traditional empirical correction methods, this formula calculates the permeability coefficient based on the fractal characteristics of pore structure and the physical mechanism of temperature-dependent changes in the properties of supercooled water, without relying on empirical parameter fitting for specific soil types. Even when soil type or temperature conditions change, this formula can still perform reasonable calculations based on measured temperatures, making it widely applicable.

[0088] Specifically, the formula for calculating the dynamic viscosity μ of subcooled water is:

[0089] Density of supercooled water The calculation formula is:

[0090] Where T represents soil temperature in Kelvin. The above formula was obtained by fitting supercooled water property data.

[0091] The above formula was obtained through nonlinear fitting of a large amount of experimental data on the physical properties of supercooled water, and it has high accuracy in the range of -40℃ to 0℃. In practical applications, the soil temperature (expressed in Kelvin) of the area to be tested can be substituted into the above formula to calculate μ and . .

[0092] The above two formulas can be used to obtain the viscosity and density of supercooled water under different sub-zero temperatures. These two parameters directly participate in the calculation of the main formula for the permeability coefficient, and their accuracy affects the final calculation result. The above formulas are simple in form and easy to use in real time in monitoring equipment.

[0093] Figure 4 The diagram shows the change of soil permeability coefficient in different test areas as temperature decreases, and the trend of the curve is consistent with the calculation results of the above formula.

[0094] Furthermore, the maximum pore diameter related to temperature The calculation formula is:

[0095] in, For the free energy of ice water, This is the freezing point of water. To melt latent heat, Let be the density of ice, and T be the soil temperature. The values ​​for each parameter are: = , =273.15K, = , = .

[0096] This formula is derived based on the balance of free energy and latent heat at the ice-water interface. Its physical meaning is: given a supercooling ΔT = - The critical pore diameter at temperature T that allows the pore to remain unfrozen. When the pore diameter is greater than... At this time, ice crystals will preferentially form in the pores and block the channels, thereby reducing the permeability. Substituting the measured soil temperature (expressed in Kelvin) into the above formula, we can obtain the temperature at the current temperature. .

[0097] It should be noted that the minimum pore diameter in the above formula... The diameter of a water molecule is taken as 0.4 nm. This value is the dynamic diameter of a water molecule and is used in related fields as an approximation of the minimum pore size that liquid water can exist in.

[0098] This formula can quantitatively describe the effect of temperature on the effective pore diameter. Under negative temperature conditions, only pores with a diameter smaller than [a certain value] can be effectively poreed. The pores can still maintain unfrozen water channels, with a diameter greater than The pores are blocked by ice crystals. Introducing this physical mechanism into the calculation of the permeability coefficient helps to make the calculation results closer to reality.

[0099] Furthermore, the formula for calculating the tortuosity τ is:

[0100] Where n is the porosity and its value is the soil saturation water content at negative temperatures. .

[0101] This formula is based on the empirical statistical relationship between the tortuosity and porosity of porous media. When the porosity decreases, the tortuosity increases, reflecting the increased curvature of the flow path after ice blocks the pores.

[0102] The formula for calculating the capillary fractal dimension D is:

[0103] in, To determine the minimum pore diameter, the diameter of a water molecule is taken as 0.4 nm. This represents the maximum pore diameter in relation to temperature.

[0104] The D value is between 1 and 2, with a value closer to 2 indicating a more uniform pore size distribution. In practical applications, the calculated value obtained above... Substitute n, and and Substitute these values ​​into the equation to calculate τ and D, then substitute them back into the main formula for the permeability coefficient.

[0105] Tortuosity reflects the degree of curvature of pore channels, while capillary fractal dimension reflects the distribution characteristics of pore size; both are important parameters describing soil pore structure. Using the above formulas, a quantitative relationship can be established between porosity, tortuosity, and fractal dimension, allowing the fractal parameters required in the main formula for permeability coefficient to be directly calculated from measured porosity.

[0106] A second aspect of the present invention also provides a monitoring device for soil moisture infiltration at negative temperatures. The device is used to automatically acquire on-site rainfall intensity and soil temperature data, and execute the above-mentioned calculation method in real time to output the infiltration result.

[0107] Reference Figure 5 As shown, Figure 5 This is a schematic diagram of a specific structure of the monitoring device provided by the present invention. Specifically, the device includes a calculation module, a rainfall intensity monitoring module 1, a soil temperature monitoring module 2, a storage medium, and a display 5.

[0108] Rainfall intensity monitoring module 1 is electrically connected to the calculation module to acquire rainfall intensity data of the area to be measured; soil temperature monitoring module 2 is connected to the calculation module to acquire soil temperature data of the area to be measured; storage medium is connected to the calculation module to store the acquired rainfall intensity data, soil temperature data, and calculated soil moisture infiltration data; display 5 is connected to the calculation module to display the monitoring data and calculation results in real time; the calculation module is used to execute the calculation method for negative temperature soil moisture infiltration of any of the above-mentioned methods.

[0109] Specifically, the calculation module can use a low-power microcontroller with the program code for all the above calculation formulas embedded inside. The microcontroller can be equipped with a real-time clock to control the sampling interval.

[0110] In practical applications, the rainfall intensity monitoring module 1 can use a tipping bucket rain gauge. The rain gauge is installed in an open, unobstructed outdoor location with the rain collection port 0.7m above the ground. It outputs a pulse signal for every 0.1mm of rainfall collected. This pulse signal is isolated and then input to the interrupt pin of the microcontroller. The microcontroller counts the number of pulses within the sampling period and calculates the rainfall intensity.

[0111] In practical applications, the soil temperature monitoring module 2 can use a ground thermometer, such as a platinum resistance temperature sensor or a digital temperature sensor, which is vertically buried in the soil of the area to be measured. The pre-buried depth can be from 0cm to 50cm, for example, buried at depths of 5cm, 10cm, and 20cm below the surface. The ground thermometer shell is made of stainless steel and is waterproof and sealed to prevent water from seeping in and damaging the sensor due to freeze-thaw cycles. The measurement accuracy is ±0.1℃. The microcontroller reads the temperature values ​​at each depth sequentially through a single bus, using the temperature at a depth of 10cm as the basis for determining the freeze-thaw state.

[0112] The storage medium can be a built-in flash memory chip or an external memory card. The display 5 can be an LCD screen, mounted on the panel of the waterproof electrical control box 4 or led out via an extension cable.

[0113] The computing module and each monitoring module can be connected via a shielded cable or via low-power wireless transmission.

[0114] The power supply can be provided by using solar panels in conjunction with batteries to ensure long-term operation in high-altitude and cold regions where there is no mains power.

[0115] The computing module, battery, storage medium, and display 5 are all housed within a waterproof electrical control box 4 with an insulation layer, which is mounted on a column. The electrical control box 4 may be equipped with buttons 3 for inputting various numerical values.

[0116] The rain gauge, ground thermometer, and electrical control box 4 all have waterproof and dustproof casings with a protection rating of no less than IP65 to adapt to long-term outdoor use in high-altitude and cold regions. The ground thermometer is buried vertically and in close contact with the soil, and all external cables are protected by conduits.

[0117] Optionally, the aforementioned monitoring device can also be integrated into a portable device. This portable device includes a data monitor, processor, storage medium, and display. The portable device can be installed entirely within a suitcase or backpack-style housing, facilitating rapid deployment and mobile observation in the field.

[0118] In practical applications, the monitoring device operates as follows: After the device is powered on, the microcontroller initializes the peripherals and enters low-power mode.

[0119] Every certain period of time (e.g., 10 minutes), the real-time clock wakes up the microcontroller. The microcontroller obtains soil temperature and rainfall intensity data at each depth through the data monitor and compares the temperature at a depth of 10cm with 0℃.

[0120] If the temperature is not lower than 0℃, it is determined to be in a thawing state. The time, temperature, and rainfall data are recorded to the storage medium, and the rainfall intensity is directly used as an approximation of the infiltration amount (or the calculation is skipped). If the temperature is lower than 0℃, it is determined to be in a frozen state. The number of rain gauge pulses in this cycle is read, the average rainfall intensity is calculated, and then the processor sequentially calls the subroutines for unfrozen water content, saturated water content, soil water potential, and soil permeability coefficient. Based on the relationship between rainfall intensity and permeability coefficient, the infiltration formula is selected to calculate the cumulative infiltration amount.

[0121] All raw data, intermediate calculation parameters, and final calculation results are stored in the storage medium and can be sent to a remote receiving end via the communication interface, and displayed in real time on display 5. After completing one sampling cycle, the microcontroller enters sleep mode again, waiting for the next cycle.

[0122] The aforementioned device enables long-term automatic monitoring and real-time calculation of the soil moisture infiltration process at sub-zero temperatures, providing data support for hydrological simulation and early warning in cold regions.

[0123] Obviously, the above embodiments are merely examples for clear illustration and are not intended to limit the embodiments. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all embodiments here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for calculating soil moisture infiltration at sub-zero temperatures, characterized in that, include: Obtain rainfall intensity and soil temperature in the area to be tested; The freeze-thaw state of the soil in the test area is determined based on the soil temperature. When the soil is determined to be in a frozen state, the actual soil unfrozen moisture content, actual soil saturated moisture content, actual soil water potential, and actual soil permeability coefficient of the area to be tested are calculated based on the calculation formulas for soil unfrozen moisture content, soil saturated moisture content, soil water potential, and actual soil permeability coefficient. The formula for calculating the soil permeability coefficient is based on fractal theory and the functional relationship between the physical properties of supercooled water and temperature. When the rainfall intensity is less than or equal to the actual soil permeability coefficient, the cumulative soil moisture infiltration is equal to the product of the rainfall intensity and time. When the rainfall intensity is greater than the actual soil permeability coefficient, the cumulative soil moisture infiltration is calculated based on the actual soil permeability coefficient, time, the difference between the actual soil saturated moisture content and the actual soil unfrozen moisture content, and the actual soil water potential.

2. The method for calculating soil moisture infiltration at negative temperatures according to claim 1, characterized in that, When the rainfall intensity is less than or equal to the actual soil permeability coefficient, the formula for calculating the cumulative soil moisture infiltration F(t) is as follows: When the rainfall intensity is greater than the actual soil permeability coefficient, the formula for calculating the cumulative soil moisture infiltration F(t) is as follows: Where R is the rainfall intensity, K is the actual soil permeability coefficient, and t is time. This refers to the saturated water content of the soil at sub-zero temperatures. This refers to the unfrozen soil moisture content at sub-zero temperatures. This represents the actual soil water potential.

3. The method for calculating soil moisture infiltration at negative temperatures according to claim 1, characterized in that, The formula for calculating the actual unfrozen soil moisture content is as follows: in, This refers to the unfrozen soil moisture content at sub-zero temperatures. denoted as residual soil moisture content, a and N are fitting parameters, and T is soil temperature.

4. The method for calculating soil moisture infiltration at negative temperatures according to claim 1, characterized in that, The formula for calculating the actual soil saturated water content is as follows: in, This refers to the saturated water content of the soil at sub-zero temperatures. This represents the saturated soil moisture content at 0℃. This refers to the unfrozen soil moisture content at 0℃. This refers to the unfrozen soil moisture content at sub-zero temperatures. This represents the volume ratio of ice to water.

5. The method for calculating soil moisture infiltration at negative temperatures according to claim 1, characterized in that, The formula for calculating the actual soil water potential is as follows: in, This represents the actual soil water potential. This refers to the saturated water content of the soil at sub-zero temperatures. This refers to the unfrozen soil moisture content at sub-zero temperatures. denoted as residual soil moisture content, and α and β are fitting parameters.

6. The method for calculating soil moisture infiltration at negative temperatures according to claim 1, characterized in that, The formula for calculating the actual soil permeability coefficient K is as follows: Where K is the actual soil permeability coefficient. Let ρ be the density of supercooled water, g be the acceleration due to gravity, D be the capillary fractal dimension, and n be the porosity, which is the saturated water content of the soil at sub-zero temperatures. τ is the maximum pore diameter as a function of temperature, μ is the dynamic viscosity of the subcooled water, and τ is the tortuosity.

7. The method for calculating soil moisture infiltration at negative temperatures according to claim 6, characterized in that, The formula for calculating the dynamic viscosity μ of the subcooled water is: The density of the supercooled water The calculation formula is: Where T represents soil temperature.

8. The method for calculating soil moisture infiltration at negative temperatures according to claim 6, characterized in that, The maximum temperature-related pore diameter The calculation formula is: in, For the free energy of ice water, This is the freezing point of water. To melt latent heat, Where is the density of ice, and T is the soil temperature, both in K.

9. The method for calculating soil moisture infiltration at negative temperatures according to claim 6, characterized in that, The formulas for calculating the tortuosity τ and the capillary fractal dimension D are as follows: Where n is the porosity and its value is the soil saturation water content at negative temperatures. Minimum pore diameter, This represents the maximum pore diameter in relation to temperature.

10. A monitoring device for soil moisture infiltration at sub-zero temperatures, characterized in that, include: The calculation module is used to execute the method for calculating the infiltration of soil moisture in negative temperature conditions as described in any one of claims 1 to 9; A rainfall intensity monitoring module (1) is connected to the calculation module and is used to obtain the rainfall intensity of the area to be measured; The soil temperature monitoring module (2) is connected to the calculation module and is used to obtain the soil temperature of the area to be measured.

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