Surface net flux calculation method and system based on frequency domain soil moisture equation

Abstract

The invention provides an earth surface net flux calculation method and system based on a frequency domain soil moisture equation. The method comprises the following steps: establishing a frequency domain soil moisture motion model of soil water changing along with depth; performing frequency domain decomposition on the time sequence observation data and the upper flux boundary of the site soil water; calibrating the soil parameters according to the obtained upper flux and the frequency component of the soil water; carrying out discrete Fourier decomposition on the soil moisture time sequence at the next time period and any depth, and extracting soil moisture fluctuation signals at different frequencies; according to the obtained parameters and models, carrying out back calculation on soil moisture at different frequencies to obtain surface net flux signals at different frequencies, and superposing the surface net flux signals in a time domain; and in combination with remote sensing data, obtaining the surface net flux of the regional range according to long-time soil moisture data. According to the method, the problem of the time domain is converted to the frequency domain, so that the long-time-sequence soil water sequence can be processed, and the increase of the calculation amount caused by step-by-step calculation by dividing the long-time sequence is reduced.

Description

Technical Field

[0001] The present invention relates to the field of unsaturated zone water flux, and more specifically, to a method and system for calculating surface net flux based on a frequency-domain soil moisture equation. Background Art

[0002] The surface net flux is the difference between the infiltration amount I (i.e., precipitation and irrigation amount minus surface runoff) and evapotranspiration ET. The combined action of the two generates the net water flux q = I - ET, and this flux determines the terrestrial water balance (i.e., the total amount of groundwater resources that can be replenished). The surface net flux is closely related to soil water content and groundwater level. When water enters the vadose zone, a part of it is consumed by evaporation and plant transpiration in the shallow soil, and the rest gradually migrates downward through the zero-flux plane of the vadose zone and finally enters the aquifer. Since this part of water finally flows into the aquifer to form groundwater, it is called potential groundwater recharge, and its recharge flux is equivalent to the soil water leakage amount. The surface net flux is an important link in the evaluation of groundwater resources and has important theoretical and practical significance for the rational development and utilization of groundwater resources. Reasonable assessment of the surface net flux helps to avoid disasters caused by overexploitation of groundwater.

[0003] Traditional methods for quantifying the surface net flux mainly include: the direct measurement method, that is, using a lysimeter to obtain local seepage data. Although it has high measurement accuracy, it is difficult to be popularized and applied on a large scale due to the high cost of equipment construction and maintenance. Therefore, there is an urgent need to develop an indirect measurement method based on easily observable data (such as dynamic changes in soil water content and groundwater depth). The groundwater level observation method, that is, indirectly calculating the potential groundwater recharge flux through groundwater level data and specific water content estimation. This method is simple and efficient and does not depend on assumptions about the recharge process (such as the existence of preferential flow paths), but it cannot clearly reveal the direct relationship between precipitation and recharge, which limits its applicability in predicting future recharge under the background of climate change. The vadose zone hydrological model, based on the Richards equation, combines instantaneous observation data (such as soil moisture content and pressure head) to invert the recharge flux, and can simulate complex processes such as soil water transport, heat and energy balance, and plant water absorption to achieve the prediction of large-scale net flux. However, this model highly depends on the accuracy of soil hydrological parameters and is limited by uncertainties caused by factors such as input data, boundary conditions, initial conditions, and scale effects. Therefore, in practical applications, it is necessary to balance model complexity and computational convenience, reasonably combine soil moisture spatial gradient information, and optimize the coordination between "internal conditions" and "boundary conditions" to improve the prediction reliability of the model.

[0004] In recent years, the analytical solution based on the Richards equation has shown significant advantages in the inversion and calculation of net water flux. First, by optimizing the analytical model of the Richards equation and taking into account the soil water movement process and several reasonable simplifying assumptions, this method effectively simplifies the parameter acquisition process while ensuring the physical meaning, balancing the complexity of the model and the efficiency of calculation. Second, the analytical solution method does not rely on the spatial gradient information of soil water, greatly improving the convenience and operability of observation. Finally, with the wide application of aerial and satellite remote sensing technologies in large-scale soil water observation, the analytical method can directly use the surface soil water data to calculate the surface net flux, enhancing the coupling of large-scale and small-scale data and significantly improving the spatial applicability and reliability of the estimation results.

[0005] Although the analytical method in the time domain can directly calculate the flux based on the single-layer soil water data, the calculation process of deriving the flux from the analytical solution is relatively complex and requires inverse operation on the already very complex analytical solution of soil water. In addition, for long-term soil water data, it needs to be divided into different time periods for step-by-step calculation, which makes the calculation amount increase significantly with the length of the time series. Therefore, it is necessary to develop a calculation model of surface net flux based on the use of soil water in the frequency domain. Through the analytical solution of the frequency-domain soil water equation, the surface net flux is inversely deduced using the soil water fluctuations at any depth, and the fluctuations of different frequencies are superimposed in the time domain to obtain a method for solving the surface net flux for a long time series. Summary of the Invention

[0006] Aiming at the technical problems existing in the prior art, the present invention provides a method and system for calculating the surface net flux based on the frequency-domain soil water equation. By transforming the problem in the time domain to the frequency domain, it helps to process long-term soil water sequences and reduce the increase in the calculation amount caused by step-by-step calculation of long time series. Through actual data testing, the method based on soil water fluctuations in the frequency domain shows excellent accuracy and reliability in calculating the surface net flux. The proposed model provides the connection between soil water and surface net flux in the frequency domain. In addition, the present invention is particularly suitable for calculating the large-scale surface net flux using the soil water information obtained by large-scale remote sensing means while maintaining a low calculation cost, making it more reliable in practical applications.

[0007] According to the first aspect of the present invention, there is provided a method for calculating the surface net flux based on the frequency-domain soil water equation, comprising the following steps: Step 1. Establish a frequency-domain soil water movement model of the variation of soil water with depth under the condition of a single-frequency fluctuation flux at the upper boundary. Step 2. Based on the discrete Fourier decomposition, decompose the time-series observation data of the soil water at the site and the upper flux boundary in the frequency domain to obtain the frequency components of the upper flux and the soil water. Step 3. Using the frequency-domain soil water movement model, calibrate the soil parameters according to the obtained upward flux and the frequency components of soil water. Step 4. Discretely Fourier decompose the soil water time series at any depth, and extract the soil water fluctuation signals at different frequencies. Step 5. According to the obtained soil water fluctuation signals at different frequencies and the frequency-domain soil water movement model, perform back-calculation on the soil water at different frequencies, obtain the surface net fluxes at different frequencies, and superimpose them in the time domain. Step 6. Combine remote sensing data, and obtain the surface net fluxes in the regional scope according to the surface net fluxes obtained from the long-term soil water series.

[0008] Based on the above technical solutions, the present invention can also be improved as follows.

[0009] Optionally, the establishment of the frequency-domain soil water movement model for the variation of soil water with depth under the condition of a single-frequency fluctuation flux at the upper boundary includes: When a single-periodic flux flows into the soil, the inflow at the top of the soil is expressed as a stable constant plus a periodic fluctuating soil water with a frequency and an amplitude In the complex domain, it is expressed as , then under this flux, the variation of the generated soil water with depth is expressed as:

[0010] In the formula, is the imaginary unit; ω j is the angular frequency of the fluctuation; t is the time; z is the soil depth; θc(z) is the stable component of the soil water at depth z; θ p (z) is a complex number representing the fluctuation of the soil water at depth z; θ p is the amplitude of the fluctuating soil water; K s is the saturated hydraulic conductivity; α is the characteristic parameter of the Gardner-Kozeny model; λ is a complex number.

[0011] Optionally, the frequency-domain decomposition of the time series observation data of the site soil water and the upper flux boundary based on the discrete Fourier decomposition to obtain the frequency components of the upper flux and soil water includes: By using the discrete Fourier decomposition method, decompose the time-domain signal into a superposition of sine waves and cosine waves with set frequencies, amplitudes and phases. The amplitude and phase corresponding to each frequency component reflect the contribution intensity and phase characteristics of that frequency in the time series.

[0012] Optionally, the amplitude of each identified frequency component and phase are quantized as:

[0013] where Re(.) and Im(.) represent the real and imaginary parts of a complex number respectively, and atan2(.) is the arctangent function.

[0014] Optionally, the calibration of soil parameters using the frequency-domain soil water movement model based on the obtained upward flux and frequency components of soil water includes: Based on the frequency-domain soil water movement model, calculate the comparison between the simulated value and the actual observed value of soil water, and verify whether the soil water observation data is consistent with the model simulation value according to the calculation result.

[0015] Optionally, the discrete Fourier decomposition of the soil water time series at any depth to extract soil water fluctuation signals at different frequencies includes: Considering the soil water change θ(z, t) in different depth z profiles of a long time series, it is decomposed into a steady-state term and a fluctuation term by the discrete Fourier decomposition method, expressed as:

[0016] where is the steady-state soil water content, reflecting the average soil water in the time series, is the complex form of soil water fluctuation, represents the amplitude, indicating the magnitude of the contribution of soil water at different frequency components, ω j is the angular frequency of the fluctuation, and the index j = 1, 2… is the frequency number.

[0017] Optionally, the combination of remote sensing data to obtain the surface net flux in the regional range based on the surface net flux obtained from the long-term soil water series includes: Given the soil water change θ(z, t) in different depth z profiles of a long time series, use the discrete Fourier decomposition method to decompose it into a steady-state term and a series of fluctuation terms , at this time, the surface net flux is expressed as:

[0018] Finally, based on a long-term soil water data, the surface net flux data is obtained.

[0019] According to a second aspect of the present invention, there is provided a system for calculating the surface net flux based on a frequency-domain soil moisture equation, comprising: A frequency-domain soil moisture movement model establishment module for establishing a frequency-domain soil moisture movement model of the change of soil water with depth under the condition of a single-frequency fluctuation flux at the upper boundary; A frequency component acquisition module for performing frequency-domain decomposition on the time-series observation data of the site soil water and the upper flux boundary based on the discrete Fourier decomposition method to obtain the frequency components of the upper flux and the soil water; and calibrating the soil parameters according to all the obtained frequency components of the upper flux and the soil water by using the frequency-domain soil moisture movement model; A surface net flux acquisition module for performing discrete Fourier decomposition on the soil moisture time series of the next time period and any depth, extracting the soil moisture fluctuation signals of different frequencies; performing back-calculation on the soil moisture of different frequencies according to the obtained parameters and the frequency-domain soil moisture movement model to obtain the surface net flux signals at different frequencies and superimposing them in the time domain; A surface net flux acquisition module for combining remote sensing data and obtaining the surface net flux of the regional scope according to the surface net flux obtained from the long-term soil water series.

[0020] According to a third aspect of the present invention, there is provided an electronic device, comprising an acquirer, a processor, a display and an outputter, and a computer program stored on the memory and executable on the processor, and the processor executes the program to perform a method for calculating the surface net flux based on a frequency-domain soil moisture equation.

[0021] The technical effects and advantages of the present invention: The present invention provides a method and a system for calculating the surface net flux based on a frequency-domain soil moisture equation. By first using the analytical solution of the frequency-domain soil water equation and using the soil moisture fluctuations at any depth to inversely calculate the surface net flux, and superimposing the fluctuations of different frequencies in the time domain, a method for solving the surface net flux with a long time series is obtained; compared with the previous time-domain analytical solution method, the present invention has no complex inverse operation process, the calculation method is simple and easy to understand; compared with the previous numerical methods, the present invention has better applicability to the actual long-term soil moisture series, shows a lower calculation cost, and provides feasibility for estimating the large-scale surface net water flux by using the remote sensing surface soil moisture data. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0023] Figure 1 Flow chart of a surface net flux calculation method based on a frequency-domain soil moisture equation provided by an embodiment of the present invention; Figure 2 Schematic diagram of the steady state and fluctuation terms of the upper boundary flux of a single-frequency fluctuation provided by an embodiment of the present invention; Figure 3 Effect diagram of the upper flux observation, soil moisture observation, and decomposition and fitting by the discrete Fourier transform method provided by an embodiment of the present invention, Figure 3 where (a) in it represents the fitting of the upper flux by the discrete Fourier transform method, Figure 3 and (b) in it represents the fitting of the soil water by the discrete Fourier transform method; Figure 4 Comparison diagram of the simulated soil moisture value calculated by the frequency-domain soil moisture model provided by an embodiment of the present invention and the actual observed value; Figure 5 Comparison diagram of the fitting value and the actual observed value of the upper flux boundary obtained by the frequency-domain algorithm based on the soil moisture observed value provided by an embodiment of the present invention; Figure 6 In an embodiment of the present invention, the upper flux simulation value of the Hetao Irrigation Area is inversely deduced according to the SMAP soil moisture observed value in the Hetao Irrigation Area, Figure 6 where (a) in it shows the variation law of soil water with time on all grids in the Hetao Irrigation Area, and the soil water of all grids is averaged; Figure 6 and (b) in it calculates the variation of the surface net flux with time on all grids in the Hetao area by using the proposed algorithm and calibrated parameters. Specific implementation manner

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts shall fall within the protection scope of the present invention.

[0025] It can be understood that, based on the defects in the background technology, an embodiment of the present invention proposes a surface net flux calculation method based on a frequency-domain soil moisture equation, specifically as Figure 1 shown, including the following steps: Step 1: Establish a frequency-domain soil moisture movement model for the variation of soil water with depth under the condition of a single-frequency fluctuation flux at the upper boundary; In this embodiment, establishing the frequency-domain soil moisture movement model includes: Assume that when a single periodic flux flows into the soil, the inflow at the top of the soil is expressed as a stable constant plus a frequency and an amplitude of the periodic fluctuation of soil moisture. In the complex domain, it is expressed as . Then, under this flux, the variation of the generated soil moisture with depth is expressed as:

[0026] where is the imaginary unit, ω j is the angular frequency of the fluctuation, t is the time, z is the soil depth, θ c (z) is the stable component of the soil moisture at depth z , θ p (z) is a complex number representing the fluctuation of the soil moisture at depth z , θ p is the amplitude of the fluctuating soil moisture, arg(θ p ) is the phase angle of the fluctuating soil moisture, arg(θ p ) is a periodic function with a range of -π to π. θ s and θ r represent the saturated water content and the residual water content of the soil respectively, K s is the saturated hydraulic conductivity, and α is the characteristic parameter of the Gardner-Kozeny model, λ is a complex number, is determined by , where:

[0027] Step 2: Based on the discrete Fourier decomposition, decompose the time series observation data of the soil water at the site and the upper flux boundary in the frequency domain to obtain the frequency components of the upper flux and the soil water; In this embodiment, the basic mathematical expression of the discrete Fourier transform method is as follows:

[0028] where y n is the observed value of the sampling point at t n time, N is the total number of sampling points of the time series, is the j th frequency component in the frequency domain, and

[0029] is the average value of the samples. The amplitude and phase

[0030] of each identified frequency component can be quantified as:

[0031] In the formula, Re(.) and Im(.) represent the real part and imaginary part of a complex number respectively, and atan2(.) is the arctangent function.

[0032] Step 3: Using the frequency-domain soil water movement model, calibrate the soil parameters according to all the obtained upward fluxes and frequency components of soil water; In this embodiment, based on the frequency-domain soil water movement model, calculate the comparison between the simulated value and the actual observed value of soil water, and calculate the root mean square error and goodness of fit R 2 , and verify the consistency between the soil water observation data and the model simulation according to the calculation results, laying a foundation for subsequent derivation of the surface net flux based on the model.

[0033] Step 4: Perform discrete Fourier decomposition on the soil water time series at any depth to extract soil water fluctuation signals at different frequencies; In this implementation step, the soil water change θ(z, t) at different depths z of a long time series can be considered, and it is decomposed into a steady-state term and a fluctuation term by the method of discrete Fourier decomposition:

[0034] In the formula, is the steady-state soil water content, reflecting the average soil water in the time series, is the complex form of soil water fluctuation, represents the amplitude, indicating the magnitude of the contribution of soil water with different frequency components, ω j is the angular frequency of the fluctuation, and the index j = 1, 2… is the serial number of the frequency.

[0035] Step 5: According to the obtained parameters and the frequency-domain soil water movement model, perform back-calculation on the soil water at different frequencies, obtain the surface net flux signals at different frequencies and superimpose them in the time domain; In this implementation step, according to the obtained parameters and the frequency-domain soil water movement model, if the soil water fluctuation θ p (z) at a certain depth is known, then the fluctuation flux of the surface soil q p can be back-calculated from θ p (z) and is expressed as:

[0036] In this model, both θ p (z) and q p (z) are complex numbers.

[0037] Given the soil water content changes θ(z, t) at different depths z of a long time series, it is decomposed into a steady-state term and a series of fluctuation terms by using the method of discrete Fourier decomposition. At this time, the surface net flux can be expressed as:

[0038] Finally, based on a long-term soil water data, the surface net flux data is obtained. Therefore, the method for calculating the surface net flux based on the frequency-domain soil water equation described in the embodiments of the present invention can invert the surface net flux according to the long-term soil water data.

[0039] The following further illustrates the above-mentioned method with specific embodiments. The method for calculating the surface net flux based on the frequency-domain soil water equation specifically includes the following steps: Step 1. Establish an equation for the variation of soil water with depth in the case of a single-frequency fluctuation flux at the upper boundary. The model is established starting from the Richards equation used to describe one-dimensional, vertical soil water movement. The Richards equation is derived from Darcy's law and the mass conservation equation. Darcy's law for soil water movement is described as:

[0040] In the formula, q is the Darcy velocity, h is the unsaturated soil matrix potential, z is the position head, K is the unsaturated hydraulic conductivity. Without considering source-sink terms such as root water uptake, the mass conservation equation is:

[0041] In the formula, θ is the soil water content. Substituting it can obtain the time-domain Richards equation as:

[0042] Furthermore, the Gardner-Kozeny model (GK model) is introduced to describe the unsaturated hydraulic conductivity curve K ~ θ and the soil water characteristic curve h The relationship between ~ θ. The significant advantage of the GK model (exponential model) is that the hydraulic diffusivity it describes shows a linear relationship, simplifying the complexity of the equation. The expression is as follows:

[0043] In the formula, α is the characteristic parameter of the GK model, and the parameter h e is the air entry suction, which reflects the maximum pore diameter of the continuous flow channels in the medium. θ s and θ r represent the saturated water content and the residual water content of the soil respectively, K s is the saturated hydraulic conductivity. When h >[[]] h e , θ = θ s , the unsaturated hydraulic conductivity K =[[]] K s , that is, the saturated hydraulic conductivity.

[0044] Furthermore, substituting Equation (4) into Equation (3) and performing a series of further transformations, we can obtain:

[0045] Equation (5) is similar to a classical diffusion equation, where v is similar to the advection velocity and is determined by .

[0046] Considering the case of a single periodic flux flowing into the soil, the inflow at the top of the soil is expressed as a steady constant plus a periodic fluctuation of soil moisture with a frequency and an amplitude . In the complex domain, it is expressed as, , Figure 2 shows a schematic diagram of the steady state of the upper boundary flux and the variation of the fluctuation term with time for a single-frequency fluctuation.

[0047] Furthermore, because K and q the relationship between is independent of t (see Equation (9)). Similarly, the variable K can also be expressed as a steady constant plus a frequency and amplitude The unsaturated hydraulic conductivity, expressed in the complex domain as, . Substitute the steady-state component and the fluctuating component into Equation (5), and eliminate the term to obtain an ordinary differential equation describing the steady component K c (z) and an ordinary differential equation describing the fluctuating component to represent soil water movement:

[0048] Furthermore, considering the lower boundary as a free drainage boundary, the solutions of Equation (6) and Equation (7) are:

[0049] wherein, λ is a complex number determined by , where:

[0050] In the case of a single-frequency fluctuating flux at the upper boundary, the movement of soil water can be obtained by substituting Equation (8) and Equation (9) into Equation (4):

[0051] wherein, is the imaginary unit, ω j is the angular frequency of the fluctuation, t is the time, z is the soil depth, θ c (z) is the steady component of soil moisture at depth z , θ p (z) is a complex number representing the fluctuation of soil moisture at depth z , |θ p | is the amplitude of the fluctuating soil moisture, arg(θ p ) is the phase angle of the fluctuating soil moisture, and arg(θ p ) is a periodic function with a range of -π to π.

[0052] Step 2. Implement the decomposition of the time series observation data of the flux and soil water at the site in the time domain based on the discrete Fourier decomposition method to obtain the components in the frequency domain.

[0053] The basic mathematical expression of the discrete Fourier decomposition method is as follows:

[0054] wherein,y n is t n the observed value of the sampling point at the moment, N is the total number of sampling points of the time series, is the j th frequency component in the frequency domain, is the average value of the sample. The amplitude and phase of each identified frequency component can be quantified as:

[0055] where Re(.) and Im(.) represent the real part and the imaginary part of the complex number respectively, and atan2(.) is the arctangent function.

[0056] Furthermore, through the method of discrete Fourier decomposition, the time-domain signal of soil water and upward flux can be decomposed into a superposition of a series of sine waves / cosine waves with specific frequencies, amplitudes and phases. The amplitude and phase corresponding to each frequency component reflect the contribution intensity and phase characteristics of that frequency in the time series.

[0057] Figure 3 This is the observation of the changes of the upward flux and soil moisture over time in the embodiment of the present invention, as well as the effects after discrete Fourier decomposition and fitting. The upward flux observation consists of rainfall plus irrigation minus evapotranspiration. By selecting 500 main frequencies for fitting, the results show that discrete Fourier decomposition can well and accurately transform time-domain data into frequency-domain data. Figure 3 In (a) represents the fitting of the discrete Fourier decomposition to the upward flux, Figure 3 In (b) represents the fitting of the discrete Fourier decomposition to the soil water. The goodness of fit R2 of both reaches above 0.99, proving that the method of discrete Fourier decomposition can be well used to transform time-domain data into the frequency domain.

[0058] Step 3. Using the obtained frequency-domain soil moisture movement model, according to all the frequency components of the obtained upward flux and soil water, perform the calibration of GK soil parameters; Figure 4 shows the comparison between the simulated soil moisture values and the actual observed values calculated by the frequency-domain soil moisture model in the embodiment of the invention. The root mean square error RMSE = 0.021, and the goodness of fit R 2 reaches 0.76, and the results verify the good consistency between the soil moisture observation data and the model simulation, laying a solid foundation for the subsequent derivation of the surface net flux based on the model.

[0059] Figure 5Shows the parameters with a fixed utilization rate in the embodiments of the invention. The comparison between the daily average of the surface net flux in 2023 deduced based on the frequency method in combination with the soil moisture observation data at a depth of 20 cm and the actually observed net flux. The fitting result shows that the model can accurately describe the change process of the surface net flux, and the simulated RMSE is 6.479 mm / d, R 2 is 0.751. Although the simulated value of the model under evaporation conditions is slightly lower than the actually observed value, it shows extremely high fitting accuracy for the positive net flux caused by rainfall and irrigation.

[0060] Step 4. Consider the soil moisture changes in different depth z profiles of a long time series θ(z, t) , and decompose it into a steady-state term and a fluctuation term by the method of discrete Fourier decomposition:

[0061] where is the steady-state soil moisture content, reflecting the average soil water in the time series, is the complex form of the soil moisture fluctuation, represents the amplitude, indicating the magnitude of the contribution of soil water with different frequency components, ω j is the angular frequency of the fluctuation, and the index j = 1, 2… is the serial number of the frequency.

[0062] In step 5, according to the model in step 1, if the soil moisture fluctuation θ p (z) at a certain depth is known, then the fluctuation flux q p of the surface soil can be calculated backward from θ p (z), and is expressed as:

[0063] In this model, both θ p (z) and q p ( z ) are complex numbers.

[0064] Furthermore, given the soil moisture changes θ(z, t) in different depth z profiles of a long time series, use the method of discrete Fourier decomposition to decompose it into a steady-state term and a series of fluctuation terms . At this time, the surface net flux is expressed as:

[0065] At this time, based on a long-term soil moisture data, the surface net flux data is obtained.

[0066] Figure 6 It shows the soil water data based on SMAP remote sensing. Combining with the algorithm for deriving surface fluxes from soil moisture in the frequency domain proposed in this embodiment, and using the soil parameters calibrated in step 3, the temporal variation law of the surface net flux from April 2016 to November 2024 in the Hetao Irrigation District is obtained; Figure 6 In (a), it shows the variation law of soil water over time for all grids in the Hetao Irrigation District, and the soil water of all grids is averaged. Figure 6 In (b), it calculates the variation of the surface net flux over time for all grids in the Hetao area using the algorithm and calibrated parameters proposed in this embodiment.

[0067] Therefore, the method for calculating surface net flux based on the frequency-domain soil moisture equation described in the embodiment of the present invention can invert the surface net flux according to long-term soil moisture data. Compared with the prior art, the embodiment of the present invention first uses the analytical solution of the frequency-domain soil water equation to obtain a method for solving the surface net flux for a long time series. Compared with the previous time-domain analytical solution methods, the present invention does not have a complex inverse operation process and has a simple calculation method; compared with the previous numerical methods, the present invention has better applicability to actual long-term soil moisture sequences, shows a lower calculation cost, and provides unprecedented possibilities for estimating large-scale surface net water fluxes using remote sensing surface soil moisture data.

[0068] According to the second aspect of the present invention, the present invention also provides a system for calculating surface net flux based on the frequency-domain soil moisture equation, including: A frequency-domain soil moisture movement model establishment module for establishing a frequency-domain soil moisture movement model of the variation of soil water with depth under the condition of a single-frequency fluctuating flux at the upper boundary; A frequency component acquisition module for performing frequency-domain decomposition on the time-series observation data of site soil water and the upper flux boundary based on the discrete Fourier decomposition method to obtain the frequency components of the upper flux and soil water; and using the frequency-domain soil moisture movement model to calibrate the soil parameters according to all the obtained upper flux and soil water frequency components; A surface net flux acquisition module for performing discrete Fourier decomposition on the soil moisture time series for the next time period and any depth, extracting soil moisture fluctuation signals of different frequencies; according to the obtained parameters and the frequency-domain soil moisture movement model, performing inverse calculation on the soil moisture of different frequencies to obtain surface net flux signals at different frequencies and superimposing them in the time domain; A surface net flux acquisition module for combining remote sensing data to obtain the surface net flux of the regional scope according to the surface net flux obtained from the long-term soil water sequence.

[0069] It can be understood that a surface net flux calculation system based on a frequency-domain soil moisture equation provided by the present invention corresponds to a surface net flux calculation method based on a frequency-domain soil moisture equation provided in each of the foregoing embodiments. The relevant technical features of a surface net flux calculation system based on a frequency-domain soil moisture equation can refer to the relevant technical features of a surface net flux calculation method based on a frequency-domain soil moisture equation, which will not be elaborated herein.

[0070] According to a third aspect of the present invention, there is provided an electronic device, including an acquirer, a processor, a display and an outputter, and a computer program stored on the memory and executable on the processor. The processor executes the program to perform a surface net flux calculation method based on a frequency-domain soil moisture equation.

[0071] In addition, when the logical instructions in the above-mentioned memory are implemented in the form of a software functional unit and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or a part of this technical solution can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as a USB flash drive, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk, or an optical disc that can store program codes.

[0072] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the appended claims are intended to be construed as including the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0073] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating surface net flux based on a frequency-domain soil moisture equation, characterized in that, Including: Establish a frequency-domain soil water movement model for the variation of soil water with depth under the condition of a single-frequency fluctuating flux at the upper boundary; Based on discrete Fourier decomposition, perform frequency-domain decomposition on the time-series observation data of soil water at the site and the upper flux boundary to obtain the frequency components of the upper flux and soil water; Using the frequency-domain soil water movement model, calibrate the soil parameters according to the obtained frequency components of the upper flux and soil water; Perform discrete Fourier decomposition on the soil water time series at any depth to extract soil water fluctuation signals at different frequencies; According to the obtained soil water fluctuation signals at different frequencies and the frequency-domain soil water movement model, perform back-calculation on the soil water at different frequencies to obtain the surface net fluxes at different frequencies and superimpose them in the time domain; Combined with remote sensing data, obtain the surface net fluxes in the regional scope according to the surface net fluxes obtained from the long-term soil water series; 2. The method for calculating the surface net flux based on the frequency-domain soil moisture equation according to claim 1, wherein The establishment of the frequency-domain soil water movement model for the variation of soil water with depth under the condition of a single-frequency fluctuating flux at the upper boundary is expressed as follows: When there is a single periodic flux flowing into the soil, the inflow at the top of the soil is expressed as a stability constant plus the frequency and the amplitude of the periodic fluctuating soil moisture. In the complex domain, it is expressed as , then under this flux, the variation of the generated soil moisture with depth is expressed as: In the formula, is the complex unit; is the angular frequency of the fluctuation; t is the time; z is the soil depth; θ c (z) is the stable component of soil moisture at depth z ; θ p (z) is a complex number representing the fluctuation of soil moisture at depth z; |θ p | is the amplitude of the fluctuating soil moisture; K s is the saturated hydraulic conductivity; α is the characteristic parameter of the Gardner-Kozeny model; λ is a complex number.

3. A method for calculating the surface net flux based on the frequency-domain soil moisture equation according to claim 1, characterized in that, The frequency-domain decomposition of the time-series observation data of soil water at the site and the upper flux boundary based on discrete Fourier decomposition to obtain the frequency components of the upper flux and soil water includes: By the discrete Fourier decomposition method, decompose the time-domain signal into a superposition of sine waves and cosine waves with set frequencies, amplitudes, and phases. Among them, the amplitude and phase corresponding to each frequency component reflect the contribution intensity and phase characteristics of that frequency in the time series.

4. The method for calculating the surface net flux based on the frequency domain soil moisture equation according to claim 3, characterized in that, The amplitude of each identified frequency component and phase are quantized to: In the formula, Re(.) and Im(.) respectively represent the real part and the imaginary part of a complex number, and atan2(.) is the arctangent function.

5. A method for calculating the surface net flux based on the frequency-domain soil moisture equation according to claim 1, characterized in that The calibration of soil parameters using the frequency-domain soil water movement model according to the obtained frequency components of the upper flux and soil water includes: Based on the frequency-domain soil water movement model, calculate the comparison between the simulated value of soil water and the actual observed value, and verify whether the soil water observation data is consistent with the model simulated value according to the calculation result.

6. The calculation method of the surface net flux based on the frequency-domain soil moisture equation according to claim 1, wherein The discrete Fourier decomposition of the soil water time series at any depth to extract soil water fluctuation signals at different frequencies includes: Consider the soil moisture variations of different depth z profiles for a long time series ( z , t ), which are decomposed into a steady-state term and a fluctuation term by the discrete Fourier decomposition method and expressed as: In the formula, is the steady-state soil moisture content, reflecting the average soil water in the time series, is the complex form of soil moisture fluctuation, represents the amplitude, indicating the magnitude of the contribution of soil water with different frequency components, is the angular frequency of the fluctuation, and the index j = 1, 2… is the serial number of the frequency.

7. A method for calculating the surface net flux based on the frequency-domain soil moisture equation according to claim 1, characterized in that, The back-calculation of soil water at different frequencies according to the obtained soil water fluctuation signals at different frequencies and the frequency-domain soil water movement model to obtain the surface net fluxes at different frequencies and superimpose them in the time domain includes: If the soil moisture fluctuation θ p (z) at a certain depth is known, then the fluctuation flux of the surface soil q p is back-calculated from θ p (z) and is expressed as: In this model, θ p (z) and q p (z) are all complex numbers.

8. A method for calculating the surface net flux based on the frequency-domain soil moisture equation according to claim 1, characterized in that, The combination of remote sensing data to obtain the surface net fluxes in the regional scope according to the surface net fluxes obtained from the long-term soil water series includes: If the soil moisture changes θ(z, t) at different depths of a long time series are known z the profile is decomposed into a steady-state term and a series of fluctuating terms by using the discrete Fourier decomposition method. At this time, the surface net flux is expressed as: Finally, according to a long-term soil water data, the surface net flux data is obtained.

9. A surface net flux calculation system based on a frequency-domain soil moisture equation, characterized in that, Including: A frequency-domain soil water movement model establishment module for establishing a frequency-domain soil water movement model for the variation of soil water with depth under the condition of a single-frequency fluctuating flux at the upper boundary; A frequency component acquisition module for performing frequency-domain decomposition on the time-series observation data of soil water at the site and the upper flux boundary based on the discrete Fourier decomposition method to obtain the frequency components of the upper flux and soil water; and calibrating the soil parameters using the frequency-domain soil water movement model according to all the obtained frequency components of the upper flux and soil water; The surface net flux acquisition module is used to perform discrete Fourier decomposition on the soil moisture time series for the next time period and any depth, extract the soil moisture fluctuation signals at different frequencies; according to the obtained parameters and the frequency-domain soil moisture movement model, perform back-calculation on the soil moisture at different frequencies, obtain the surface net flux signals at different frequencies and superimpose them in the time domain; The surface net flux acquisition module is used to combine remote sensing data and obtain the surface net flux within the regional scope based on the surface net flux obtained from the long-term soil water series.

10. An electronic device, characterized in that, It includes: An acquirer, a processor, a display and an outputter, and a computer program stored on the memory and executable on the processor, and the processor executes the program to implement a method for calculating the surface net flux based on the frequency-domain soil moisture equation according to any one of claims 1 to 8.

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