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

Abstract

The present invention provides a method and system for calculating surface net flux based on a frequency-domain soil moisture equation. The method comprises: establishing a frequency-domain soil moisture movement model that shows how soil moisture varies with depth; performing frequency-domain decomposition on site soil moisture time series observation data and upper flux boundaries; calibrating soil parameters based on the obtained upper flux and soil moisture frequency components; performing discrete Fourier decomposition on the soil moisture time series for the next time period and at any depth to extract soil moisture fluctuation signals at different frequencies; inversely calculating soil moisture at different frequencies based on the obtained parameters and model to obtain surface net flux signals at different frequencies, which are then superimposed in the time domain; and combining remote sensing data with long-term soil moisture data to obtain regional surface net flux. By transforming time-domain problems into the frequency domain, the present invention facilitates processing long-term soil moisture series and reduces the increased computational effort caused by dividing the long-term series into stepwise calculations.

Description

Technical Field

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

[0002] The net surface flux is the difference between infiltration (i.e., precipitation and irrigation minus surface runoff) and evapotranspiration (ET). The two work together to produce the net water flux. q = I - ET. This flux determines the terrestrial water balance (i.e., the total amount of groundwater resources that can be replenished). Net surface flux is closely related to soil moisture content and the groundwater level. Once water enters the vadose zone, a portion is consumed by evaporation and plant transpiration in the shallow soil layer, while the remainder gradually migrates downward through the zero-flux surface of the vadose zone, ultimately entering the aquifer. Because this portion of water ultimately flows into the aquifer and forms groundwater, it is considered potential groundwater recharge, and its recharge flux is equivalent to soil water seepage. Net surface flux is a crucial component of groundwater resource assessment and has important theoretical and practical implications for the rational development and utilization of groundwater resources. A sound assessment of net surface flux can help prevent disasters caused by overexploitation of groundwater.

[0003] Traditional methods for quantifying net surface fluxes primarily include direct measurement, which uses lysimeters to obtain localized seepage data. While these methods offer high accuracy, they are difficult to implement on a large scale due to the high cost of equipment construction and maintenance. Therefore, there is an urgent need to develop indirect measurement methods based on readily observable data, such as soil moisture content and dynamic changes in groundwater depth. Groundwater level observations indirectly calculate potential groundwater recharge fluxes using groundwater level data and specific water content estimates. This method is simple and efficient, and does not rely on assumptions about recharge processes (such as the existence of preferential flow pathways). However, it cannot clearly reveal the direct relationship between precipitation and recharge, limiting its applicability for future recharge predictions in the context of climate change. Vadose zone hydrological models, based on the Richards equation and combined with instantaneous observational data (such as soil moisture content and pressure head), can infer recharge fluxes. These models can simulate complex processes such as soil water transport, heat and energy balance, and plant water uptake, enabling large-scale net flux predictions. However, this model is highly dependent on the accuracy of soil hydrological parameters and is subject to 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 with computational convenience, rationally incorporate information on the spatial gradient of soil moisture, and optimize the coordination between "internal conditions" and "boundary conditions" to improve the model's predictive reliability.

[0004] In recent years, analytical solutions based on the Richards equation have demonstrated significant advantages in inverting and calculating net water fluxes. First, by optimizing the analytical model of the Richards equation, this method takes into account the soil moisture movement process and several reasonable simplifying assumptions. While ensuring physical significance, it effectively simplifies the parameter acquisition process and balances the complexity of the model with the efficiency of calculation. Second, the analytical solution method does not rely on spatial gradient information of soil moisture, which greatly improves the convenience and operability of observations. Finally, with the widespread application of aerial and satellite remote sensing technologies in large-scale soil moisture observations, analytical methods can directly use surface soil water data to infer surface net fluxes, enhance the coupling of large-scale and small-scale data, and significantly improve the spatial applicability and reliability of the estimation results.

[0005] Although analytical methods in the time domain can directly infer fluxes from single-layer soil water data, the computational process for deriving fluxes from analytical solutions is complex, requiring the inverse calculation of the already complex analytical soil water solution. Furthermore, for long-term soil water data series, they must be divided into different time periods for step-by-step calculation, which significantly increases the computational effort with the length of the time series. Therefore, it is necessary to develop a surface net flux calculation model based on frequency-domain soil water. By using the analytical solution of the frequency-domain soil water equation and soil water fluctuations at arbitrary depths, the surface net flux can be inferred. By superimposing fluctuations of different frequencies in the time domain, a method for calculating surface net fluxes from long-term series is developed. Summary of the Invention

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

[0007] According to a first aspect of the present invention, a method for calculating surface net flux based on a frequency domain soil moisture equation is provided, comprising the following steps:

[0008] Step 1. Establish a frequency-domain soil moisture movement model in which soil moisture varies with depth under the condition of a single-frequency fluctuation flux at the upper boundary.

[0009] Step 2. Based on discrete Fourier decomposition, the time series observation data of soil water at the site and the upper flux boundary are decomposed in the frequency domain to obtain the frequency components of the upper flux and soil water;

[0010] Step 3. Using the frequency domain soil water movement model, calibrate soil parameters based on the obtained upflux and frequency components of soil water;

[0011] Step 4. Perform discrete Fourier decomposition on the soil moisture time series at any depth to extract soil moisture fluctuation signals of different frequencies;

[0012] Step 5. Based on the acquired soil moisture fluctuation signals of different frequencies and the frequency domain soil moisture movement model, the soil moisture at different frequencies is back-calculated to obtain the surface net flux at different frequencies and superimposed in the time domain;

[0013] Step 6. Combine remote sensing data with the surface net flux obtained from the long-term soil water series to obtain the regional surface net flux.

[0014] On the basis of the above technical solution, the present invention can also make the following improvements.

[0015] Optionally, establishing a frequency-domain soil moisture movement model in which soil moisture varies with depth under the condition of a single-frequency fluctuation flux at the upper boundary includes:

[0016] When a single periodic flux flows into the soil, the inflow from the top of the soil Expressed as a stability constant Add a frequency and amplitude The periodic fluctuation of soil moisture is expressed in the complex domain as , then under this flux, the variation of soil moisture with depth is expressed as:

[0017]

[0018] Where, is a plural 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 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 soil moisture fluctuation; K s is the saturated hydraulic conductivity; α is the characteristic parameter of the Gardner-Kozeny model; λ is a complex number.

[0019] Optionally, the frequency-domain decomposition of the time series observation data of soil water at the site and the upper flux boundary is performed based on discrete Fourier decomposition to obtain frequency components of the upper flux and soil water, including:

[0020] Through the discrete Fourier decomposition method, the time domain signal is decomposed into a superposition of sine waves and cosine waves with set frequency, amplitude and phase. The amplitude and phase corresponding to each frequency component reflect the contribution intensity and phase characteristics of the frequency in the time series.

[0021] Optionally, the amplitude of each identified frequency component and phase Quantified as:

[0022]

[0023] In the formula, Re(.) and Im(.) represent the real part and imaginary part of the complex number respectively, is the first j frequency components; N is the total number of sampling points in the time series, and atan2(.) is the inverse tangent function.

[0024] Optionally, the calibrating of soil parameters using the frequency domain soil moisture movement model according to the obtained upflux and the frequency component of soil water includes:

[0025] Based on the frequency domain soil moisture movement model, the simulated soil moisture values ​​and the actual observed values ​​are calculated, and the consistency between the soil moisture observation data and the model simulation values ​​is verified based on the calculation results.

[0026] Optionally, performing discrete Fourier decomposition on the soil moisture time series at any depth to extract soil moisture fluctuation signals of different frequencies includes:

[0027] Considering the long-term soil moisture variation θ(z, t) at different depths z, the discrete Fourier decomposition method is used to decompose it into steady-state terms and fluctuation terms, which can be expressed as:

[0028]

[0029] Where, is the steady-state soil moisture, reflecting the average soil moisture in the time series. is the plural form of soil moisture fluctuation, The amplitude represents the contribution of soil water to different frequency components. ω j is the angular frequency of the fluctuation, index j = 1,2… are the frequency numbers.

[0030] Optionally, combining remote sensing data with a surface net flux obtained from a long-term soil water sequence to obtain a regional surface net flux includes:

[0031] Different depths of known long time series z The soil moisture variation of the profile θ(z, t) is decomposed into steady-state terms using the discrete Fourier decomposition method and a series of fluctuation terms , at this time, the net flux on the surface is expressed as:

[0032]

[0033] Where: is a plural unit; ω j is the angular frequency of the fluctuation, index j = 1,2… is the frequency sequence number; t For time; z is the depth of soil water observation; θs and θr represent the saturated soil moisture content and residual soil moisture content, respectively; θ c (z) is the depth z The stable component of soil moisture at θ; p (z) is a complex number representing the fluctuation of soil moisture at depth z; |θ p | is the amplitude of fluctuation soil moisture; K s is the saturated hydraulic conductivity; α is the characteristic parameter of the Gardner-Kozeny model; λ is plural;

[0034] Finally, the surface net flux data was obtained based on a long-term soil moisture data. q ( t ).

[0035] According to a second aspect of the present invention, there is provided a surface net flux calculation system based on a frequency domain soil moisture equation, comprising:

[0036] Frequency domain soil moisture movement model establishment module, used to establish a frequency domain soil moisture movement model of soil moisture variation with depth under the condition of single frequency fluctuation flux at the upper boundary;

[0037] The frequency component acquisition module is used to perform frequency domain decomposition on the time series observation data of soil water at the site and the upflux boundary based on the discrete Fourier decomposition method to obtain the frequency components of upflux and soil water. The frequency domain soil water movement model is then used to calibrate soil parameters based on all the obtained upflux and soil water frequency components.

[0038] 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 at any depth to extract soil moisture fluctuation signals at different frequencies. Based on the acquired parameters and the frequency-domain soil moisture movement model, the soil moisture at different frequencies is back-calculated to obtain the surface net flux signals at different frequencies and superimpose them in the time domain.

[0039] The surface net flux acquisition module is used to combine remote sensing data with the surface net flux obtained from long-term soil water series to obtain the regional surface net flux.

[0040] According to a third aspect of the present invention, an electronic device is provided, comprising an acquirer, a processor, a display and output device, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to perform a surface net flux calculation method based on the frequency domain soil moisture equation.

[0041] Technical effects and advantages of the present invention:

[0042] The present invention provides a surface net flux calculation method and system based on the frequency-domain soil moisture equation. By first utilizing the analytical solution of the frequency-domain soil water equation and soil moisture fluctuations at any depth, the surface net flux is inferred, and fluctuations of different frequencies are superimposed in the time domain to obtain a method for solving the surface net flux using a long-term series. Compared with previous time-domain analytical solution methods, the present invention does not have a complex inverse operation process, and the calculation method is simple and easy to understand. Compared with previous numerical methods, the present invention has better applicability to actual long-term soil moisture series and exhibits lower computational cost, providing feasibility for using remote sensing surface soil moisture data to achieve large-scale surface net water flux estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 A flow chart of a method for calculating surface net flux based on the frequency domain soil moisture equation provided by an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of the upper boundary flux steady state and fluctuation terms of a single-frequency fluctuation provided by an embodiment of the present invention;

[0046] Figure 3The above diagram shows the effect of upflow observation and soil moisture observation provided by the embodiment of the present invention and the decomposition and fitting method using the discrete Fourier decomposition method. Figure 3 (a) in the figure shows the fitting of the upper flux by the discrete Fourier decomposition method. Figure 3 (b) shows the fitting of soil water by discrete Fourier decomposition method;

[0047] Figure 4 A comparison chart of soil moisture simulation values ​​calculated by the frequency-domain-based soil moisture model provided in an embodiment of the present invention and actual observed values;

[0048] Figure 5 A comparison chart of the fitted value of the upper flux boundary obtained by using a frequency domain algorithm based on soil moisture observations and the actual observed value provided by an embodiment of the present invention;

[0049] Figure 6 The embodiment of the present invention provides a method for inferring the upper flux simulation value of the Hetao Irrigation District based on the SMAP soil moisture observation value in the Hetao Irrigation District. Figure 6 (a) shows the temporal variation of soil water content in all grids in the Hetao Irrigation District, and the soil water content in all grids is averaged. Figure 6 (b) uses the proposed algorithm and calibrated parameters to calculate the temporal variation of the surface net flux of all grids in the Hetao region. DETAILED DESCRIPTION

[0050] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0051] It is understandable that, based on the defects in the background technology, the embodiment of the present invention proposes a surface net flux calculation method based on the frequency domain soil moisture equation, specifically as follows: Figure 1 As shown, the following steps are included:

[0052] Step 1: Establish a frequency domain soil moisture movement model in which soil water varies with depth under the condition of a single frequency fluctuation flux at the upper boundary;

[0053] In this embodiment, establishing a frequency domain soil moisture movement model includes:

[0054] Assuming a single periodic flux into the soil, the inflow from the top of the soil Expressed as a stability constant Add a frequency and amplitude The periodic fluctuation of soil moisture is expressed in the complex domain as , then under this flux, the variation of soil moisture with depth is expressed as:

[0055]

[0056] Where, is a plural unit, ω j is the angular frequency of the fluctuation, t For time, z is the soil depth, θ c (z) For depth z The stable component of soil moisture at θ p (z) Plural, indicating depth z Fluctuation of soil moisture at p is the amplitude of soil moisture fluctuation, arg(θ p ) is the phase angle of fluctuating soil moisture, arg(θ p ) is a periodic function ranging from -π to π. s and θ r represent the saturated moisture content and residual moisture content of the soil, K s is the saturated hydraulic conductivity, α is the characteristic parameter of the Gardner-Kozeny model, λ is plural;

[0057] Depend on Decision, among which:

[0058]

[0059] Step 2: Decompose the time series observation data of soil water and the upper flux boundary of the site in the frequency domain based on discrete Fourier decomposition to obtain the frequency components of the upper flux and soil water;

[0060] In this embodiment, the basic mathematical expression of the Discrete Fourier Transform method is as follows:

[0061]

[0062] Where, y n for t n The observation value of the sampling point at time, N is the total number of sampling points in the time series, is the firstj frequency components, is the mean of the sample.

[0063] The amplitude of each identified frequency component and phase It can be quantified as:

[0064]

[0065] Where Re(.) and Im(.) represent the real and imaginary parts of the complex number, respectively, and atan2(.) is the inverse tangent function.

[0066] Using discrete Fourier decomposition, a time domain signal can be decomposed into a series of sine and cosine waves with specific frequencies, amplitudes, and phases. The amplitude and phase corresponding to each frequency component reflect the contribution strength and phase characteristics of that frequency in the time series.

[0067] Step 3: Using the frequency domain soil water movement model, the soil parameters are calibrated based on all the obtained upfluxes and frequency components of soil water;

[0068] In this embodiment, based on the soil moisture movement model in the frequency domain, the soil moisture simulation value and the actual observation value are compared, and the root mean square error and goodness of fit are calculated. R 2 , based on the calculation results, the consistency between the soil moisture observation data and the model simulation was verified, laying the foundation for the subsequent model-based derivation of the surface net flux.

[0069] Step 4: Perform discrete Fourier decomposition on the soil moisture time series at any depth to extract soil moisture fluctuation signals of different frequencies;

[0070] In this implementation step, a long-term series of soil moisture changes θ(z, t) at different depths z can be considered and decomposed into steady-state terms and fluctuation terms using the discrete Fourier decomposition method:

[0071]

[0072] Where, is the steady-state soil moisture, reflecting the average soil moisture in the time series. is the plural form of soil moisture fluctuation, The amplitude represents the contribution of soil water to different frequency components. ω j is the angular frequency of the fluctuation, index j = 1,2… are the frequency numbers.

[0073] Step 5: Based on the acquired parameters and the frequency domain soil moisture movement model, the soil moisture at different frequencies is back-calculated to obtain the surface net flux signals at different frequencies and superimpose them in the time domain;

[0074] In this implementation step, based on the acquired parameters and the frequency domain soil moisture movement model, if the soil moisture fluctuation θ at a certain depth is known, p (z), then the fluctuation flux of the surface soil q p It can be determined by θ p (z) is calculated inversely and expressed as:

[0075]

[0076] In this model, θ p (z) and q p (z) All are plural.

[0077] Given a long time series of soil moisture changes θ(z, t) at different depths z, the discrete Fourier decomposition method is used to decompose it into steady-state terms: and a series of fluctuation terms , at this time, the net surface flux can be expressed as:

[0078]

[0079] Finally, the surface net flux data is obtained based on the long-term soil moisture data. Therefore, the surface net flux calculation method based on the frequency-domain soil moisture equation described in this embodiment of the invention can invert the surface net flux based on the long-term soil moisture data series.

[0080] The above method is further described below with reference to a specific embodiment. The surface net flux calculation method based on the frequency domain soil moisture equation specifically includes the following steps:

[0081] Step 1. Establish an equation for the variation of soil water with depth under the condition of a single-frequency fluctuation flux at the upper boundary. The model is established based on the Richards equation, which is used to describe the one-dimensional, vertical movement of soil water. The Richards equation is derived from Darcy's law and the mass conservation equation. Darcy's law for soil water movement is described as:

[0082]

[0083] Where q is the Darcy velocity, h is the unsaturated soil matrix potential, z is the position head, and K is the unsaturated hydraulic conductivity. Ignoring source and sink terms such as root water absorption, the mass conservation equation is:

[0084]

[0085] Where, θ is the soil moisture content. Substituting this into the time domain, we can get the Richards equation:

[0086]

[0087] Furthermore, the Gardner-Kozeny model (GK model) is introduced to describe the unsaturated hydraulic conductivity curve. K ~ θ and soil moisture characteristic curve h The significant advantage of the GK model (exponential model) is that the hydraulic diffusivity it describes presents a linear relationship, which simplifies the complexity of the equation. The expression is as follows:

[0088]

[0089] Where, α is the characteristic parameter of the GK model, parameter h e is the negative pressure of the inlet, reflecting the maximum pore size of the continuous flow channel in the medium. s and θ r represent the saturated moisture content and residual moisture content of the soil, K s is the saturated hydraulic conductivity. h > h e When θ = θ s , unsaturated hydraulic conductivity K = K s , that is, saturated hydraulic conductivity.

[0090] Furthermore, by substituting equation (12) into equation (11) and performing a series of transformations, we can obtain:

[0091]

[0092] Equation (13) is similar to a classical diffusion equation, where v is similar to the advection velocity, given by Decide.

[0093] Considering a single periodic flux into the soil, the inflow from the top of the soil Expressed as a stability constant Add a frequency and amplitude The periodic fluctuation of soil moisture is expressed in the complex domain as, , Figure 2 Schematic diagram showing the steady-state upper boundary flux of single-frequency fluctuation and the time variation of the fluctuation term.

[0094] Furthermore, because K and q The relationship between t Irrelevant (see equation (9)), similarly, the variable K It can also be expressed as a stability constant Add a frequency and amplitude The unsaturated hydraulic conductivity of is expressed in the complex domain as, . The steady-state component and the fluctuation component Substitute into equation (13) and eliminate term, and obtain a description of the stable component K c (z) The soil water movement is represented by an ordinary differential equation and an ordinary differential equation describing the wave component:

[0095]

[0096] Furthermore, considering the lower boundary as a free drainage boundary, the solution of equations (14) and (15) is:

[0097]

[0098] Where, λ is plural, by Decision, among which:

[0099]

[0100] In the case of a single-frequency fluctuating flux at the upper boundary, the movement of soil water can be obtained by substituting equations (16) and (17) into equation (12):

[0101]

[0102] Where, is a plural unit, ω j is the angular frequency of the fluctuation, t For time, z is the soil depth, θ c (z) For depth z The stable component of soil moisture at p (z) Plural, indicating depth z Fluctuation of soil moisture at |θ p | is the amplitude of soil moisture fluctuation, arg(θ p ) is the phase angle of fluctuating soil moisture, arg(θ p) is a periodic function ranging from -π to π.

[0103] Step 2. Decompose the time series observation data of flux and soil water at the site in the time domain based on the discrete Fourier decomposition method to obtain components in the frequency domain.

[0104] The basic mathematical expression of the discrete Fourier decomposition method is as follows:

[0105]

[0106] Where, y n for t n The observation value of the sampling point at time, N is the total number of sampling points in the time series, is the first j frequency components, is the average value of the samples. The amplitude of each identified frequency component and phase It can be quantified as:

[0107]

[0108] Where Re(.) and Im(.) represent the real and imaginary parts of the complex number, respectively, and atan2(.) is the inverse tangent function.

[0109] Furthermore, using discrete Fourier decomposition, the time domain signals of soil water and upwelling flux can be decomposed into a superposition of a series of sine and cosine waves with specific frequencies, amplitudes, and phases. The amplitude and phase corresponding to each frequency component reflect the contribution strength and phase characteristics of that frequency in the time series.

[0110] Figure 3 This example shows the temporal variation of upwelling flux and soil moisture observed in an embodiment of the present invention, along with the results of discrete Fourier decomposition and fitting. The upwelling flux observation consists of rainfall plus irrigation minus evapotranspiration. Fitting was performed using 500 key frequencies. The results demonstrate that discrete Fourier decomposition can accurately convert time-domain data into frequency-domain data. Figure 3 (a) in the figure represents the fitting of the upper flux by discrete Fourier decomposition. Figure 3 (b) shows the fitting of soil water by discrete Fourier decomposition. The goodness of fit R2 of both methods is above 0.99, which proves that the discrete Fourier decomposition method can be used to convert time domain data into frequency domain.

[0111] Step 3. Using the obtained frequency domain soil water movement model, calibrate the GK soil parameters according to all the obtained upfluxes and frequency components of soil water;

[0112] Figure 4 The frequency domain-based soil moisture model in the embodiment of the invention is shown, and the calculated soil moisture simulation value and the actual observation value are compared. RMSE = 0.021, goodness of fit R 2 The result reached 0.76, which verified the good consistency between the soil moisture observation data and the model simulation, and laid a solid foundation for the subsequent model-based derivation of the surface net flux.

[0113] Figure 5 The comparison between the surface net flux in 2023 calculated based on the frequency method and the daily average of the actual observed net flux is shown in the embodiment of the invention using the parameters determined by the rate of utilization, combined with the soil moisture observation data at a depth of 20 cm. The fitting results show 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 Although the model's simulated values ​​under evaporation conditions are slightly lower than the actual observed values, it shows extremely high fitting accuracy for the positive net fluxes caused by rainfall and irrigation.

[0114] Step 4. Consider a long series of soil moisture changes at different depth z profiles θ(z, t) , decompose it into steady-state terms and fluctuation terms by discrete Fourier decomposition:

[0115]

[0116] Where, is the steady-state soil moisture, reflecting the average soil moisture in the time series. is the plural form of soil moisture fluctuation, The amplitude represents the contribution of soil water to different frequency components. ω j is the angular frequency of the fluctuation, index j = 1,2… are the frequency numbers.

[0117] In step 5, according to the model in step 1, if the soil moisture fluctuation θ at a certain depth is known p (z), then the fluctuation flux of the surface soil q p It can be determined by θ p (z) is calculated inversely and expressed as:

[0118]

[0119] In this model, θ p (z) and qp ( z ) are all plural.

[0120] Furthermore, given a long time series with different depths z The soil moisture variation of the profile θ(z, t) is decomposed into steady-state terms using the discrete Fourier decomposition method and a series of fluctuation terms , at this time, the net flux on the surface is expressed as:

[0121] (25)

[0122] At this time, the surface net flux data was obtained based on a long period of soil moisture data. .

[0123] Figure 6 This paper presents soil water data based on SMAP remote sensing, combined with the frequency-domain soil water content estimation algorithm proposed in this example, and using the soil parameters calibrated in step 3, obtains the temporal variation pattern of the net surface flux in the Hetao Irrigation District from April 2016 to November 2024. Figure 6 (a) shows the temporal variation of soil water content in all grids in the Hetao Irrigation District, and the soil water content of all grids is averaged. Figure 6 (b) in the figure uses the algorithm and calibrated parameters proposed in this embodiment to calculate the changes in the surface net flux of all grids in the Hetao region over time.

[0124] Therefore, the surface net flux calculation method based on the frequency domain soil moisture equation described in the embodiment of the present invention can invert the surface net flux based on the long time series soil moisture data. Compared with the existing technology, the embodiment of the present invention uses the analytical solution of the frequency domain soil water equation for the first time to obtain a method for solving the surface net flux of a long time series. Compared with the previous time domain analytical solution method, the present invention does not have a complicated inverse operation process and the calculation method is simple; compared with the previous numerical method, the present invention has better applicability to actual long-term soil moisture series and shows a lower computational cost, which provides unprecedented possibilities for realizing large-scale surface net water flux estimation using remote sensing surface soil moisture data.

[0125] According to a second aspect of the present invention, the present invention further provides a surface net flux calculation system based on a frequency domain soil moisture equation, comprising:

[0126] Frequency domain soil moisture movement model establishment module, used to establish a frequency domain soil moisture movement model of soil moisture variation with depth under the condition of single frequency fluctuation flux at the upper boundary;

[0127] The frequency component acquisition module is used to perform frequency domain decomposition on the time series observation data of soil water at the site and the upflux boundary based on the discrete Fourier decomposition method to obtain the frequency components of upflux and soil water. The frequency domain soil water movement model is then used to calibrate soil parameters based on all the obtained upflux and soil water frequency components.

[0128] 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 at any depth to extract soil moisture fluctuation signals at different frequencies. Based on the acquired parameters and the frequency-domain soil moisture movement model, the soil moisture at different frequencies is back-calculated to obtain the surface net flux signals at different frequencies and superimpose them in the time domain.

[0129] The surface net flux acquisition module is used to combine remote sensing data with the surface net flux obtained from long-term soil water series to obtain the regional surface net flux.

[0130] It can be understood that the surface net flux calculation system based on the frequency domain soil moisture equation provided by the present invention corresponds to the surface net flux calculation method based on the frequency domain soil moisture equation provided in the aforementioned embodiments. The relevant technical features of a surface net flux calculation system based on the frequency domain soil moisture equation can refer to the relevant technical features of a surface net flux calculation method based on the frequency domain soil moisture equation, which will not be repeated here.

[0131] According to a third aspect of the present invention, an electronic device is provided, comprising an acquirer, a processor, a display and output device, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to perform a surface net flux calculation method based on the frequency domain soil moisture equation.

[0132] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the 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 enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0133] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0134] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A surface net flux calculation method based on the frequency domain soil moisture equation, characterized in that: include: A frequency domain soil moisture movement model is established in which soil moisture varies with depth under the condition of a single frequency fluctuation flux at the upper boundary. Based on discrete Fourier decomposition, the time series observation data of soil water at the site and the upper flux boundary are decomposed in the frequency domain to obtain the frequency components of the upper flux and soil water. Using the frequency domain soil water movement model, soil parameters are calibrated based on the obtained upflux and frequency components of soil water. The soil moisture time series at any depth is subjected to discrete Fourier decomposition to extract soil moisture fluctuation signals of different frequencies; Based on the obtained soil moisture fluctuation signals of different frequencies and the frequency domain soil moisture movement model, the soil moisture at different frequencies is back-calculated to obtain the surface net flux at different frequencies and superimpose them in the time domain. Combined with remote sensing data, the surface net flux at the regional scale is obtained based on the surface net flux obtained from long-term soil water series.

2. The surface net flux calculation method based on the frequency domain soil moisture equation according to claim 1 is characterized in that: The frequency domain soil moisture movement model for the soil moisture variation with depth under the condition of single frequency fluctuation flux at the upper boundary is expressed as follows: When a single periodic flux flows into the soil, the inflow from the top of the soil Expressed as a stability constant Add frequency and amplitude The periodic fluctuation of soil moisture is expressed in the complex domain as, , then under this flux, the variation of soil moisture with depth is expressed as: Where, is a plural unit; is the angular frequency of the fluctuation; t For time; z is the soil depth; θs and θr represent the soil saturated moisture content and residual moisture content, respectively; θ c (z) is the depth z The stable component of soil moisture at θ; p (z) is a complex number representing the fluctuation of soil moisture at depth z; |θ p | is the amplitude of fluctuation of soil moisture; K s is the saturated hydraulic conductivity; α is the characteristic parameter of the Gardner-Kozeny model; λ plural.

3. The surface net flux calculation method based on the frequency domain soil moisture equation according to claim 1 is characterized in that: The discrete Fourier decomposition is used to 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, including: Through the discrete Fourier decomposition method, the time domain signal is decomposed into a superposition of sine waves and cosine waves with set frequency, amplitude and phase, where the amplitude and phase corresponding to each frequency component reflect the contribution intensity and phase characteristics of the frequency in the time series.

4. The surface net flux calculation method based on the frequency domain soil moisture equation according to claim 3 is characterized in that: The amplitude of each identified frequency component and phase Quantified as: In the formula, Re(.) and Im(.) represent the real part and imaginary part of the complex number respectively, is the first j frequency components; N is the total number of sampling points in the time series, and atan2(.) is the inverse tangent function.

5. The surface net flux calculation method based on the frequency domain soil moisture equation according to claim 1 is characterized in that: The method of calibrating soil parameters using the frequency domain soil moisture movement model according to the obtained upflux and the frequency component of soil water includes: Based on the frequency domain soil moisture movement model, the simulated soil moisture values ​​and the actual observed values ​​are calculated, and the consistency between the soil moisture observation data and the model simulation values ​​is verified based on the calculation results.

6. The surface net flux calculation method based on the frequency domain soil moisture equation according to claim 1 is characterized in that: The method of performing discrete Fourier decomposition on the soil moisture time series at any depth to extract soil moisture fluctuation signals of different frequencies includes: Considering the soil moisture changes at different depth z profiles of long time series ( z , t ), which is decomposed into steady-state terms and fluctuation terms by discrete Fourier decomposition method, expressed as: Where, is the steady-state soil moisture, reflecting the average soil moisture in the time series. is the plural form of soil moisture fluctuation, Represents the amplitude, indicating the contribution of soil water at different frequency components. is the angular frequency of the fluctuation, index j = 1,2… are the frequency numbers.

7. The surface net flux calculation method based on the frequency domain soil moisture equation according to claim 1 is characterized in that: The back-calculation of soil moisture at different frequencies based on the acquired soil moisture fluctuation signals at different frequencies and the frequency domain soil moisture movement model to obtain the surface net flux at different frequencies and superimpose them in the time domain includes: If the soil moisture fluctuation θ at a certain depth is known p (z), then the fluctuation flux of the surface soil q p By θ p (z) is calculated inversely and expressed as: In this model, θs and θr represent the saturated soil moisture content and residual soil moisture content, respectively. λ is plural, K s is the saturated hydraulic conductivity; α is the characteristic parameter of the Gardner-Kozeny model, z is the depth of soil water observation; θ p (z) and q p (z) are all complex numbers, representing the fluctuation of soil moisture at depth z.

8. The surface net flux calculation method based on the frequency domain soil moisture equation according to claim 7 is characterized in that: The surface net flux obtained by combining remote sensing data with the long-term soil water series to obtain the regional surface net flux includes: If we know the different depths of a long time series z The soil moisture variation of the profile θ(z, t) is decomposed into steady-state terms using the discrete Fourier decomposition method and a series of fluctuation terms , ω j is the discrete frequency j angular frequency, at this time, the net flux on the surface is expressed as: Where: is a plural unit; ω j is the angular frequency of the fluctuation, index j = 1,2… is the frequency sequence number; t is time; θ c (z) is the depth z The stable component of soil moisture at θs and θr represent the saturated soil moisture content and residual soil moisture content, respectively. p (z) is a complex number, representing the fluctuation of soil moisture at depth z; |θ p | is the amplitude of fluctuation soil moisture; Finally, the surface net flux was obtained based on a long-term soil moisture data. q ( t ).

9. A surface net flux calculation system based on the frequency domain soil moisture equation, characterized in that: include: Frequency domain soil moisture movement model establishment module, used to establish a frequency domain soil moisture movement model of soil moisture variation with depth under the condition of single frequency fluctuation flux at the upper boundary; The frequency component acquisition module is used to perform frequency domain decomposition on the time series observation data of soil water at the site and the upflux boundary based on the discrete Fourier decomposition method to obtain the frequency components of upflux and soil water. The frequency domain soil water movement model is then used to calibrate soil parameters based on all the obtained upflux and soil water frequency components. 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 at any depth to extract soil moisture fluctuation signals at different frequencies. Based on the acquired parameters and the frequency-domain soil moisture movement model, the soil moisture at different frequencies is back-calculated to 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 with the surface net flux obtained from long-term soil water series to obtain the regional surface net flux.

10. An electronic device, characterized in that: include: An acquirer, a processor, a display and an output device, and a computer program stored in a memory and capable of running on the processor, wherein the processor executes the computer program to implement a surface net flux calculation method based on the frequency domain soil moisture equation as described in any one of claims 1 to 8.

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