Deep learning gravity satellite groundwater vertical signal separation method fusing physical constraints

Abstract

The invention discloses a physical constraint fused deep learning gravity satellite groundwater vertical signal separation method, which comprises the following steps: S1, acquiring and preprocessing basic data: calculating to obtain total groundwater reserve abnormities needing vertical separation, unifying all data to a preset temporal-spatial resolution, and removing abnormal values; s2, constructing a deep learning model, which is configured to receive the preprocessed time sequence including the total groundwater reserve abnormality and meteorological data as input, and output shallow groundwater reserve abnormality and deep groundwater reserve abnormality at corresponding time; s3, the deep learning model is trained, optimization is carried out by adopting a composite loss function, and the composite loss function comprises a data-driven loss item Ldata and a physical constraint loss item Lwater based on water balance; and S4, after training is completed, inputting a total groundwater reserve abnormal signal into the deep learning model for processing, and outputting a separated shallow groundwater reserve abnormal time sequence and a separated deep groundwater reserve abnormal time sequence.

Description

Technical Field

[0001] This invention belongs to the field of groundwater resource monitoring technology. Specifically, it relates to a deep learning gravity satellite groundwater vertical signal separation method that integrates physical constraints. This method is primarily applicable to scenarios where gravity satellites are used for large-scale dynamic monitoring of groundwater resources. It specifically addresses the technical challenge of separating the contributions of shallow (usually corresponding to phreatic aquifers) and deep (usually corresponding to confined aquifers) groundwater storage variables from the total groundwater storage change signal observed by gravity satellites. This separation primarily aims to distinguish between portions that respond relatively quickly to surface climate drivers and portions that respond more slowly and may be affected by deeper mining. This method uses a deep learning model to effectively integrate gravity satellite observation data, relevant meteorological and hydrological data, and other auxiliary environmental information, and incorporates physical constraint mechanisms to achieve automated and refined vertical separation of groundwater storage variables. Its results can provide a key scientific basis for regional groundwater resource assessment, the identification and management of groundwater overexploitation areas, and have broad application prospects in areas such as sustainable groundwater resource management, water resource optimization and scheduling decisions, and the construction of smart water conservancy systems. Background Art

[0002] With the impact of global climate change and human activities, groundwater overexploitation is becoming increasingly prominent. Accurately monitoring groundwater storage variables is crucial for water resource management and ecological and environmental protection. Gravity satellite measurement technology, by detecting time-varying information about the Earth's gravity field, enables monitoring of groundwater storage changes over large regions and has become a crucial tool for groundwater resource monitoring. The GRACE binary satellite system, launched in 2002, and the subsequent GRACE-FO satellite system, launched in 2018, provide long-term, continuous observational data for global groundwater resource monitoring.

[0003] In terms of vertical groundwater monitoring, stratified water well monitoring can obtain groundwater level information at different depths, but deep water wells are sparsely distributed and the monitoring cost is high; gravity satellite monitoring can obtain changes in regional total groundwater reserves, but it obtains vertically integrated signals, making it difficult to directly distinguish the contributions of deep and shallow groundwater; although hydrological model simulation can provide information on changes in various hydrological elements, global or large-scale models such as GLDAS often have a relatively simplified depiction of groundwater, especially a lack of detailed description of the vertical structure of groundwater, which limits its direct application in groundwater vertical dynamic analysis.

[0004] Existing research on vertical groundwater separation using gravity satellite data primarily relies on combining well observations to separate shallow and deep groundwater. These studies often use well observations in conjunction with other information (such as models or remote sensing) to attempt to separate shallow and deep groundwater storage changes in different regions (such as the North China Plain) and analyze their respective contributions and rates of change. However, these methods generally rely heavily on well observations with high temporal and spatial coverage as the direct basis or key reference for separation, making them difficult to apply in areas with limited observational data, and a universal framework for separation methods has yet to be established.

[0005] At present, the groundwater storage change signal obtained by gravity satellites is the superposition effect of deep and shallow groundwater changes in the region. There is an urgent need to develop effective signal separation methods to reveal the dynamics of different layers. The existing vertical separation methods have the problem of over-reliance on high-quality, high-density water well observation data, which limits their widespread application. At the same time, how to effectively integrate multi-source data information such as meteorological, hydrological, and surface characteristics, and incorporate hydrological physical laws (such as water balance) to constrain the separation process to improve the reliability and physical consistency of the results remains a challenge in this field. In addition, establishing a systematic evaluation system that can evaluate the various performance aspects of the separation results (including data accuracy, physical rationality, spatiotemporal consistency, etc.) is also a weak link in current research.

[0006] Therefore, this field urgently needs to develop a new method that can effectively integrate multi-source data, combine physical constraint mechanisms, and automatically realize the vertical separation of gravity satellite groundwater storage variables to support the stratified monitoring and management of groundwater resources. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for separating vertical signals of groundwater storage variables from gravity satellites by deep learning with physical constraints. This method addresses the shortcomings of existing vertical separation technologies for groundwater storage variables from gravity satellites and solves the following technical problems:

[0008] 1) Vertical separation of groundwater signals from gravity satellites: Current groundwater storage change signals acquired by gravity satellites represent the combined effects of deep and shallow groundwater. This is particularly challenging in areas with limited hydrogeological data. The lack of high-quality well observation data makes it difficult to effectively separate groundwater signals vertically (particularly distinguishing shallow layers, such as phreatic water, from deep layers, such as confined water) for predictive applications. Therefore, a new method for vertical separation of groundwater signals that does not rely heavily on dense well observation data is needed.

[0009] 2) Comprehensive Utilization of Multi-Source Data: Existing vertical separation methods often focus on a single data source or simple combination, failing to fully utilize the comprehensive reflection and constraints of multi-source data—gravity satellite data itself, as well as related meteorological and hydrological data, hydrological model outputs, and surface characteristics—on the groundwater system (especially its vertical structure). How to effectively integrate this multi-source information, extract deep-seated features relevant to the vertical distribution of groundwater, and construct a stable and reliable data-driven model is a technical challenge that urgently needs to be addressed in this field.

[0010] 3) Integrating constraints on hydrophysical laws: When applied to this problem, traditional machine learning or statistical downscaling methods are sometimes viewed as "black box" processes, potentially overlooking the fundamental physical laws governing groundwater system operation. This paper focuses on effectively incorporating key physical constraints, particularly those related to water balance, into data-driven models to ensure that the separation results not only have a high degree of data fit but also adhere to fundamental hydrophysical laws, thereby improving the model's physical interpretability and generalization capabilities under diverse conditions.

[0011] 4) Reliability evaluation of separation results: Existing technologies often lack a systematic, multi-dimensional evaluation system to comprehensively verify the reliability of groundwater vertical separation results. Establishing a comprehensive evaluation framework encompassing data accuracy verification, physical plausibility assessment, and spatiotemporal consistency testing to quantitatively assess and control separation results, while also exploring the universality of evaluation criteria, is crucial for ensuring the practical application of this technology.

[0012] To achieve the above objectives, the present invention provides a deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints, which specifically includes the following steps:

[0013] Step S1: Acquire and preprocess basic data, including: total terrestrial water storage anomaly (TWSA) data from gravity satellite observations, hydrological model data for separating non-groundwater components in the total terrestrial water storage anomaly (TWSA), meteorological data including precipitation P and evapotranspiration ET in the study area, and reference benchmark data representing shallow and deep groundwater storage anomalies used in the model training phase; the preprocessing includes: calculating the total groundwater storage anomaly (Total GWSA) to be separated vertically, unifying all data to a preset spatiotemporal resolution, and removing outliers;

[0014] Step S2: Construct a deep learning model, which is configured to receive the pre-processed time series including the total groundwater storage anomaly (Total GWSA) and meteorological data as input, and output the shallow groundwater storage anomaly (Shallow_GWSA) at the corresponding time. pred) and deep groundwater storage anomaly (Deep_GWSA pred );

[0015] Step S3: Train the deep learning model and optimize it using a composite loss function, where the composite loss function includes:

[0016] A data-driven loss term L data , used to quantify the shallow groundwater storage anomaly (Shallow_GWSA) output by the model pred ) and deep groundwater storage anomaly (Deep_GWSA pred ) and the reference benchmark data obtained in step S1; and

[0017] A physical constraint loss term L based on water balance water , used to quantify the monthly change in total groundwater storage (ΔG total_pred ) and the water balance residual (Water_Balance_Residual) calculated based on external input meteorological data (P, ET) and hydrological data (such as runoff R, surface water storage change ΔS);

[0018] Step S4: After the training is completed, the total groundwater storage anomaly (Total GWSA) signal is input into the deep learning model for processing, and the separated shallow groundwater storage anomaly and deep groundwater storage anomaly time series are output.

[0019] In one embodiment of the present invention, the hydrological model data in step S1 includes soil moisture storage anomaly (SMA), snow water equivalent anomaly (SWEA) and canopy water storage anomaly (CWSA), and the total groundwater storage anomaly (TotalGWSA) is calculated by deducting the soil moisture storage anomaly, snow water equivalent anomaly and canopy water storage anomaly from the total terrestrial water storage anomaly (TWSA).

[0020] In one embodiment of the present invention, the deep learning model in step S2 adopts an encoder-decoder architecture, the encoder and decoder both include two-dimensional convolutional layers, and jump connections for feature fusion are set between corresponding layers of the encoder and decoder, and the jump connections are implemented by feature map splicing.

[0021] In one embodiment of the present invention, a multi-head attention module is included at the end of the encoder or at the bottleneck position of the network, and the multi-head attention module acts on the spatial dimension of the feature map to capture spatial dependencies.

[0022] In one embodiment of the present invention, the input of the deep learning model in step S2 can selectively include at least one auxiliary variable of vegetation index (NDVI), land use / cover type (LULC), and terrain elevation.

[0023] In one embodiment of the present invention, the data driven loss term L in step S3 is data The mean square error is used for calculation, and the calculation formula is:

[0024]

[0025] Where N is the total number of grid points in the batch sample, Shallow_GWSA ref Deep_GWSA, a reference benchmark representing shallow groundwater storage anomalies ref Shallow_GWSA represents the reference baseline data for deep groundwater storage anomalies. pred Represents shallow groundwater storage anomaly, Deep_GWSA pred It indicates abnormal deep groundwater reserves.

[0026] In one embodiment of the present invention, the physical constraint loss term L based on water balance in step S3 is water The monthly change in total groundwater storage (ΔG total_pred ) and the water balance residual (Water_Balance_Residual).

[0027] In one embodiment of the present invention, the composite loss function in step S3 is expressed as L=λ1·L data +λ2·L water , where the weight coefficients λ1 and λ2 are determined by hyperparameter optimization or adaptively adjusted using a dynamic adjustment strategy during training.

[0028] In one embodiment of the present invention, the dynamic adjustment strategy is a weight adjustment algorithm based on the gradient norm.

[0029] In one embodiment of the present invention, the termination condition for completing the training in step S4 includes any one of the following conditions or a combination of at least two conditions:

[0030] Monitor the data-driven loss term L on the validation set data Or whether the composite loss function L no longer decreases significantly over multiple consecutive cycles;

[0031] Whether the satisfaction of the physical constraints on the validation set reaches the preset threshold;

[0032] The preset maximum number of training iterations has been reached;

[0033] After training is completed, the reliability and physical rationality of the model separation results on the test set must be evaluated, including: evaluating the uncertainty of the prediction results, analyzing the rationality of spatial distribution, verifying time series characteristics, and external verification.

[0034] Compared with the existing technology, the deep learning gravity satellite groundwater vertical signal separation method integrated with physical constraints provided by the present invention effectively overcomes the limitations of the existing technology in the vertical separation of gravity satellite groundwater through the organic combination of deep learning technology and hydrophysical knowledge, and provides a new method with higher accuracy, wider applicability, stronger physical significance and easier evaluation and verification of results, providing strong technical support for the stratified and refined monitoring and management of regional groundwater resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in 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 only 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.

[0036] Figure 1 A schematic flow chart of the method provided by the present invention;

[0037] Figure 2 This is a schematic diagram of the structure of the deep learning network model (based on the encoder-decoder structure) adopted by the present invention;

[0038] Figure 3 This is a schematic diagram of the composite loss function used in the present invention;

[0039] Figure 4 This is a schematic diagram of the separation result evaluation system framework adopted in the present invention. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0041] Figure 1 A schematic flow chart of the method provided by the present invention is shown in FIG. Figure 2 This is a schematic diagram of the structure of the deep learning network model (based on the encoder-decoder structure) adopted in the present invention. Figure 3This is a schematic diagram of the composite loss function used in the present invention. Figure 4 Schematic diagram of the separation result evaluation system framework used in the present invention. Figures 1 to 4 As shown, the present invention provides a deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints, which specifically includes the following steps:

[0042] Step S1: Acquire and preprocess basic data, the basic data including at least: total terrestrial water storage anomaly (TWSA) data derived from gravity satellite observations, hydrological model data for separating non-groundwater components from the total terrestrial water storage anomaly (TWSA), meteorological data of the study area including at least precipitation P and evapotranspiration ET, and reference benchmark data representing shallow and deep groundwater storage anomalies used in the model training phase; the preprocessing includes at least: calculating the total groundwater storage anomaly (Total GWSA) to be separated vertically, unifying all data to a preset spatiotemporal resolution, and removing outliers;

[0043] The method provided by the present invention begins with the acquisition and preprocessing of multi-source data. The data required in this stage include, but are not limited to: monthly-scale total terrestrial water storage anomalies (TWSA) provided by the Mascon grid data product from the GRACE / GRACE-FO satellites; hydrological model data that are spatiotemporally matched with gravity satellite data, such as soil moisture anomalies (SMA), snow water equivalent anomalies (SWEA), and canopy water storage anomalies (CWSA) output by the GLDAS Noah model; monthly-scale gridded meteorological and surface data for the study area, with the core data being precipitation (P) and actual evapotranspiration (ET), as well as surface runoff (R) and surface water storage change (ΔS) for physical constraints; and other auxiliary variables, such as the vegetation index (NDVI), land use / cover type (LULC), and terrain elevation, optionally incorporated as needed to provide richer environmental context. In particular, for model training, it is also necessary to obtain groundwater level monitoring well data with shallow and deep observation records in the study area, and convert them into shallow (Shallow_GWSA) based on the layer information of the well monitoring (such as distinguishing between phreatic and confined water wells) and the corresponding aquifer parameters (such as water supply degree and water release coefficient). ref ) and Deep_GWSA ref ) groundwater storage anomalies, serving as a reference for the model to distinguish between these two response characteristics. It should be clarified that these reference data are only used to establish supervised learning objectives during the model training phase. Once trained, the model no longer relies on this reference data input in subsequent prediction applications, thus possessing certain potential for prediction in areas lacking in-situ observation data.

[0044] The raw multi-source data obtained above undergo a series of preprocessing operations. First, the total groundwater storage anomaly (Total GWSA), which requires vertical separation, is calculated by subtracting other terrestrial water storage components (SMA, SWEA, CWSA, etc.) from the total groundwater storage anomaly (TWSA). Subsequently, a spatiotemporal unification operation is performed, resampling all selected data, including Total GWSA, meteorological surface data, auxiliary variables, physical constraints, and reference benchmark data, to a uniform, predefined spatiotemporal resolution (e.g., 0.25° × 0.25° spatial resolution and monthly timescale). Next, outliers can be detected and removed using methods such as the 3σ criterion, and the feature data for input into the model can be normalized, for example, using Z-score or Min-Max normalization. Finally, the dataset can be partitioned into training, validation, and test sets in a predetermined ratio (e.g., 7:2:1) to ensure that the time series meets the required continuity or randomness and that the training input samples are correctly paired with the reference outputs.

[0045] Step S2: Construct a deep learning model, which is configured to receive the pre-processed time series including the total groundwater storage anomaly (Total GWSA) and meteorological data as input, and output the shallow groundwater storage anomaly (Shallow_GWSA) at the corresponding time. pred ) and deep groundwater storage anomaly (Deep_GWSA pred );

[0046] In the construction link of the deep learning network model of the present invention, it is preferred to adopt a network model with an encoder-decoder architecture. Both the encoder part and the decoder part of the model can be composed of multiple convolution units, for example, including five layers but not limited to this. Each convolution unit usually includes a two-dimensional convolution layer (Conv2D, for example, using a 3×3 convolution kernel, but not limited to this), a batch normalization layer (BatchNormalization) and a nonlinear activation function (such as LeakyReLU) in sequence, but not limited to this. In the encoder, the number of channels of the convolution layer can be increased layer by layer, and the spatial resolution of the feature map can be gradually reduced in combination with the pooling layer (such as MaxPooling); in the decoder, the spatial resolution can be restored by upsampling operations (such as transposed convolution or interpolation plus convolution), and the number of channels of the convolution layer is reduced layer by layer. In order to promote information flow and alleviate the problem of gradient disappearance, a skip connection (Skip Connection) is set between the corresponding layers of the encoder and decoder, and the encoder features are usually transferred to the decoder by concatenation of feature maps. In addition, a multi-head attention module (MHA) can be integrated at specific locations in the network, such as the bottleneck layer at the end of the encoder or other bottleneck locations. This module primarily operates on the spatial dimensions of the feature map, aiming to capture the spatial contextual dependencies of key regions and improve the model's perception of spatial heterogeneity. The input of this network model can be designed as a five-dimensional tensor, whose dimensions correspond to the batch size, input time step (e.g., the past 12 months), number of input feature channels, spatial height, and spatial width. The input feature channels include at least total groundwater storage anomaly (Total GWSA), precipitation (P), and evapotranspiration (ET), and other auxiliary variables (such as vegetation index NDVI, land use / cover type LULC, terrain elevation, etc., with static variables serving as constant channels) can be added based on the aforementioned selections. The output of the model is a four-dimensional tensor, whose dimensions correspond to the batch size, number of output channels (which can be fixed to 2, representing shallow and deep signals, respectively), spatial height, and spatial width, specifically the predicted shallow groundwater storage anomaly (Shallow_GWSA) for the current month. pred ) and deep groundwater storage anomaly (Deep_GWSA pred ). Network parameters can be initialized using standard methods such as Xavier, and optimizers such as Adam can be used for subsequent training, but are not limited to these.

[0047] Step S3: Train the deep learning model and optimize it using a composite loss function, where the composite loss function includes:

[0048] A data-driven loss term (L data), used to quantify the shallow groundwater storage anomaly (Shallow_GWSA) output by the model pred ) and deep groundwater storage anomaly (Deep_GWSA pred ) and the reference benchmark data obtained in step S1; and

[0049] A physical constraint loss term based on water balance (L water ), which is used to quantify the monthly change in total groundwater storage (ΔG total_pred ) and the water balance residual (Water_Balance_Residual) calculated based on external input meteorological data (P, ET) and hydrological data (such as runoff R, surface water storage change ΔS);

[0050] After the model is built, the method provided by the present invention enters the training and optimization phase. This phase adopts an end-to-end joint optimization strategy, the core of which is to design and use a composite loss function that combines data-driven and physical constraints. The total loss function L is defined as the data-driven loss term L data and the physical constraint loss term L water The weighted sum of: L = λ1·L data +λ2·L water Among them, the weight coefficients λ1 and λ2 are used to balance the relative importance of these two types of losses. Data-driven loss term L data It can be calculated based on the water well reference benchmark data in the training set. The mean square error (MSE) is usually used to quantify the difference between the shallow and deep GWSA predicted by the model and the corresponding reference true values. The calculation formula is:

[0051]

[0052] Where N is the total number of grid points in the batch sample, Shallow_GWSA ref Reference benchmark data representing shallow groundwater storage anomalies (shallow reference true value in water well reference benchmark data), Deep_GWSA ref Reference benchmark data representing deep groundwater storage anomalies (deep reference true value in water well reference benchmark data). This loss term is intended to drive the model to learn the mapping relationship between input and output, so that the prediction is as close to the observation as possible. Physical constraint loss term L water It is based on the principle of water balance, which does not rely on well observations, but uses recognized physical laws to constrain the model output. In the specific calculation, the predicted total groundwater monthly change ΔG is first calculated from the shallow and deep groundwater storage anomalies (GWSA) output by the model. total_pred

[0053] ΔG total_pred=(Shallow_GWSA pred,t -Shallow_GWSA pred,t-1 )+(Deep_GWSA pred,t -Deep_GWSA pred,t-1 )

[0054] Where t represents time (month).

[0055] The local water balance residuals are then calculated using external input data on precipitation, evapotranspiration, runoff, and surface water storage changes. It should be noted that surface runoff (R) and surface water storage changes (ΔS) are usually obtained through other hydrological model outputs (such as global or regional models), remote sensing inversion products, or simplified assumptions based on specific regional characteristics. These data themselves have certain uncertainties. Despite these uncertainties, the physical constraints of the gridded water balance (i.e., the assumption that, under large-scale regional averages, groundwater storage changes are mainly caused by vertical flux P) are used to calculate the local water balance residuals. t -ET t -R t -ΔS t Control) can still provide important physical consistency guidance for the model, avoid serious violations of physical laws, and help improve the generalization ability of the model. water The deviation between the two can be quantified, and the average of the absolute value of the difference is:

[0056] L water =mean(|ΔG total_pred -Water_Balance_Residual|)

[0057] Where Water_Balance_Residual is the water balance residual calculated based on externally input meteorological data (P, ET) and hydrological data (such as runoff R and surface water storage change ΔS). This loss term aims to improve the physical consistency and generalization ability of the model. The weight coefficients λ1 and λ2 can be determined by optimizing on the validation set using hyperparameter optimization methods (such as grid search) or adaptively adjusting during training using dynamic adjustment strategies (such as the gradient-based GradNorm algorithm). Model training uses a mini-batch stochastic gradient descent method with the Adam optimizer, setting an appropriate batch size and initial learning rate, and applying a learning rate decay strategy.

[0058] Step S4: After the training is completed, the total groundwater storage anomaly (Total GWSA) signal is input into the deep learning model for processing, and the separated shallow groundwater storage anomaly and deep groundwater storage anomaly time series are output.

[0059] The final stage is convergence judgment and result evaluation. The termination condition of the training process can be based on one or more criteria, such as: monitoring the loss function value on the validation set (such as the data-driven loss term L data Or whether the composite loss function L) no longer decreases significantly for multiple consecutive cycles (epochs); whether the satisfaction of the physical constraint item on the validation set reaches the preset threshold, which can be defined as

[0060] Satisfaction = mean(1-|ΔG total_pred -Water_Balance_Residual| / (|ΔG total_GRACE |+∈))

[0061] Where ΔG total_GRACE To observe the absolute value of the abnormal monthly change of total groundwater storage, the goal is to make this indicator reach a high level (such as an average greater than 95%); or to reach the preset maximum number of training iterations. ∈ is a very small positive number (such as e -6 or e -8 ) is used to prevent the denominator of the formula from being zero and to ensure the stability of the calculation. After the training is completed, a comprehensive reliability and physical rationality evaluation of the separation results of the model on the test set is required. The evaluation content includes: evaluating the uncertainty of the prediction results through methods such as Monte Carlo Dropout; conducting spatial distribution rationality analysis, such as qualitatively comparing the predicted shallow / deep groundwater storage anomaly spatial pattern with the known hydrogeological background, land use, surface water system, etc. and calculating quantitative spatial correlation; verifying time series characteristics, such as testing the response relationship of shallow groundwater storage anomaly to effective precipitation (calculating the correlation coefficient), the time inertia of deep groundwater storage anomaly (analyzing the autocorrelation function), and the consistency between the predicted total groundwater storage anomaly and the original input total groundwater storage anomaly (calculating R, R 2 , RMSE and other statistical indicators); if there is independent observation data that is not used for training, external validation can also be performed to further evaluate the generalization performance of the model.

[0062] In summary, the present invention integrates multi-source data, constructs a specific deep learning model structure, and adopts a training strategy that combines data-driven and physical constraints. It can effectively achieve the vertical separation of the total groundwater storage signal of gravity satellites, produce spatiotemporally continuous shallow and deep groundwater storage change products, and has the potential to make predictions in areas where there is a lack of on-site observation data.

[0063] To further illustrate the technical solutions, implementation details and expected effects of the present invention, the following specific embodiments in different regions are provided for illustration.

[0064] Example 1: Implementation process applied to the multi-layer aquifer system in the North China Plain

[0065] This embodiment describes in detail the specific implementation process of the method of the present invention in the North China Plain region where hydrogeological conditions are relatively complex. The North China Plain region has a multi-layer aquifer structure, and both shallow and deep groundwater resources are under significant development pressure. Therefore, in the data preparation stage, the study area is first defined as the North China Plain (for example, the geographical scope is 34.0°-41.0° north latitude, 112.0°-120.0° east longitude), and the study period is determined (for example, from April 2002 to December 2023). On this basis, the total terrestrial water storage anomaly (TWSA) data of the period is obtained, for example, the GRACE / GRACE-FO Mascon RL06M v02 product released by JPL is used, but is not limited to this. At the same time, the hydrological model data of the same period are collected, such as the monthly soil moisture (SMA), snow water equivalent (SWEA) and canopy water (CWSA) data provided by the GLDAS Noah v2.1 model, but is not limited to this. In terms of meteorological data, gridded datasets of monthly total precipitation (P) and total actual evapotranspiration (ET) provided by ERA5-Land are available, but not limited to these.

[0066] In order to establish the reference benchmark required for model training, it is also necessary to collect groundwater level observation records in the study area that can distinguish between shallow layers (such as the upper Quaternary) and deep layers (such as the Neogene). Based on regional hydrogeological data, using representative water supply and release coefficients, the water level data is converted into shallow layers (Shallow_GWSA ref ) and Deep_GWSA ref ) Groundwater storage anomaly reference baseline data, which is used only in the training phase. In addition, land use and land cover (LULC) data and digital elevation model (DEM) data of the region can be optionally integrated as auxiliary information.

[0067] The acquired raw data are first preprocessed systematically. The core step is to calculate the total groundwater storage anomaly (Total GWSA), which is to deduct the non-groundwater component from the total terrestrial water storage anomaly (TWSA). The calculation formula can be expressed as:

[0068] Total GWSA=TWSA-SMA-SWEA-CWSA

[0069] Subsequently, all data, including the calculated total groundwater storage anomaly (Total GWSA), meteorological data, auxiliary data, and reference data, are unified to a preset spatiotemporal resolution (e.g., a 0.25° × 0.25° spatial grid with a monthly time step) using interpolation methods (e.g., bilinear interpolation). Each characteristic variable input into the model is then standardized (e.g., using the Z-Score). Finally, the dataset is divided into training, validation, and test sets in chronological order (e.g., a ratio of 70%:15%:15%).

[0070] Next, we construct a deep learning model using an encoder-decoder architecture, which includes, for example, five layers of convolutional units, each of which contains Conv2D, BatchNormalization, and LeakyReLU activation functions. The encoder compresses features by increasing the number of channels and pooling operations, while the decoder restores the resolution by upsampling and reducing the number of channels. The layers use feature map concatenation to achieve jump connections. A spatial multi-head self-attention module (e.g., 8 heads) is deployed at the bottleneck of the network to capture spatial dependencies. The model input is designed to be a time series tensor, and the time length T_in is set to, for example, 12 months. The feature channels include Total GWSA, P, ET, elevation, and one-hot encoded LULC type. The model output is two channels, corresponding to the shallow layer (Shallow_GWSA) predicted for the current month. pred ) and Deep_GWSA pred ) Abnormal groundwater reserves.

[0071] The model training uses the Adam optimizer, setting the initial learning rate (for example, 1×10 -4 ) and apply the cosine annealing scheduling strategy. The core of the training is to optimize the composite loss function L, which is composed of the data-driven term L data and the physical constraint L water Weighted composition:

[0072] L=λ1·L data +λ2·L water

[0073] Among them, the driving loss term L data To quantify the difference between the model prediction and the reference benchmark data, the mean square error (MSE) can be used to calculate:

[0074]

[0075] The physical constraint loss L water Based on the water balance principle, the monthly change of total groundwater volume predicted by the constraint model is ΔG total_predShould be close to the water balance residual calculated from external data Water_Balance_Residual. First calculate the total change predicted by the model as

[0076] ΔG total_pred =(Shallow_GWSA pred,t -Shallow_GWSA pred,t-1 )+(Deep_GWSA pred,t -Deep_GWSA pred,t-1 )

[0077] The residual in the water balance calculation is:

[0078] Water_Balance_Residual=P t -ET t -R t -ΔS t

[0079] Where R t and ΔS t Depending on the regional situation, an estimated value or simplified processing can be used. The physical constraint loss quantifies the deviation between the two, for example, taking the average of the absolute values ​​of the difference:

[0080] L water =mean(|ΔG total_pred -Water_Balance_Residual)

[0081] The weight coefficients λ1 and λ2 can be determined by hyperparameter optimization or dynamic weighting methods. The training process sets the batch size (for example, to 16) and can implement an early stopping strategy.

[0082] After training, the best-performing model is used to predict the test data set, generating high-resolution monthly spatiotemporal products of shallow and deep groundwater storage anomalies for the study area. The final results are evaluated through a series of validation steps, including quantitative comparison with the test data set reference (calculation of R, RMSE, etc.), consistency testing of the total volume, physical constraint satisfaction (for example, calculating the Satisfaction metric as shown below), analysis of the spatial pattern's conformity with the known hydrogeological context, and reasonableness testing of time series characteristics (such as response relationships and inertia).

[0083] Satisfaction = mean(1-|ΔG total_pred -Water_Balance_Residual| / (|ΔG total_GRACE |+∈))

[0084] Example 2: Adaptive implementation process applied to the Huanghuai Plain and considering the impact of agricultural mining

[0085] This embodiment illustrates the implementation process of the method of the present invention when applied to the Huanghuai Plain, with particular attention paid to the fact that deep groundwater in the region is mainly used for agricultural irrigation. The parts that are the same as those in the above-mentioned embodiment 1 will not be repeated.

[0086] The process of this example is largely the same as that of Example 1, but with a different emphasis on the data preparation and results analysis stages. During data collection, it is important to ensure that the "deep" groundwater levels used for training are representative of the primary agricultural aquifers in the area. Furthermore, land use data or related remote sensing indices that reflect the distribution of high-intensity agricultural activities (such as greenhouse cultivation areas) should be included as model inputs.

[0087] The model structure and training parameters can follow the settings of Example 1. When evaluating and verifying the output results, in addition to conventional indicators, emphasis should be placed on analyzing the spatial distribution of predicted deep groundwater reserves changes and the spatial consistency of known major agricultural production areas and irrigation intensity distributions. At the same time, it is necessary to examine whether the deep GWSA time series has seasonal characteristics that match the regional agricultural irrigation cycle. When interpreting the results, the shallow water quality background of the region should be considered, and it should be clarified that the model output is water quantity information. It is recommended to combine water quality data for comprehensive water resource evaluation.

[0088] The above examples elaborate on the specific operation process, parameter setting examples and verification ideas of the method of the present invention, proving that the method has clear operability for deployment and application under different hydrogeological conditions and can ensure the reliability of the results through a systematic evaluation system.

[0089] The deep learning gravity satellite groundwater vertical signal separation method based on fusion of physical constraints provided by the present invention shows the following significant beneficial effects compared with the existing technology:

[0090] 1) It breaks through the dependence on dense observation data and enhances regional applicability: The traditional gravity satellite groundwater vertical separation method is highly dependent on the reference data provided by the high-coverage groundwater level monitoring well network, which greatly limits its application in areas with scarce hydrogeological data or sparse monitoring wells. The present invention constructs a deep learning model and innovatively introduces a physical constraint loss term, so that the model can get rid of the dependence on real-time well data in the prediction application stage after learning the separation pattern using limited well data in the training stage. The physical constraint ensures that the model can still produce separation results that conform to the laws of hydrophysical laws in areas lacking direct observation constraints, thereby improving the application potential and generalization ability of the model in areas lacking direct observation constraints (especially in areas with hydrogeological and climatic conditions similar to the training area) to a certain extent, and significantly improving the spatial coverage capability and regional applicability of the method, especially in the vast developing regions or remote areas. It has important application value.

[0091] 2) It realizes the effective fusion of multi-source information and improves the separation accuracy and reliability: The method of the present invention not only utilizes the core gravity satellite total groundwater storage signal, but also systematically integrates key meteorological driving factors such as precipitation and evapotranspiration, and allows the inclusion of multi-source auxiliary geographic environmental information such as vegetation, land use, and topography. The deep learning model's powerful nonlinear feature extraction and fusion capabilities can mine complex patterns and potential correlations related to the vertical differentiation of groundwater from these heterogeneous data. Compared with methods that rely solely on a single data source or simple statistical relationships, this multi-source data fusion strategy can more comprehensively characterize the complexity of the groundwater system, thereby improving the accuracy and physical realism of the vertical separation results.

[0092] 3) Strengthened physical mechanism constraints to ensure the physical interpretability and generalization ability of the results: Different from pure "black box" data-driven models, the present invention explicitly introduces physical constraints based on the principle of water balance during the model training process. This constraint directly acts on the changes in total groundwater reserves predicted by the model, forcing it to follow the basic law of conservation of matter. This hybrid modeling paradigm that combines data-driven and physical knowledge not only helps to avoid the model from producing predictions that violate physical common sense and improves the physical interpretability of the separation results, but also strengthens the constraints of the model by introducing prior physical knowledge, which helps to improve the model's generalization potential when facing unseen data or different hydrological conditions, especially under conditions that follow similar physical laws, reducing the risk of overfitting.

[0093] 4) Establishment of a systematic evaluation system to facilitate quality control and verification of results: This paper not only proposes the separation method itself but also incorporates a comprehensive evaluation system encompassing multiple dimensions, including uncertainty assessment, spatial distribution rationality testing, time series feature verification, and independent data validation. This provides a clear framework and metrics for quantitatively assessing the reliability, physical rationality, and model performance of separation results. This evaluation system allows users to conduct comprehensive quality control and verification of model outputs, enhancing the method's technical integrity and credibility in practical applications.

[0094] In summary, the present invention effectively overcomes the limitations of existing technologies in the vertical separation of groundwater using gravity satellites through the organic combination of deep learning technology and hydrophysical knowledge, and provides a new method with higher accuracy, wider applicability, stronger physical significance, and results that are easier to evaluate and verify, providing strong technical support for the stratified and refined monitoring and management of regional groundwater resources.

[0095] Those skilled in the art will appreciate that the accompanying drawings are merely schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0096] Those skilled in the art will appreciate that the modules in the apparatuses of the embodiments may be distributed in the apparatuses of the embodiments as described in the embodiments, or may be located in one or more apparatuses different from the embodiments with corresponding changes. The modules in the above embodiments may be combined into one module or further divided into multiple sub-modules.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints, characterized by: The following steps are involved: Step S1: Acquire and preprocess basic data, wherein the basic data includes: total terrestrial water storage anomaly data derived from gravity satellite observations, hydrological model data for separating non-groundwater components from the total terrestrial water storage anomaly, meteorological data including precipitation P and evapotranspiration ET in the study area, and reference baseline data representing shallow and deep groundwater storage anomalies used in the model training phase; the preprocessing includes: calculating the total groundwater storage anomaly that needs to be vertically separated, unifying all data to a preset spatiotemporal resolution, and removing outliers; Step S2: constructing a deep learning model, wherein the deep learning model is configured to receive a preprocessed time series including total groundwater storage anomalies and meteorological data as input, and output shallow groundwater storage anomalies and deep groundwater storage anomalies at corresponding times; Step S3: Train the deep learning model and optimize it using a composite loss function, where the composite loss function includes: A data-driven loss term L data , used to quantify the difference between the shallow groundwater storage anomaly and the deep groundwater storage anomaly output by the model and the reference benchmark data obtained in step S1; and A physical constraint loss term L based on water balance water , used to quantify the deviation between the monthly change in total groundwater storage calculated from the model output and the water balance residual calculated based on external meteorological and hydrological data input; Step S4: After the training is completed, the total groundwater reserve anomaly signal is input into the deep learning model for processing, and the separated shallow groundwater reserve anomaly and deep groundwater reserve anomaly time series are output.

2. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 1 is characterized in that: The hydrological model data in step S1 include soil moisture storage anomaly, snow water equivalent anomaly and canopy water storage anomaly. The total groundwater storage anomaly is calculated by deducting the soil moisture storage anomaly, snow water equivalent anomaly and canopy water storage anomaly from the total land water storage anomaly.

3. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 1 is characterized in that: The deep learning model in step S2 adopts an encoder-decoder architecture, and both the encoder and decoder include two-dimensional convolutional layers, and jump connections for feature fusion are set between the corresponding layers of the encoder and decoder, and the jump connections are implemented by feature map splicing.

4. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 3 is characterized in that: A multi-head attention module is included at the end of the encoder or at the bottleneck position of the network. The multi-head attention module acts on the spatial dimension of the feature map to capture spatial dependencies.

5. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 1 is characterized in that: The input of the deep learning model in step S2 can also selectively include at least one auxiliary variable of vegetation index, land use / cover type, and terrain elevation.

6. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 1 is characterized in that: The data-driven loss term L in step S3 data The mean square error is used for calculation, and the calculation formula is: Where N is the total number of grid points in the batch sample, Shallow_GWSA ref Deep_GWSA, a reference benchmark representing shallow groundwater storage anomalies ref Shallow_GWSA represents the reference baseline data for deep groundwater storage anomalies. pred Represents shallow groundwater storage anomaly, Deep_GWSA pred It indicates abnormal deep groundwater reserves.

7. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 1 is characterized in that: The physical constraint loss term L based on water balance in step S3 water It is obtained by calculating the mean or mean square error of the absolute values ​​of the differences between the monthly changes in total groundwater storage and the water balance residuals.

8. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 1 is characterized in that: The composite loss function in step S3 is expressed as: L=λ1·L data +λ2·L water Wherein, the weight coefficients λ1 and λ2 are determined by hyperparameter optimization or adaptively adjusted using a dynamic adjustment strategy during training.

9. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 8 is characterized in that: The dynamic adjustment strategy is a weight adjustment algorithm based on the gradient norm.

10. The deep learning gravity satellite groundwater vertical signal separation method integrating physical constraints according to claim 1 is characterized in that: The termination conditions for completing the training in step S4 include any one of the following conditions or a combination of at least two of the following conditions: Monitor the data-driven loss term L on the validation set data Or whether the composite loss function L no longer decreases significantly over multiple consecutive cycles; Whether the satisfaction of the physical constraints on the validation set reaches the preset threshold; The preset maximum number of training iterations has been reached; After training is completed, the reliability and physical rationality of the model separation results on the test set are evaluated, including: evaluating the uncertainty of the prediction results, analyzing the rationality of spatial distribution, verifying time series characteristics, and external verification.

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