Inplausible soil moisture inversion method based on radiation transfer model and machine learning

Abstract

The invention discloses an interpretable soil moisture inversion method based on a radiation transfer model and machine learning, and the method comprises the steps: simulating the relation between soil moisture and microwave brightness temperature under different land coverage conditions through a radiation transfer theory, and generating a simulation data set of multiple environment parameters; designing characteristic variables with physical significance based on a microwave radiation transmission mechanism; carrying out model training by adopting an interpretable neural network architecture, and establishing a nonlinear mapping relation through sparsification and structure optimization; converting the training model into an explicit mathematical expression, and directly representing the physical correlation between the soil moisture and the observation signal; and inverting global soil moisture by using the formula and carrying out multi-source verification. According to the method, a physical model and interpretable machine learning are innovatively combined, the problems that a traditional method is high in calculation complexity and lacks physical interpretation are solved, the calculation efficiency is remarkably improved (20,000 times faster than that of the traditional method) while physical consistency is guaranteed, the inversion precision is high, and the method is suitable for global-scale near-real-time soil moisture monitoring.

Description

Technical Field

[0001] The present invention relates to satellite remote sensing monitoring and machine learning technologies, and particularly to an interpretable soil moisture inversion method based on a radiative transfer model and machine learning. Background Art

[0002] Soil moisture is a key state variable in terrestrial ecosystems and plays a central role in regulating the coupled water - energy - carbon emissions in land - atmosphere interactions. This key hydrological parameter has multifaceted impacts on different scientific disciplines. In agricultural systems, soil moisture dynamics regulate crop phenology and determine the efficiency of irrigation scheduling. In hydrology, soil moisture fundamentally controls processes such as infiltration capacity and base flow generation. In climate science, soil moisture is considered a key regulator of land - atmosphere feedback and has the ability to mitigate anthropogenic warming through evapotranspiration - mediated cooling. Notably, soil moisture variability directly restricts photosynthesis and biomass accumulation, thus controlling the spatio - temporal dynamics of the global terrestrial carbon sink. Obtaining a large amount of long - term soil moisture data in real - time is crucial for understanding global climate change, optimizing water resource management, and monitoring droughts and floods, which is essential for both scientific research and daily human activities.

[0003] Passive microwave soil moisture inversion:

[0004] Passive microwave soil moisture inversion is a method for monitoring surface soil moisture using satellite remote sensing technology. It receives the microwave radiation signals naturally emitted by the surface through a passive microwave radiometer carried on a satellite, and then estimates the water content in the shallow soil layer. Since soil moisture significantly changes the electromagnetic properties of the soil, the wetness of the soil can be indirectly inverted by analyzing the brightness temperature data at different frequencies. The advantages of this method are that it does not rely on external light sources, can conduct observations all - weather and all - time, and has a certain penetration ability, thus being not affected by clouds and some vegetation, and is very effective for monitoring soil moisture in large - scale and continuous regions.

[0005] Radiative transfer model:

[0006] The radiative transfer model is a physical theoretical framework that describes the propagation process of electromagnetic waves in a medium. In the field of soil moisture inversion, it specifically simulates the whole process of how microwave signals are emitted from the soil, pass through the vegetation layer, and are finally received by satellite sensors. The model contains multiple key components: a soil dielectric model (converting soil moisture into dielectric constant), a rough surface scattering model (considering the influence of soil surface unevenness on reflection), a vegetation layer radiative transfer equation (describing the attenuation and emission of microwave signals by vegetation), and atmospheric transmission correction. Based on strict physical laws, the model can be applied to different regions and times, but inversely solving for soil moisture through brightness temperature signals usually requires a complex iterative calculation process.

[0007] Kolmogorov - Arnold Network:

[0008] The Kolmogorov - Arnold Network (KAN) aims to construct machine learning models that can explain their decision - making processes and internal structures. It is based on the Kolmogorov - Arnold theorem, which states that any high - dimensional continuous function can be decomposed into simpler univariate components. Different from traditional neural networks, KAN places learnable spline - parameterized activation functions at the network edges rather than at nodes, eliminating the need for fixed activation functions and linear weight matrices, which enhances the interpretability of the network. The key advantage of KAN is that it can be converted into an explicit mathematical formula after training, revealing the functional relationship between input variables and outputs while maintaining high expressiveness.

[0009] The single - channel algorithm uses the brightness temperature signal of vertical polarization to invert soil moisture within the radiative transfer framework. Since a single polarization channel is insufficient to solve for two unknown variables, the single - channel algorithm introduces the vegetation optical depth as an auxiliary variable to facilitate the inversion process.

[0010] The dual - channel algorithm extends the concept of the single - channel algorithm. By utilizing the differential responses of horizontal and vertical polarization measurements to various surface parameters, it can estimate soil moisture and vegetation canopy moisture simultaneously. This method performs well on multiple sensors, but the computational complexity increases.

[0011] In recent years, various deep - learning methods have been applied to soil moisture inversion. The latest research direction is to integrate physical models with machine learning, also known as physics - informed machine learning. For example, Mao et al. proposed a framework that combines deep learning with physical and statistical methods, capable of simultaneously inverting soil moisture and surface temperature from passive microwave observations. This hybrid method aims to utilize the theoretical basis of physical models and the pattern - recognition ability of machine learning, but it still has not established a fully interpretable, physically consistent, and generally applicable physical formula for soil moisture inversion.

[0012] The existing technical methods mainly have the following disadvantages:

[0013] 1. High computational complexity of physical models: Traditional single - channel and dual - channel algorithms require complex parameterization and iterative optimization algorithms for inverse solution, resulting in a significant increase in computational time and resource requirements for large - scale applications.

[0014] 2. Lack of interpretability of machine - learning methods: Although machine - learning methods are computationally efficient, they are essentially "black - box" models that cannot reveal the underlying physical processes, limiting scientific understanding and model improvement.

[0015] 3. Lack of an interpretable physical formula: Although existing hybrid methods combine physical models and machine learning, a fully interpretable, physically consistent, and generally applicable physical formula for soil moisture inversion has not been established.

[0016] It should be noted that the information disclosed in the above background art section is only used for understanding the background of this application, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0017] The main objective of the present invention is to overcome the deficiencies in the above background art and provide an interpretable soil moisture inversion method based on the radiative transfer model and machine learning.

[0018] To achieve the above objective, the present invention adopts the following technical solutions:

[0019] An interpretable soil moisture inversion method based on the radiative transfer model and machine learning, comprising the following steps:

[0020] S1. Data simulation: Based on the radiative transfer theory, simulate the physical relationship between soil moisture and microwave brightness temperature under different land cover conditions to generate a simulation dataset covering multiple environmental parameters;

[0021] S2. Physical feature construction: According to the microwave radiative transfer mechanism, design feature variables with clear physical meanings to enhance the model's ability to represent the relationship between soil moisture and the observed signal;

[0022] S3. Interpretable model training: Adopt an interpretable neural network architecture, and through sparse training and structure optimization, establish a non-linear mapping relationship from the input features to soil moisture, while retaining the explicit expression ability of the model function;

[0023] S4. Physical formula analysis: Convert the trained model into an explicit mathematical expression to directly represent the physical relationship between soil moisture, microwave observation signals, and environmental parameters;

[0024] S5. Inversion and verification: Use the analyzed physical formula to invert soil moisture based on satellite microwave observation data and verify the accuracy through multi-source measured data.

[0025] Further, in step S1, the data simulation based on the radiative transfer model includes:

[0026] Establish a quantitative relationship between soil moisture and dielectric constant through a soil dielectric model;

[0027] Adopt a rough surface scattering model to calculate the actual surface reflection characteristics;

[0028] Combined with the radiative transfer equation of the vegetation layer, simulate the whole process of microwave signals emitted from the soil and received by the sensor;

[0029] Generate a simulation dataset covering various land cover types through systematic parameter combinations.

[0030] Further, in step S2, the construction of physical features specifically includes:

[0031] Extract the vegetation optical depth as the core variable characterizing the influence of vegetation;

[0032] Construct the normalized brightness temperature feature, integrating the microwave brightness temperature, surface temperature, and vegetation attenuation effect;

[0033] Determine the coupling relationship between features through physical mechanism analysis to form an input feature combination with clear physical meaning.

[0034] Further, in step S3, the training of the interpretable model specifically includes:

[0035] Adopt an edge activation network architecture and deploy learnable activation functions on the network connection edges;

[0036] Realize the sparsity of the network structure through joint optimization of L1 regularization and entropy regularization;

[0037] Prune the network based on the node contribution degree threshold to simplify the model topology;

[0038] Remove the regularization constraints in the fine-tuning training stage to improve the model fitting accuracy.

[0039] Further, the interpretable neural network architecture is the Kolmogorov - Arnold network (KAN), and the nodes only perform summation operations.

[0040] Further, step S4 includes a symbolic conversion process:

[0041] Match the mathematical expressions of each activation function in the sparsified network;

[0042] Convert the network mapping relationship into an explicit non - linear function combination;

[0043] Finally, form the physical equation for soil moisture inversion.

[0044] Further, step S4 specifically includes:

[0045] Decompose the non - linear mapping relationship in the trained network into a combination of basic mathematical functions;

[0046] Determine the best mathematical expression form of each network layer through function library matching;

[0047] Construct explicit physical equations to characterize the quantitative relationships among soil moisture, vegetation parameters, and microwave radiation characteristics, including the quadratic dependence of soil moisture on normalized radiation characteristics and the non-linear effect of vegetation optical depth on soil moisture inversion.

[0048] In step S5, the inversion and verification include:

[0049] Apply the symbolic formula to multi-source satellite microwave brightness temperature data;

[0050] Generate a spatio-temporally continuous global soil moisture distribution product;

[0051] Verify the correlation coefficient and error index of the inversion results through measured site data;

[0052] Perform cross-validation with satellite products to evaluate the adaptability of the model under different vegetation coverage conditions.

[0053] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the interpretable soil moisture inversion method based on the radiative transfer model and machine learning.

[0054] A computer program product includes a computer program, and when the computer program is executed by a processor, it implements the interpretable soil moisture inversion method based on the radiative transfer model and machine learning.

[0055] The present invention has the following beneficial effects:

[0056] The present invention proposes an interpretable soil moisture inversion method based on the radiative transfer model and machine learning. By innovatively combining the radiative transfer model with an interpretable machine learning architecture (such as the Kolmogorov-Arnold network), it successfully solves the key problems in existing soil moisture inversion technologies, such as the high computational complexity of physical models, the lack of interpretability of machine learning methods, and the failure to establish interpretable physical formulas. This method constructs a physically consistent simulation dataset based on the radiative transfer theory, designs characteristic variables with clear physical meanings, uses an interpretable neural network architecture to establish a non-linear mapping relationship, and transforms it into an explicit mathematical expression through symbolic processing, realizing the efficient and accurate inversion of soil moisture from microwave brightness temperature signals. Compared with traditional methods, the present invention has the advantages of physical consistency and interpretability, and can clearly reveal the physical relationships among soil moisture, brightness temperature, surface temperature, and vegetation optical depth; at the same time, it significantly improves the computational efficiency, and the speed is nearly 20,000 times higher than that of traditional iterative algorithms when processing large-scale data; on the basis of ensuring high accuracy (the correlation coefficient with the SMAP product reaches 0.98 in non-forest areas, and the error is only 0.03 cm 3 / cm 3), which greatly simplifies the parameter requirements, enhances the generalization ability of the model under different environmental conditions, is particularly suitable for soil moisture monitoring in areas with low to medium vegetation density, and provides reliable technical support for near-real-time soil moisture monitoring, drought warning, and climate model verification at the global scale.

[0057] Compared with the prior art, the main advantages of the present invention are reflected in the following aspects:

[0058] 1) Physical consistency and interpretability: Through the KAN architecture, the theoretical consistency of the physical model is maintained, and at the same time, clear mathematical formulas are provided to explain the underlying physical relationships.

[0059] 2) Computational efficiency: Avoids the computational overhead of iterative algorithms, and only a single forward calculation is required to obtain the result. It takes only 0.005 seconds to process 140,000 pieces of data, which is nearly 20,000 times faster than the traditional iterative algorithm (97.2 seconds).

[0060] 3) High accuracy: In non-forest areas, compared with the official SMAP soil moisture product, a high correlation coefficient (R = 0.98) and low error (ubRMSE = 0.03 cm 3 / cm 3 ) are achieved.

[0061] 4) Simplified parameter requirements: Requires fewer variables compared with traditional algorithms, reducing the dependence on auxiliary data.

[0062] 5) Generalization ability: Performs robustly under various environmental conditions, especially in areas with low to medium vegetation density.

[0063] Other beneficial effects in the embodiments of the present invention will be further described below. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 FIG. is a flowchart of an interpretable soil moisture inversion method based on a radiative transfer model and machine learning according to an embodiment of the present invention.

[0065] Figure 2 FIG. is a schematic diagram of the principle of the radiative transfer model according to an embodiment of the present invention.

[0066] Figure 3a and Figure 3b FIG. respectively show the comparison between the global soil moisture inverted by the method of the embodiment of the present invention and the official SMAP product.

[0067] Figures 4a to 4d FIG. shows the quantitative evaluation of the global soil moisture inverted by the method of the embodiment of the present invention and the official SMAP product.

[0068] Figures 5a to 5d FIG. shows the verification results of the method of the embodiment of the present invention at different measured sites.

[0069] Figure 6 This is the overall flowchart of the interpretable soil moisture inversion method based on the radiation transfer model and machine learning of the present invention. Detailed implementation manners

[0070] The following makes a detailed description of the implementation manners of the present invention. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0071] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0072] Currently, passive microwave remote sensing has become the dominant method for large-scale soil moisture inversion due to its sensitivity to the dielectric properties of liquid water and dry soil. Microwave radiation has unique advantages, including vegetation penetration ability, soil detection depth, and minimal atmospheric interference, ensuring the operation ability under cloud cover and night conditions. However, the existing microwave soil moisture inversion methods are mainly divided into two categories: the radiation transfer model method based on physical mechanisms and the data-driven machine learning method. Although the radiation transfer model method has physical consistency and generalization ability, it usually requires complex parameterization and iterative optimization algorithms. While the machine learning method has high computational efficiency, it lacks physical interpretability. It is essentially a "black box" that maps the input to the output and cannot reveal the underlying physical process. To solve these problems, the present invention proposes an interpretable soil moisture inversion method based on the radiation transfer model and machine learning, which combines the radiation transfer model and interpretable machine learning to obtain an interpretable symbolic expression, so as to be able to efficiently and directly invert the soil moisture from the microwave signal, taking into account physical consistency and computational efficiency while ensuring accuracy.

[0073] Refer to Figure 6 , an embodiment of the present invention provides an interpretable soil moisture inversion method based on the radiation transfer model and machine learning, including the following steps:

[0074] Step S1. Data simulation: Based on the radiation transfer theory, simulate the physical relationship between soil moisture and microwave brightness temperature under different land cover conditions, and generate a simulation dataset covering multiple environmental parameters.

[0075] In some embodiments, in step S1, the data simulation based on the radiative transfer model includes: establishing a quantitative relationship between soil moisture and dielectric constant through a soil dielectric model; calculating the actual surface reflection characteristics using a rough surface scattering model; combining the vegetation layer radiative transfer equation to simulate the whole process of microwave signal emission from the soil to sensor reception; generating a simulation dataset covering various land cover types through systematic parameter combinations.

[0076] Step S2. Physical feature construction: According to the microwave radiative transfer mechanism, design feature variables with clear physical meanings to enhance the model's ability to represent the relationship between soil moisture and the observed signal.

[0077] In some embodiments, in step S2, the physical feature construction specifically includes: extracting the vegetation optical depth as the core variable characterizing the vegetation effect; constructing a normalized brightness temperature feature by integrating microwave brightness temperature, surface temperature, and vegetation attenuation effect; determining the coupling relationship between features through physical mechanism analysis to form an input feature combination with clear physical meanings.

[0078] Step S3. Interpretable model training: Adopt an interpretable neural network architecture, and through sparse training and structure optimization, establish a non-linear mapping relationship from input features to soil moisture while retaining the explicit expression ability of the model function.

[0079] In some embodiments, in step S3, the interpretable model training specifically includes: adopting an edge activation network architecture and deploying learnable activation functions on the network connection edges; realizing the sparsity of the network structure through joint optimization of L1 regularization and entropy regularization; pruning the network based on the node contribution degree threshold to simplify the model topology; removing the regularization constraints in the fine-tuning training stage to improve the model fitting accuracy.

[0080] In some embodiments, the interpretable neural network architecture is a Kolmogorov - Arnold network (KAN), and the nodes only perform summation operations.

[0081] Step S4. Physical formula parsing: Convert the trained model into an explicit mathematical expression to directly represent the physical relationship between soil moisture, microwave observation signals, and environmental parameters;

[0082] In some embodiments, step S4 includes a symbolic conversion process, in which: perform mathematical expression matching on each activation function in the sparsified network; convert the network mapping relationship into an explicit non-linear function combination; finally form a physical equation for soil moisture inversion.

[0083] In some embodiments, step S4 specifically includes: decomposing the non-linear mapping relationship in the trained network into a combination of basic mathematical functions; determining the optimal mathematical expression form of each network layer through function library matching; constructing an explicit physical equation to characterize the quantitative relationship between soil moisture, vegetation parameters, and microwave radiation characteristics, including the quadratic dependence relationship between soil moisture and normalized radiation characteristics, and the non-linear effect of vegetation optical depth on soil moisture inversion.

[0084] Step S5. Inversion and verification: Using the analytically obtained physical formula, invert soil moisture based on satellite microwave observation data, and verify the accuracy through multi-source measured data.

[0085] In some embodiments, in step S5, the inversion and verification include: applying the symbolic formula to multi-source satellite microwave brightness temperature data; generating a spatio-temporally continuous global soil moisture distribution product; verifying the correlation coefficient and error index of the inversion result through measured site data; and performing cross-verification with mainstream satellite products to evaluate the adaptability of the model under different vegetation coverage conditions.

[0086] Aiming at the shortcomings of the prior art, the preferred embodiment of the present invention innovatively integrates the radiative transfer model with the KAN architecture to develop an interpretable soil moisture inversion framework with both physical consistency and interpretability. By utilizing the formula recovery ability of the KAN network, the present invention can transform complex non-linear physical processes into interpretable mathematical expressions, achieving a clear characterization of the relationships between variables such as microwave brightness temperature, surface temperature, and vegetation optical depth. This method not only significantly improves the computational efficiency, avoiding the resource consumption of iterative algorithms, but also maintains a high degree of physical consistency and accuracy, especially outstanding in areas with low to medium vegetation density.

[0087] The following further describes the specific embodiments, algorithm examples, and experimental verification of the present invention.

[0088] An interpretable soil moisture inversion method based on a radiative transfer model and machine learning specifically includes the following processes:

[0089] Data simulation based on the radiative transfer model: Simulate the complete radiative transfer process from soil moisture to brightness temperature through the radiative transfer model to generate simulation datasets of various land cover types with specific parameters.

[0090] Auxiliary variable design: According to the mechanism analysis of the radiative transfer model, introduce auxiliary variables with physical meanings, such as Enhance the expression ability and interpretability of the neural network.

[0091] KAN model training and sparsification: Train the KAN network using the simulation dataset, and obtain a simplified network structure through sparse training, pruning, and refinement training.

[0092] Symbolic processing: Convert the trained KAN network into an explicit mathematical formula to reveal the relationship between soil moisture and variables such as brightness temperature, surface temperature, and vegetation optical depth.

[0093] Global verification and application: Apply the derived symbolic model to satellite brightness temperature data, create a global soil moisture distribution map, and verify it with the measured values at the actual measurement sites.

[0094] Generation of simulation data based on the radiative transfer model

[0095] The present invention first performs data simulation based on the radiative transfer model. By simulating the radiative transfer process from soil moisture to brightness temperature, a simulation data set of various land cover types is generated. The Topp model is used as the soil dielectric constant model:

[0096] k' = 3.03 + 9.3mv + 146mv 2 -76.7mv 3

[0097] where mv represents the volumetric water content and k' is the soil dielectric constant. The dielectric constant of dry soil is approximately 3, and that of pure water is approximately 80. Therefore, the dielectric constant of soil moisture is between these two values. For a smooth soil surface, the surface reflectance is described by the Fresnel equation:

[0098]

[0099] θ represents the satellite incidence angle, and R V represents the soil reflectance in the V polarization. However, considering that the surface of the soil in the actual physical world is rough, the Q - H model is adopted:

[0100]

[0101] where represents the actual surface reflectance, ε p is the soil emissivity, and h is a parameter related to the roughness. For the case of vegetation cover, the radiative signal transmission is described by the τ - ω model:

[0102]

[0103] where T S and T crepresent the effective temperatures of soil and vegetation, respectively; ω is the single-scattering albedo of vegetation; τ is the vegetation optical depth. The simulation parameter settings include: soil moisture (0.02 - 0.55), vegetation optical depth (0 - 0.5), and surface temperature (273 - 325 K). According to the surface roughness parameter (h) and the albedo (ω) value, the land cover types are regrouped into 10 types. Through this physics-based data simulation framework, the present invention generates a large-scale and physically consistent dataset, fully controlling environmental conditions, ensuring comprehensive coverage under various soil moisture levels, vegetation densities, and surface temperatures, and overcoming the limitations of actual datasets.

[0104] KAN-based soil moisture inversion model

[0105] Analyze the radiative transfer model equation and introduce auxiliary variables with physical meanings: X1 = τ and where X2 is directly related to the soil emissivity. This design improves the expression ability and interpretability of the network.

[0106] Adopt KAN as the framework for soil moisture inversion. KAN places learnable activation functions on the network edges and only performs summation operations at the nodes, without a fixed activation function and linear weight matrix, enhancing the network interpretability. The initial configuration of the network is a [2, 2, 1] layer structure, with inputs X1 and X2 and output being the soil moisture mv.

[0107] Model training and optimization

[0108] The training process of the present invention includes four steps: sparse training, network pruning, fine-tuning training, and symbolization.

[0109] Sparse training adopts the total training objective:

[0110]

[0111] where l pred is the mean square error between the predicted value and the actual value, and λ L1 and λ entropy control L1 regularization and entropy regularization respectively, prompting the network to learn a simpler model.

[0112] Network pruning is performed by calculating the input and output scores of each node:

[0113]

[0114] If the score exceeds the threshold (10 -2 ), the node is retained; otherwise, it is pruned. After pruning, the network is simplified to a [2, 1, 1] structure.

[0115] The refined training removes the regularization term and focuses on data fitting. Symbolization selects the best-fitting function to represent each activation function by matching the basic function library, and finally obtains the physical symbolic expression for soil moisture inversion:

[0116]

[0117] This expression reveals the physical relationship between soil moisture, brightness temperature, surface temperature, and vegetation optical depth.

[0118] Alternative embodiments

[0119] In addition to using V-polarized brightness temperature data, it can be extended to simultaneously utilize dual-channel data of both H-polarization and V-polarization, potentially improving the inversion accuracy.

[0120] This method can be extended to other microwave sensors to fuse data from other sensors and increase the richness of the input data.

[0121] Experimental verification

[0122] Comparison with the SMAP product: The soil moisture inverted by the present invention is highly consistent with the SMAP official product, and the correlation coefficient R exceeds 0.9 in most regions of the world. Especially in non-forest areas, the correlation coefficient reaches 0.98, and the error (ubRMSE) is only 0.03 cm 3 / cm 3 , indicating that this method has high accuracy. Figure 3a and Figure 3b are respectively the comparison of the global soil moisture inverted by the method of the embodiment of the present invention with the SMAP official product. Figures 4a to 4d Shows the quantitative evaluation of the global soil moisture inverted by the method of the embodiment of the present invention and the SMAP official product. Verification at measured sites: Compared with the actual measurement data of the International Soil Moisture Network, the correlation coefficient R of most grid points exceeds 0.6, and the RMSE value is generally lower than 0.15 cm 3 / cm 3 . Especially the Txson and NGARI grid sites show particularly low ubRMSE values, with an average value lower than 0.04 cm 3 / cm 3 . Figures 5a to 5d Shows the verification results of the method of the embodiment of the present invention at different measured sites.

[0123] Comparison with machine learning methods: On SMAP, the present invention achieved higher correlation coefficients and lower RMSE than the multilayer perceptron (MLP) on 7 out of 10 land cover types, indicating that the present invention has stronger generalization ability. Compared with traditional machine learning methods such as decision trees, linear regression, and random forests, the present invention performed better on 8 out of 10 land cover types in the SMAP product. This highlights the effectiveness of the present method in capturing complex patterns and data dependencies.

[0124] Computational efficiency test: A speed test was performed using a data set containing 140,000 data items. The iterative algorithm required 97.2 seconds, while the symbolic model of the present invention only required 0.005 seconds to complete the task, demonstrating a significant speed advantage.

[0125] In general, the experimental results demonstrate that the present invention is a highly feasible, efficient and accurate soil moisture inversion method that is robust under various conditions, especially in areas with medium and low vegetation density.

[0126] The embodiment of the present invention proposes an interpretable soil moisture inversion method based on KAN, which integrates the radiation transfer model with the KAN architecture, can directly invert soil moisture from microwave brightness temperature measurements, and provides an interpretable physical formula. A data simulation method based on the radiation transfer model is proposed, which generates a simulated data set containing multiple land cover types through systematic variation parameters for training the KAN network.

[0127] The efficient soil moisture inversion method of the present invention can be applied to real-time drought monitoring systems to provide large-scale, high-frequency soil moisture status assessments. Using the present invention, high-quality global soil moisture data can also be used to verify land surface process simulations in climate models and improve the accuracy of climate change predictions.

[0128] Compared with the prior art, the main advantages of the present invention are:

[0129] 1) Physical consistency and interpretability: Different from the "black box" machine learning method, the present invention provides a clear symbolic mathematical formula, which reveals the physical relationship between soil moisture and brightness temperature, surface temperature, and vegetation optical depth, making the inversion process completely transparent and interpretable.

[0130] 2) High computational efficiency: Compared with traditional iterative algorithms (such as single-channel algorithm iteration), the present invention only takes 0.005 seconds to process 140,000 data, while the traditional method takes 97.2 seconds, which improves the computational efficiency by nearly 20,000 times. This efficiency is crucial for near-real-time soil moisture monitoring at a global scale.

[0131] 3) No complex parameter settings: The present invention simplifies the inversion process, avoids the complex parameter settings and iterative optimization algorithms in traditional methods, and reduces the computational resource requirements and operational complexity.

[0132] An embodiment of the present invention also provides a storage medium for storing a computer program, which when executed performs at least the method described above.

[0133] An embodiment of the present invention also provides a control device, including a processor and a storage medium for storing a computer program; wherein, the processor is configured to perform at least the method described above when executing the computer program.

[0134] An embodiment of the present invention also provides a processor, which executes a computer program and performs at least the method described above.

[0135] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. Among them, the non-volatile memory can be a read-only memory (ROM, Read Only Memory), a programmable read-only memory (PROM, Programmable Read-Only Memory), an erasable programmable read-only memory (EPROM, Erasable Programmable Read-Only Memory), an electrically erasable programmable read-only memory (EEPROM, Electrically Erasable Programmable Read-Only Memory), a ferromagnetic random access memory (FRAM, Ferromagnetic Random Access Memory), a flash memory (Flash Memory), a magnetic surface memory, an optical disc, or a compact disc read-only memory (CD-ROM, Compact Disc Read-Only Memory); the magnetic surface memory can be a disk memory or a tape memory. The storage medium described in the embodiments of the present invention is intended to include but not limited to these and any other suitable types of memories.

[0136] In several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division, and there may be other division methods in actual implementation. For example, multiple units or components can be combined, or integrated into another system, or some features can be ignored, or not executed. In addition, the couplings, direct couplings, or communication connections between the components shown or discussed may be through some interfaces, and the indirect couplings or communication connections of the devices or units may be electrical, mechanical, or other forms.

[0137] The units described above as separate components may or may not be physically separated. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed over multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0138] In addition, each functional unit in the embodiments of the present invention may all be integrated into one processing unit, or each unit may be separately used as one unit, or two or more units may be integrated into one unit. The above-mentioned integrated units may be implemented in the form of hardware, or in the form of a combination of hardware and software functional units.

[0139] Those of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps including the above method embodiments. The foregoing storage medium includes: various media that can store program codes such as removable storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs.

[0140] Alternatively, if the above-mentioned integrated units of the present invention are implemented in the form of software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the embodiments of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. The 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 methods described in the various embodiments of the present invention. The foregoing storage medium includes: various media that can store program codes such as removable storage devices, ROM, RAM, magnetic disks, or optical discs.

[0141] The methods disclosed in the several method embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0142] The features disclosed in the several product embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0143] The features disclosed in the several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments or device embodiments.

[0144] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several equivalent substitutions or obvious variations can be made, and if the performance or use is the same, they should all be regarded as falling within the protection scope of the present invention.

Claims

1. An interpretable soil moisture inversion method based on radiative transfer model and machine learning, characterized in that, It includes the following steps: S1. Data simulation: Based on the radiation transfer theory, simulate the physical relationship between soil moisture and microwave brightness temperature under different land cover conditions, and generate a simulation dataset covering multiple environmental parameters; S2. Physical feature construction: According to the microwave radiation transfer mechanism, design feature variables with clear physical meanings to enhance the model's ability to represent the relationship between soil moisture and the observed signal; S3. Interpretable model training: Adopt an interpretable neural network architecture, and through sparse training and structure optimization, establish a non-linear mapping relationship from input features to soil moisture, while retaining the explicit expression ability of the model function; S4. Physical formula analysis: Convert the trained model into an explicit mathematical expression to directly represent the physical relationship between soil moisture, microwave observation signals, and environmental parameters; S5. Inversion and verification: Use the analytically obtained physical formula to invert soil moisture based on satellite microwave observation data, and verify the accuracy through multi-source measured data.

2. The method according to claim 1, characterized in that In step S1, the data simulation based on the radiation transfer model includes: Establish a quantitative relationship between soil moisture and dielectric constant through a soil dielectric model; Use a rough surface scattering model to calculate the actual surface reflection characteristics; Combine the vegetation layer radiation transfer equation to simulate the entire process of microwave signal emission from the soil to sensor reception; Generate a simulation dataset covering multiple land cover types through systematic parameter combinations.

3. The method according to claim 1 or 2, characterized in that, In step S2, the physical feature construction specifically includes: Extract the vegetation optical depth as the core variable characterizing the vegetation effect; Construct a normalized brightness temperature feature by integrating microwave brightness temperature, surface temperature, and vegetation attenuation effect; Determine the coupling relationship between features through physical mechanism analysis to form an input feature combination with clear physical meanings.

4. The method according to any one of claims 1 to 3, characterized in that, In step S3, the interpretable model training specifically includes: Adopt an edge activation network architecture and deploy learnable activation functions on the network connection edges; Realize the sparsity of the network structure through joint optimization of L1 regularization and entropy regularization; Prune the network based on the node contribution degree threshold to simplify the model topology; Remove the regularization constraints in the refined training stage to improve the model fitting accuracy.

5. The method according to claim 4, characterized in that The interpretable neural network architecture is the Kolmogorov-Arnold network (KAN), and the nodes only perform summation operations.

6. The method according to claim 4 or 5, characterized in that, Step S4 includes a symbolic conversion process: Match the mathematical expressions of each activation function in the sparsified network; Convert the network mapping relationship into an explicit non-linear function combination; Finally, form a physical equation for soil moisture inversion.

7. The method according to any one of claims 1 to 6, characterized in that, Step S4 specifically includes: Decompose the non-linear mapping relationship in the trained network into a combination of basic mathematical functions; Determine the best mathematical expression form of each network layer through function library matching; Construct an explicit physical equation to represent the quantitative relationship between soil moisture, vegetation parameters, and microwave radiation characteristics, including the quadratic dependence of soil moisture on the normalized radiation characteristics and the non-linear effect of vegetation optical depth on soil moisture inversion.

8. The method according to any one of claims 1 to 7, characterized in that, In step S5, the inversion and verification include: Apply the symbolic formula to multi-source satellite microwave brightness temperature data; Generate a spatio-temporally continuous global soil moisture distribution product; Verify the correlation coefficient and error index of the inversion results through measured site data; Perform cross-validation with satellite products to evaluate the adaptability of the model under different vegetation coverage conditions.

9. A computer-readable storage medium storing a computer program, characterized in that, When executed by a processor, the computer program implements the interpretable soil moisture inversion method based on the radiative transfer model and machine learning according to any one of claims 1 to 8.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the interpretable soil moisture inversion method based on the radiative transfer model and machine learning according to any one of claims 1 to 8.

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