Method and device for predicting vadose zone water flow flux based on temperature time series

Abstract

The present invention discloses a method and device for predicting the water flux in the vadose zone based on temperature time series, including: setting the initial conditions of the heat transfer model; using the measured temperature time series at two monitoring depths adjacent to the target depth as boundary conditions; obtaining the measured values of the temperature time series and water content time series at the target depth; solving the model by the finite difference method to obtain the predicted values of the temperature time series and water content time series at the target depth; calculating the L2 loss function of the model and determining whether the loss function reaches the minimum value. If so, output the liquid water and gaseous water fluxes; otherwise, use an optimization algorithm to optimize the undetermined parameters of the model and output the optimal liquid water and gaseous water fluxes. The present invention can calculate the soil liquid water and gaseous water fluxes at different depths below the ground surface using the measured temperature time series, which is simple and has high calculation efficiency, providing a new tool for quantitatively evaluating the water flux in the vadose zone.

Description

Technical Field

[0001] The present invention relates to the technical field of groundwater measurement, and particularly relates to a method and device for predicting the water flow flux in the vadose zone based on temperature time series. Background Art

[0002] The temperature tracer method has been widely used in the estimation of groundwater flow flux in the saturated zone. The groundwater hydrothermal coupling model is a commonly used tool for calculating water flow flux using the temperature tracer method. According to different model solving methods, such calculation methods can be divided into analytical calculation methods and numerical model methods. The analytical calculation method is mainly a calculation method developed based on the analytical solution of the one-dimensional groundwater hydrothermal coupling model. The upward water flow flux has the advantages of fast calculation speed and high resolution. The advantage of the analytical solution is that the calculation speed is fast, and the calculation results of water flow flux at multiple point positions can be accurately obtained. However, the analytical solution model has high requirements for boundary conditions and needs to highly generalize the actual field situation, making it difficult to avoid errors between the calculation results and the actual flux, and it is difficult for the analytical calculation method to comprehensively evaluate the groundwater-surface water exchange volume in a large area. Compared with the analytical calculation method, the numerical calculation method is more flexible in terms of boundary conditions and hydrothermal parameters, so it has a wider application in the study of groundwater-surface water interaction in the study area.

[0003] The water flow and heat transfer processes in the unsaturated zone are extremely complex, posing a severe challenge to the application of temperature tracing. Currently, the water flow flux prediction methods based on the temperature tracer method are limited to the saturated zone, and there is little research on the applicability of predicting water flow flux in the unsaturated zone by the temperature tracer method. The research on water and heat transfer in the unsaturated zone mainly focuses on theoretical research fields such as model establishment, soil evaporation, and saturation (water content) calculation. Since the vadose zone hydrothermal coupling model is relatively complex, this type of model generally uses numerical solution methods to solve the model. The numerical solution methods for solving the unsaturated zone hydrothermal coupling model include the finite difference method and the finite element method. The model is written into software such as HYDRUS1D, SUTRA, and VS2DH and applied to simulate the water and heat transfer in the vadose zone.

[0004] However, the existing software that can simulate the water flow flux in the vadose zone is based on a more complex hydrothermal coupling model, and software simulation requires more hydraulic parameters and thermodynamic parameter inputs as well as subsequent cumbersome calibration parameters. The applicability of software simulation is limited, and there are situations where the simulation effect is not ideal. Summary of the Invention

[0005] In view of this, the present invention proposes a new method for predicting one-dimensional vertical water flux based on the soil temperature profile. This method uses a finite difference numerical format, and by solving the heat transfer equation in the vadose zone and combining a parameter optimization algorithm, the prediction of soil water flow flux is achieved.

[0006] The technical solution adopted by the present invention is as follows: A method for predicting the water flux in the vadose zone based on temperature time series, comprising the following steps:

[0007] Set the initial conditions of the heat transfer model;

[0008] For a given target depth B, use the measured temperature time series T A 、T C at two adjacent monitoring depths A and C as the boundary conditions of the heat transfer model;

[0009] Obtain the measured values of the temperature time series and the water content time series at the target depth;

[0010] Based on the boundary conditions and the initial conditions, solve the heat transfer model by the finite difference method to obtain the predicted value of the temperature time series at the target depth;

[0011] Obtain the predicted value of the water content at the target depth based on the empirical equation;

[0012] Based on the predicted values and the measured values of the temperature time series and the water content time series at the target depth, construct and calculate the L2 loss function of the heat transfer model, and determine whether the L2 loss function reaches the minimum value. If so, output the liquid water and gaseous water fluxes; otherwise, use a preset optimization algorithm to optimize the undetermined parameters of the heat transfer model. The undetermined parameters include the thermal conductivity, liquid water and gaseous water fluxes, until the L2 loss function reaches the minimum value, and output the optimal liquid water and gaseous water fluxes as the predicted values of the water flux in the vadose zone.

[0013] Preferably, the heat transfer model is represented by the following convection-dispersion equation:

[0014]

[0015] In the formula, C w , C v and C p are the volumetric heat capacities of liquid water, gaseous water and wet soil respectively; λ(θ) is the thermal conductivity of the soil, which changes with the volumetric water content θ; q l and q v are the liquid water and gaseous water fluxes respectively; T represents temperature, t represents time, and z represents one-dimensional vertical direction, with the downward direction being positive.

[0016] Preferably, obtaining the predicted value of the water content at the target depth based on the empirical equation includes:

[0017] Estimate the corresponding water content through the thermal conductivity:

[0018] λ(θ) = b1 + b2θ + b3θ0.5

[0019] In the formula, θ is the volumetric water content; b1, b2, and b3 are empirical coefficients.

[0020] Preferably, after the step of using the measured temperature time series T A , T C of two adjacent monitoring depths A and C as the boundary conditions of the heat transfer model for a given target depth B, it further includes:

[0021] Obtaining spatially discrete points i - 1, i, i + 1 (i = 1, 2, 3,... N) and temporally discrete points j - 1, j, and j + 1 (j = 1, 2, 3,... n) through spatio-temporal discretization; where is the number of spatially discrete points, is the number of temporally discrete points, d is the vertical interval distance between depths A and C, t is the observation time length, Δx is the spatial step size, and Δt is the time step size.

[0022] Preferably, the setting of the initial conditions of the heat transfer model includes:

[0023] Setting the empirical values of the volumetric heat capacities C w , C v and C p of liquid water, gaseous water, and wet soil, the thermal conductivity coefficient λ(θ) of the soil, the initial values of the liquid water flux q l and the gaseous water flux q v .

[0024] Preferably, the solving of the heat transfer model by the finite difference method includes:

[0025] Discretizing the heat transfer model into the following difference equation using the Crank - Nicolson six - point format:

[0026]

[0027] where

[0028]

[0029]

[0030]

[0031]

[0032] In the formula, represents the temperatures of three adjacent spatially discrete points at time j; represent the temperatures corresponding to three spatially adjacent discrete points at the (j + 1)-th moment; λ i-1 , λ i , λ i+1 are the thermal conductivity coefficients corresponding to three adjacent discrete points i - 1, i, and i + 1 in the vertical direction;

[0033] Solve the unknown variable temperature T in the differential equation, and the obtained solution is the predicted value of the temperature time series at the target depth.

[0034] Preferably, the L2 loss function of the heat migration model is constructed as follows:

[0035]

[0036] In the formula, α, β, and γ are weight coefficients, and satisfy α + β + γ = 1; is the measured temperature, is the average value of the measured water content time series θ B , and θ B (q l , q v , λ i ) is the predicted value corresponding to ; when the L2 loss function reaches the minimum value, the target optimization parameter reaches the optimal value.

[0037] Preferably, the preset optimization algorithm includes any one of the Newton optimization algorithm, genetic algorithm, search optimization algorithm, and neural network algorithm.

[0038] According to the second aspect of the present invention, the present invention provides a vadose zone water flow rate prediction device based on temperature time series, including the following modules:

[0039] Initial condition setting module, used to set the initial conditions of the heat migration model;

[0040] Boundary condition setting module, for a given target depth B, taking the measured temperature time series T A , T C of the two adjacent monitoring depths A and C as the boundary conditions of the heat migration model;

[0041] Measured value acquisition module, used to acquire the measured values of the temperature time series and water content time series at the target depth;

[0042] Finite difference solution module, used to solve the heat migration model by the finite difference method based on the boundary conditions and the initial conditions, and obtain the predicted value of the temperature time series at the target depth;

[0043] A predicted value acquisition module, configured to acquire a predicted value of the water content at a target depth based on an empirical equation;

[0044] A loss calculation and parameter optimization module, configured to construct and calculate an L2 loss function of the heat transfer model based on the predicted values and measured values of the temperature time series and water content time series at the target depth, and determine whether the L2 loss function reaches the minimum value. If so, output the liquid water and gaseous water flux; otherwise, optimize the undetermined parameters of the heat transfer model, including the thermal conductivity, liquid water and gaseous water flux, using a preset optimization algorithm until the L2 loss function reaches the minimum value, and output the optimal liquid water and gaseous water flux as the predicted value of the vadose zone water flux.

[0045] According to a third aspect of the present invention, there is provided an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the vadose zone water flux prediction method described above are implemented.

[0046] The beneficial effects brought by the technical solution provided by the present invention are:

[0047] 1. For the target depth below the ground surface, the proposed method only requires the temperature time series at three positions below the ground surface (the target depth and the two adjacent depths), and can reverse-trace the soil water flux at the target depth without the need to additionally input other hydraulic parameters and calibration parameters. Therefore, the method provided by the present invention is simple and clear, and easy to implement.

[0048] 2. The optimization algorithm is used to optimize the soil thermal conductivity, liquid water and gaseous water flux simultaneously, and the liquid water flux and gaseous water flux can be predicted simultaneously. Preferably, the L-BFGS-B algorithm is used to optimize the undetermined parameters. This algorithm has global convergence and superlinear convergence speed, with a clear goal and a faster convergence speed than other heuristic algorithms. Therefore, the calculation efficiency of the present invention is high.

[0049] 3. The thermal conductivity is discretized and optimized in space, and this series of refined processing improves the prediction accuracy of the heat transfer model. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0051] Figure 1 is a flowchart of a method for predicting vadose zone water flux based on temperature time series in an embodiment of the present invention;

[0052] Figure 2 is a schematic diagram of the discretization of the one-dimensional heat transfer model of the vadose zone in an embodiment of the present invention;

[0053] Figure 3It is the design drawing of the experimental device in the embodiment of the present invention;

[0054] Figure 4 It is the temperature fitting curves at depths of 3, 10, 20, and 30 cm for three groups of experiments (1.3, 1.4, 1.5) on sand column 1 and three groups of experiments (2.3, 2.4, 2.5) on sand column 2 in the embodiment of the present invention; each symbol represents the measured value (the measured), and the solid line represents the predicted value (the predicted);

[0055] Figure 5 It is the structural diagram of a vadose zone water flux prediction device based on temperature time series in the embodiment of the present invention. Specific implementation manners

[0056] For a clearer understanding of the technical features, objectives, and effects of the present invention, the specific implementation manners of the present invention will now be described in detail with reference to the accompanying drawings.

[0057] Reference Figure 1 , this embodiment provides a vadose zone water flux prediction method based on temperature time series, which can calculate the fluxes of soil liquid water and gaseous water at different depths below the ground surface using the measured temperature time series. The specific steps are as follows:

[0058] Step 1: Set the initial conditions of the heat transfer model;

[0059] Specifically, without considering root water uptake and the latent heat of liquid water evaporation, the one-dimensional heat transfer model can be represented by the following convective-dispersive equation:

[0060]

[0061] C w 、C v and C p (Jm -3 k -1 ) are the volumetric heat capacities of liquid water, gaseous water, and wet soil, respectively; λ(θ) [unit: J m -1 s -1 K -1 is the thermal conductivity of the soil, which changes with the volumetric water content θ [unit: rn 3 m -3 ; q l and q v [unit: ms -1 are the fluxes of liquid water and gaseous water, respectively. T (unit: K) represents temperature, t [unit: s] is time, and z [unit: m] represents one-dimensional vertical direction, with the downward direction being positive.

[0062] The Chung and Horton (1987) model gives an empirical formula to estimate the corresponding thermal conductivity through water content:

[0063] λ(θ) = b1 + b2θ + b3θ 0.5 (2)

[0064] where θ is the volumetric water content; b1, b2, and b3 are empirical coefficients (see Table 1); λ(θ) is the soil thermal conductivity.

[0065] Regarding the above model, the set initial conditions include: the volumetric heat capacities C w , C v and C p of liquid water, gaseous water, and wet soil, and the initial value of the soil thermal conductivity λ(θ) at the observation depth. The specific values are shown in the first row of Table 4.

[0066] Step 2: For a given target depth B, take the measured temperature time series T A and T C of the two adjacent monitoring depths A and C as the boundary conditions of the heat transport model;

[0067] In Step 2, it also includes: obtaining the spatial discrete points i - 1, i, i + 1 (i = 1, 2, 3,... N) and time discrete points j - 1, j, and j + 1 (j = 1, 2, 3,... n) through space - time discretization, as specifically shown in Figure 2 . Among them, is the number of spatial discrete points, is the number of time discrete points. Here, d is the vertical interval distance between depths A and C, the observation time length is t. Δx is the spatial step size, and Δt is the time step size.

[0068] Step 3: Obtain the measured values of the temperature time series T B and the water content time series θ B at the target depth;

[0069] Step 4: Based on the boundary conditions and the initial conditions, solve the heat transport model by the finite - difference method to obtain the predicted value T B of the temperature time series at the target depth;

[0070] Specifically, Step 4 includes:

[0071] Using the Crank - Nicolson six - point format, Equation (1) can be discretized as:

[0072]

[0073] Here

[0074]

[0075]

[0076]

[0077]

[0078] In equations (3) and (4), represents the temperatures of three spatially adjacent discrete points at any time j, represents the corresponding temperatures of three spatially adjacent discrete points at time j + 1; λ i-1 and λ i and λ t+1 are the thermal conductivity coefficients corresponding to any three adjacent discrete points i - 1, i, and i + 1 vertically.

[0079] Solving for the unknown variable temperature T in the difference equation (3), the obtained solution is the predicted value of the temperature time series at the target depth.

[0080] During the calculation process, the parameters C w , C v , and C p take empirical values, and the specific values are shown in Table 2.

[0081] Step 5: Obtain the predicted value of the water content θ at the target depth based on the empirical equation (2);

[0082] Step 6: Construct and calculate the L2 loss function of the one-dimensional heat transfer model based on the predicted values and measured values of the temperature time series and water content time series at the target depth, and determine whether the L2 loss function reaches the minimum value. If so, output the liquid water and gaseous water fluxes; otherwise, use the L-BFGS-B optimization algorithm to optimize the undetermined parameters of the one-dimensional heat transfer model, including the thermal conductivity coefficient, liquid water and gaseous water fluxes, until the L2 loss function reaches the minimum value, and output the optimal liquid water and gaseous water fluxes as the predicted values of the vadose zone water fluxes;

[0083] The loss function is designed to simultaneously fit the temperature time series and water content, so that the temperature calculated by the model is in good agreement with the measured temperature, and the water content calculated is in good agreement with the measured water content.

[0084] Specifically, the loss function of this model is constructed as follows:

[0085]

[0086] In the formula, α, β, and γ are weight coefficients and satisfy α + β + γ = 1; is the measured temperature, is the average value of the measured moisture content time series θ B , and θ B (q l , q v , λ i ) are the predicted values corresponding to and ; when the L2 loss function reaches the minimum value, the target optimization parameters reach the optimal values.

[0087] It should be noted that: α, β, γ, Δx, Δt are not fixed and can be set according to actual needs.

[0088] Optimize the parameters λ i , q l , q v in equation (5):

[0089] If the L2 loss function does not reach the minimum value, use the optimization algorithm L-BFGS-B to further optimize the undetermined parameters λ i , q l , q v . The L-BFGS-B algorithm can optimize the spatio-temporal distributions of both the soil thermal conductivity and the soil water vapor flux simultaneously. When the loss function value is the smallest, the model outputs the optimal λ, q l , q v (Table 4) at the target depth.

[0090] It should be noted that the L-BFGS-B algorithm is only a preferred Newton optimization algorithm in this embodiment, and genetic algorithms (such as particle swarm optimization algorithms), search optimization algorithms (such as grid search algorithms), neural network algorithms (such as reinforcement learning algorithms), etc. can also be selected.

[0091] In addition, the root mean square error (RMSE) is used to evaluate the fitting degree of the temperature time series at any depth.

[0092]

[0093] where T0 represents the measured temperature at the initial moment, T j represents the measured temperature at the j-th moment, and T j (q l , q v , λ i ) is the corresponding predicted temperature.

[0094] Table 1 Empirical coefficients

[0095] Coefficient Clay Loam Sand <![CDATA[b1]]> -0.197 0.243 0.228 <![CDATA[b2]]> -0.962 0.393 -2.406 <![CDATA[b3]]> 2.521 1.534 4.909

[0096] To verify the proposed method, an unsaturated sand column was designed in the laboratory to simulate the soil vadose zone affected by the periodic fluctuations of surface temperature, and temperature and water content data were collected using 5TE probes. The prediction method proposed in the present invention was applied to backtrack the water fluxes in different sand columns. The calculated results were compared with the measured data to verify the effectiveness of the method.

[0097] Table 2 Volume heat capacity

[0098]

[0099]

[0100] Hydrothermal transport experiment of unsaturated sand column:

[0101] An unsaturated medium was selected to simulate the near-surface soil. Medium-coarse quartz sand was evenly filled in the plexiglass column. For comparison, two sand columns were filled with the same quartz sand in the same steps in this embodiment, denoted as sand column 1 and sand column 2 respectively here. Soil moisture sensors (5TE, Decagon) and temperature sensors (Hobo S-TMB-M006) were installed longitudinally along the sand column to monitor water content and temperature. During the experiment, the volume method was used to measure the water flow flux.

[0102] Each experiment had two steps. First, the water supply source used a peristaltic pump to provide an approximately stable water supply at a constant rotation speed to ensure a stable but non-uniform water content (the water content did not change with time but changed with depth). Second, the water supply water tank used a heating rod to heat periodically so that the water temperature changed sinusoidally with time. The outlet of sand column 1 was slightly higher than the bottom of the sand column to generate an unsaturated flow with a stable water content, and the experimental device was as Figure 3 shown.

[0103] Under the prediction method of this embodiment, the simulated water content was basically consistent with the measured values at different depths (as shown in Table 2). The comparison between the simulated temperature and the measured temperature was as Figure 4 shown, and the corresponding RMSE values were shown in Table 3. Through the output of the numerical model, the liquid water flux and the vapor water flux were obtained simultaneously, and the vapor flux was in the range of 0.004 - 0.029 m / h, accounting for 10% of the total water flux; generally speaking, the results showed that the water flux calculated based on temperature was basically consistent with the measured water flux, proving the accuracy and reliability of the method of the present invention.

[0104] Table 2 Measured and predicted values of water flow flux and water content in 5 groups of experiments for sand column 1 and sand column 2 respectively

[0105]

[0106]

[0107] Table 3 Root Mean Square Error (RMSE) of measured temperature and predicted temperature (°C).

[0108]

[0109]

[0110] During the above experiment, the optimization results of the thermal conductivity at the observation depth of the two sand columns are shown in Table 4:

[0111] Table 4 Optimal values of thermal conductivity

[0112]

[0113] In this embodiment, the above prediction method is used to calculate the water flux under different saturated boundary conditions and flow velocity conditions. The results show that the calculated values are basically consistent with the measured temperature, water content and soil flux, verifying the reliability of the new method. This method is also applied to estimate the soil water flux in the field site. The time variation of the calculated soil flux at different depths below the ground surface reflects the field observations and hydrological conditions, further confirming the effectiveness of the new method for determining the soil flux. Compared with other methods for predicting soil water flux, the proposed new method neither requires prior knowledge of hydrodynamic parameters nor any assumptions; it only needs to input the temperature time series data. In addition, the water content at the target depth can also be used as a constraint condition for optimizing the thermal conductivity. This method is simple to implement and has high computational efficiency, providing a new tool for quantitatively evaluating the water flux in the vadose zone.

[0114] In addition, to implement the above prediction method, this embodiment also provides a device for predicting the water flux in the vadose zone based on the temperature time series, as Figure 5 shown, including the following modules:

[0115] Initial condition setting module 1, used to set the initial conditions of the heat transfer model;

[0116] Boundary condition setting module 2, used for a given target depth B, taking the measured temperature time series T A 、T C of the two adjacent monitoring depths A and C as the boundary conditions of the heat transfer model;

[0117] Measured value acquisition module 3, used to acquire the measured values of the temperature time series and the water content time series at the target depth;

[0118] Finite difference solution module 4, used to solve the heat transfer model by the finite difference method based on the boundary conditions and the initial conditions, and obtain the predicted values of the temperature time series at the target depth;

[0119] A predicted value acquisition module 5 for obtaining a predicted value of the water content at a target depth based on an empirical equation;

[0120] A loss calculation and parameter optimization module 6 for constructing and calculating the L2 loss function of the heat transfer model based on the predicted values and measured values of the temperature time series and water content time series at the target depth, and determining whether the L2 loss function reaches the minimum value. If so, output the liquid water and gaseous water fluxes; otherwise, optimize the undetermined parameters of the heat transfer model, including the thermal conductivity, liquid water and gaseous water fluxes, using a preset optimization algorithm until the L2 loss function reaches the minimum value, and output the optimal liquid water and gaseous water fluxes as the predicted values of the vadose zone water fluxes.

[0121] Based on the above device, the preset optimization algorithm preferably adopts the L-BFGS-B algorithm.

[0122] In addition, an embodiment of the present invention further provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the vadose zone water flux prediction method are implemented.

[0123] In addition, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the vadose zone water flux prediction method are implemented.

[0124] It should be noted that in this article, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or system. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or system including that element.

[0125] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments. In the several unit claims listing several devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not denote any order and these words may be interpreted as identifiers.

[0126] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present invention.

Claims

1. A method for predicting the water flux in the vadose zone based on temperature time series, characterized in that, Including the following steps: Setting the initial conditions of the heat transfer model; For a given target depth B, the measured temperature time series T A and T C of the two adjacent monitoring depths A and C are used as the boundary conditions of the heat migration model; Obtaining the measured values of the temperature time series and the water content time series at the target depth; Based on the boundary conditions and the initial conditions, solving the heat transfer model by the finite difference method to obtain the predicted values of the temperature time series at the target depth; Obtaining the predicted value of the water content at the target depth based on the empirical equation; Constructing and calculating the L2 loss function of the heat transfer model based on the predicted values and the measured values of the temperature time series and the water content time series at the target depth, and determining whether the L2 loss function reaches the minimum value. If so, output the liquid water and gaseous water fluxes; otherwise, use a preset optimization algorithm to optimize the undetermined parameters of the heat transfer model, where the undetermined parameters include the thermal conductivity, the liquid water and gaseous water fluxes, until the L2 loss function reaches the minimum value, and output the optimal liquid water and gaseous water fluxes as the predicted values of the vadose zone water fluxes.

2. The vadose zone water flow flux prediction method based on temperature time series according to claim 1, wherein The heat transfer model is represented by the following convection-dispersion equation: where C w , C v and C p are the volumetric heat capacities of liquid water, gaseous water, and moist soil, respectively; λ(θ) is the thermal conductivity of the soil, which varies with the volumetric water content θ; q l and q v are the liquid water and gaseous water fluxes, respectively; T represents temperature, t represents time, z represents one-dimensional vertical direction, and the downward direction is positive.

3. The vadose zone water flow flux prediction method based on temperature time series according to claim 1, characterized in that The obtaining the predicted value of the water content at the target depth based on the empirical equation includes: Estimating the corresponding water content through the thermal conductivity: λ(θ) = b1 + b2θ + b3θ 0.5 where θ is the volumetric water content; b1, b2, and b3 are empirical coefficients.

4. The method for predicting the vadose zone water flux based on the temperature time series according to claim 2, wherein After the step of using the measured temperature time series T A and T C at two adjacent monitoring depths A and C as the boundary conditions of the heat migration model for a given target depth B, it further includes: By discretizing space and time respectively, spatial discrete points \(i - 1\), \(i\), \(i + 1\) (\(i=1,2,3,\cdots,N\)) and temporal discrete points \(j - 1\), \(j\), \(j + 1\) (\(j = 1,2,3,\cdots,n\)) are obtained; where is the number of spatial discrete points, is the number of temporal discrete points, \(d\) is the vertical interval distance between depths \(A\) and \(C\), \(t\) is the observation time length, \(\Delta x\) is the spatial step, and \(\Delta t\) is the time step.

5. The method for predicting the vadose zone water flow flux based on the temperature time series according to claim 2, wherein The setting the initial conditions of the heat transfer model includes: Set the empirical values of the volumetric heat capacities C w of liquid water, C v of gaseous water, and C p of moist soil, the thermal conductivity λ(θ) of the soil, the liquid water flux q l and the initial value of the gaseous water flux q v .

6. The method for predicting the vadose zone water flux based on the temperature time series according to claim 4, wherein The solving the heat transfer model by the finite difference method includes: Using the Crank-Nicolson six-point format to discretize the heat transfer model into the following difference equation: where In the formula, represents the temperatures of three spatially adjacent discrete points at time j; represents the corresponding temperatures of three spatially adjacent discrete points at time j + 1; λ i-1 and λ i and λ i+1 are the thermal conductivity coefficients corresponding to three adjacent discrete points i - 1, i, and i + 1 in the vertical direction; Solving the unknown variable temperature T in the difference equation, and the obtained solution is the predicted value of the temperature time series at the target depth.

7. The vadose zone water flow flux prediction method based on temperature time series according to claim 6, wherein The L2 loss function of the heat transfer model is constructed as follows: where α, β, and γ are weight coefficients and satisfy α + β + γ = 1; is the measured temperature, is the average value of the measured water content time series θ B ; and θ B (q l , q v , λ i ) are the predicted values corresponding to ; when the L2 loss function reaches the minimum value, the target optimization parameters reach the optimal values.

8. The method for predicting the vadose zone water flow flux based on the temperature time series according to claim 1, wherein The preset optimization algorithm includes any one of the Newton optimization algorithm, the genetic algorithm, the search optimization algorithm, and the neural network algorithm.

9. A vadose zone water flow flux prediction device based on temperature time series, characterized in that, Including the following modules: An initial condition setting module for setting the initial conditions of the heat transfer model; Boundary condition setting module, which is used to take the measured temperature time series T A and T C of two adjacent monitoring depths A and C as the boundary conditions of the heat migration model; A measured value obtaining module for obtaining the measured values of the temperature time series and the water content time series at the target depth; A finite difference solving module for solving the heat transfer model by the finite difference method based on the boundary conditions and the initial conditions to obtain the predicted values of the temperature time series at the target depth; A predicted value obtaining module for obtaining the predicted value of the water content at the target depth based on the empirical equation; A loss calculation and parameter optimization module for constructing and calculating the L2 loss function of the heat transfer model based on the predicted values and the measured values of the temperature time series and the water content time series at the target depth, and determining whether the L2 loss function reaches the minimum value. If so, output the liquid water and gaseous water fluxes; otherwise, use a preset optimization algorithm to optimize the undetermined parameters of the heat transfer model, including the thermal conductivity, the liquid water and gaseous water fluxes, until the L2 loss function reaches the minimum value, and output the optimal liquid water and gaseous water fluxes as the predicted values of the vadose zone water fluxes.

10. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the vadose zone water flux prediction method according to any one of claims 1 to 8.

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