Global soil moisture prediction method based on average cluster sampling strategy

Abstract

This paper presents a global soil moisture prediction method based on an average cluster sampling strategy, using group samples uniformly extracted from regions with heterogeneous soil moisture variation characteristics for training. Ensuring diversity in samples from different regions and uniformity in sample selection helps to stably learn features during model training. Experiments were conducted on the LandBench dataset, using five different seeds for a 1-day global forecast. The results for each seed were averaged, and the results show that the proposed group sampling strategy outperforms several traditional LSTM-based models that do not adopt this strategy, with a median R 2 Improvements range from 2.36% to 4.31%, while improvements from KGE range from 1.95% to 3.16%. Furthermore, at high latitudes, especially in specific regions, the proposed strategy demonstrates significant improvements in explanatory power, with R² improvements exceeding 40%. This validates the effectiveness of the proposed sampling strategy and introduces a new training paradigm to enhance generalization capabilities for the deep learning community.

Description

Technical Field

[0001] The present invention belongs to the technical field of soil moisture prediction, and in particular relates to a global soil moisture prediction method based on an average cluster sampling strategy. Background Art

[0002] Soil moisture (SM) is a key state variable in climate, hydrology, and ecosystems. It couples atmospheric processes with land surface states, further influencing precipitation patterns, surface temperature, surface-atmosphere energy exchange, and ecosystem health and productivity. Accurately predicting global soil moisture is therefore crucial for effectively addressing climate change, ensuring water security, and promoting ecosystem health.

[0003] Currently, soil moisture prediction models are primarily divided into two categories: physics-based process models and data-driven empirical models. Process models employ physical equations to govern hydrological processes governing soil moisture dynamics. Short-term soil moisture forecasts based on process models can be categorized into two approaches. The first approach involves hydrological forecast models operating in a real-time prediction mode. This approach relies on atmospheric model-generated (online) or observed meteorological fields such as precipitation and radiation to drive the model (offline), and soil moisture calculations are integrated into the land surface data assimilation scheme. The second approach involves land surface process models, which can operate at scales ranging from single points to regions and even global locations, and can also be performed online or offline. However, land surface and hydrological forecast models suffer from strong statistical distribution assumptions, uncertain soil properties, and inaccurate meteorological input data. Furthermore, land surface process models suffer from imperfect representations of physical processes and large errors in parameterization schemes. These limitations lead to significant errors in soil moisture predictions.

[0004] Data-driven empirical models achieve forecasts by mapping explanatory variables (atmospheric observations: temperature, precipitation, and solar radiation, etc.; surface observations: soil temperature and vegetation, etc.) to soil moisture, describing the nonlinear relationship between the two in an end-to-end manner. Data-driven methods are mainly divided into statistical methods, machine learning, and deep learning. In recent years, data-driven models, represented by deep learning, have demonstrated significant advantages in the field of global soil moisture forecasting and achieved remarkable results. The LSTM network is an advanced deep learning technology. Its significant advantage comes from its unique memory gate mechanism. By capturing long-term dependencies and continuously transmitting information, it effectively solves the vanishing or exploding gradient problem that traditional neural networks often encounter when processing sequential data, thereby achieving accurate forecasts. Therefore, it is widely used in soil moisture forecasting.

[0005] Based on this, a global soil moisture prediction method based on the average cluster sampling strategy is proposed. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a global soil moisture prediction method based on an average cluster sampling strategy to address the deficiencies of the above-mentioned prior art, so as to solve the problems raised in the above-mentioned background technology.

[0007] To solve the above technical problems, the technical solution adopted by the present invention is: a global soil moisture prediction method based on an average cluster sampling strategy, comprising the following steps:

[0008] Six key variables were selected as the basis for distinguishing soil properties: soil water capacity, land type, soil sand, soil clay, soil silt, and digital elevation model (DEM). These variables were clustered using the K-means clustering algorithm, and the classification results were visualized. A batch size of k samples was uniformly sampled from each region and passed to an LSTM-based model. The idea of ​​cluster average sampling was incorporated into three models: the LSTM model, the Encoder-Decoder LSTM, and the Attention LSTM. This was used to train the prediction model, which was then evaluated.

[0009] As a further illustration of the present invention, to cluster a certain static variable using the K-means clustering algorithm, it is first necessary to pre-specify the number of initial clusters, i.e., the number of defined soil moisture variation characteristic categories;

[0010] Then randomly initialize the cluster centers in the cluster. Secondly, for each sample x in the static variable j , calculate it to each cluster center The distance between two points is calculated using the Euclidean distance formula:

[0011]

[0012] Afterwards, for each cluster, the cluster center is recalculated to make it the mean of all points in the cluster. The cluster center update formula is:

[0013]

[0014] Among them, C i represents the set of all samples in the i-th cluster,

[0015] | C i | is cluster C iRepeat until the cluster center no longer changes, and assign a corresponding label to each sample in the corresponding static variable to mark the cluster to which the sample belongs;

[0016] Then, in the area corresponding to the samples in each cluster, the input corresponding to the area is uniformly extracted and placed in the model for training. The formula is as follows:

[0017]

[0018] Indicates the number of clusters;

[0019] Indicates the size of each batch, that is, the number of samples entering the model training;

[0020] int represents the rounding function;

[0021] represents the kth sample belonging to the i-th cluster;

[0022] C i represents the set of all samples in the i-th cluster;

[0023] Finally, each batch of Input into the model for training.

[0024] As a further illustration of the present invention, the experimental setting input data of the prediction model of the LSTM Model consists of 15 variables from T-365 days to T-1 day, the batch size is set to 64, the input size of the prediction model is 64×365×15, and the output is the predicted soil moisture for the next day, which is the same size as the input. For the LSTM-based prediction model, the size of the hidden layer is set to 128, which is sent to the dropout layer, and finally the predicted SM for the next day is obtained through the fully connected layer based on the output of LSTM on T-1 day. The number of iterations is empirically set to 400, the batch size is set to 128, and the Adam optimizer is used for training.

[0025] As a further illustration of the present invention, the encoder in the EncoderDecoder LSTM uses an LSTM model and a fully connected layer to extract input data features related to soil moisture and capture the key factors affecting soil moisture changes. The fully connected layer mainly integrates the extracted features and maps the output of the LSTM layer to the output dimension. The decoder processes the output features of the encoder through the LSTM layer, which helps the model further refine the analysis of time series features related to soil moisture. The EncoderDecoder LSTM model effectively captures the dynamic change trend of time series data by analyzing the current data and the soil moisture change trend, thereby improving the prediction accuracy of future soil moisture changes.

[0026] As a further illustration of the present invention, the experimental setup of the AttentionLSTM prediction model uses the same input data as the LSTM model. Through parallel processing, the multi-head attention mechanism effectively distinguishes and quantifies the specific impact of each prediction variable on soil moisture at different time scales. Finally, the fully connected layer is used to convert the last day's data into the prediction result.

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] 1. This paper integrates a group sampling mechanism into different LSTM-based models, including CAS-LSTM, CAS-EncoderDecoderLSTM, and CAS-AttentionLSTM. This study investigates whether this improves soil moisture prediction for the next day. The CAS-LSTM-based model is tested for different soil attributes (soil water capacity, land type, soil sand, soil clay, soil silt, and DEM) to determine the best representative attribute and use this to predict soil moisture.

[0029] 2. The method in this invention demonstrates that the cluster average sampling method has significant advantages in model batch training. This method can enhance the diversity of batch training, reduce the deviation caused by data imbalance, improve the generalization ability and stability of the model, and provide a new paradigm for other researchers in global land surface element prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of group sampling in the present invention;

[0031] Figure 2 It is the density scatter plot of the predicted and observed SMs using the CAS-LSTM model with all different numbers of groups and different static variables in the present invention;

[0032] (a) shows a scatter plot with regression density lines for LSTM. Figures (b, c, d, e, f, g) show scatter plots with regression density lines comparing the performance of CAS-LSTM in predicting one-day soil moisture using the optimal number of groups.

[0033] Figure 3 It is the cumulative distribution plot of KGE and RMSE of LSTM and cluster average sampling (CAS-LSTM) based on different soil characteristics as grouping in the present invention;

[0034] Among them, (a) and (b) are the overall effects, (c) and (d) are the locally enlarged cumulative distribution diagrams in the red box, showing (b) and (d) to more clearly show the subtle differences between different models in the high-performance range;

[0035] Figure 4 Figure 2 is a box plot showing the performance of two deep learning models in this invention (the CAS-LSTM model performs clustered average sampling based on different soil characteristics) in predicting the results for the next day in different climate regions.

[0036] (a) The climate zone box plot shows the R of each model. 2 .

[0037] (b) Box plot depicting the KGE of climate regions.

[0038] (c) Boxplots showing the RMSE across different climate zones. The horizontal axis of each plot represents a different climate zone. The 30 climate regions are divided into five zones based on the Köppen climate zoning: tropical (R1), arid (R2), temperate (R3), cold (R4), and polar (R5). The vertical axis represents the corresponding metric value. Each boxplot consists of five horizontal lines, representing the maximum, 75th percentile, median, 25th percentile, and minimum value derived from the simulations of each deep learning model.

[0039] Figure 5 It is a time series diagram of one-day prediction of the two models in different regions 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. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0041] like Figure 1As shown, the present invention provides a technical solution: a global soil moisture prediction method based on an average cluster sampling strategy. First, six key variables, namely soil water capacity, land type, soil sand, soil clay, soil silt, and digital elevation model (DEM), are selected as the basis for distinguishing soil characteristics. The K-means clustering algorithm is used to cluster the above variables, and the classification results are visualized. Samples of batch size / k are evenly extracted from each area, and the selected samples are passed to the LSTM-based model. The idea of ​​cluster average sampling is integrated into three models: LSTM Model, EncoderDecoderLSTM, and AttentionLSTM to complete the training of the prediction model, and finally an evaluation is performed.

[0042] The process structure of soil moisture prediction is as follows: Figure 1 The proposed structure consists of two key pipelines: a deep learning model for random sampling and a deep learning model for cluster average sampling. Figure 1 (a) is the input data. Input data is input to Figure 1 (b) and Figure 1 (c).

[0043] Figure 1 (b) shows the traditional training method: random sampling. The arrow on the left of this strategy represents all model input data, with four colored circles representing samples with different soil moisture characteristics. The arrow on the right represents the randomly selected samples to be trained. These samples are then fed into the three LSTM-based models for training.

[0044] The LSTM-based models used in this example are the traditional LSTM model, the LSTM model with encoder-decoder, and the LSTM model with attention mechanism. Figure 1 (d) Conduct an assessment.

[0045] Evaluation index (determination coefficient R 2 , root mean square error (RMSE), and Kling-Gupta efficiency coefficient (KGE) were used to evaluate whether the model improved the performance of global soil moisture prediction with a lead time of 1 day.

[0046] Figure 1(c) shows the CAS-LSTM process. This process first selects six key variables: soil water capacity, landtype, soil sand, soil clay, soil silt, and DEM as the basis for distinguishing soil characteristics. Considering that the K-means algorithm can effectively divide samples into categories with similar characteristics, this embodiment uses the K-means clustering algorithm to cluster these variables.

[0047] Figure 1 (c) Taking the cluster center equal to 4 as an example, the K-means clustering algorithm automatically divides the above variable into four different soil moisture parameter clusters, each of which is assumed to characterize a characteristic of soil moisture changes.

[0048] To visualize these classification results, red, blue, green, and yellow are used to indicate samples in four regions with different soil moisture characteristics. Next, batch size / k samples are uniformly sampled from each region. This sampling method ensures that samples with different soil characteristics are evenly transmitted during each batch training, allowing the model gradient descent to fully account for the diversity of global soil moisture changes. The selected samples are passed to the LSTM-based model. Then, input Figure 1 (d) Conduct an assessment.

[0049] To cluster a static variable using the K-means clustering algorithm, the number of initial clusters must first be specified in advance, i.e., the number of defined soil moisture change characteristic categories;

[0050] Then randomly initialize the cluster centers in the cluster. Secondly, for each sample x in the static variable j , calculate it to each cluster center The distance between two points is calculated using the Euclidean distance formula:

[0051]

[0052] Afterwards, for each cluster, the cluster center is recalculated to make it the mean of all points in the cluster. The cluster center update formula is:

[0053]

[0054] Among them, C i represents the set of all samples in the i-th cluster,

[0055] | C i | is cluster C iRepeat until the cluster center no longer changes, and assign a corresponding label to each sample in the corresponding static variable to mark the cluster to which the sample belongs;

[0056] Then, in the area corresponding to the samples in each cluster, the input corresponding to the area is uniformly extracted and placed in the model for training. The formula is as follows:

[0057]

[0058] Indicates the number of clusters;

[0059] Indicates the size of each batch, that is, the number of samples entering the model training;

[0060] int represents the rounding function;

[0061] represents the kth sample belonging to the i-th cluster;

[0062] C i represents the set of all samples in the i-th cluster;

[0063] Finally, each batch of Input into the model for training.

[0064] In the experimental setup for the LSTM-based forecasting model, the input data consisted of the 15 variables mentioned in Chapter 2 from days T-365 to T-1, and the batch size was set to 64. Therefore, the input size of the forecasting model was 64 × 365 × 15. The output was the predicted soil moisture for the first day in the future, the same size as the input. For the LSTM-based forecasting model, the hidden layer size was set to 128.

[0065] To reduce overfitting in the deep learning model, a dropout layer was applied. Finally, a fully connected layer based on the LSTM output on day T-1 was used to obtain the predicted SM for the next day. The number of iterations was empirically set to 400, the batch size to 128, and training was performed using the Adam optimizer.

[0066] In the EDLSTM model, the encoder explores the complex features of the input variables in the time dimension through deep learning methods, while the decoder generates predictions based on the features extracted by the encoder, thereby enhancing the accuracy of the predictions.

[0067] The encoder uses an LSTM model and fully connected layers to extract input data features related to soil moisture, such as soil temperature, precipitation, soil composition, and other parameters, thereby accurately capturing the key factors influencing soil moisture changes. The fully connected layer primarily integrates the extracted features and maps the LSTM layer output to the output dimension. The decoder processes the encoder's output features through the LSTM layer, helping the model further refine its analysis of time series features related to soil moisture. Subsequent steps are similar to the LSTM model, with a dropout layer used to reduce the risk of overfitting. At the final time step, a fully connected layer is used to convert the network output into a prediction result. By analyzing current data and soil moisture trends, the EDLSTM model effectively captures the dynamic trends of time series data, thereby improving the accuracy of predictions of future soil moisture changes.

[0068] The input data in the experimental setting of the AttLSTM prediction model is the same as that of the LSTM model.

[0069] The output of the LSTM layer is then converted into the input of a multi-head attention mechanism, whose dimensions (365, 64, 128) represent the time length, the number of grid points, and the number of hidden units, respectively. Through parallel processing, the multi-head attention mechanism effectively distinguishes and quantifies the specific impact of each predictor variable on soil moisture at different time scales, significantly improving the model's ability to capture changing trends in soil moisture characteristics. The subsequent processing is the same as that of the LSTM model, including a dropout layer to reduce overfitting, and finally a fully connected layer to convert the last day's data into a forecast result.

[0070] Through extensive experiments, this embodiment determines a set of optimized long short-term memory (LSTM) model parameters.

[0071] The learning rate is set to 0.001 to promote stable convergence of the model during training;

[0072] The batch size is set to 64, which effectively reduces the risk of overfitting;

[0073] Set the training epochs to 1000 to ensure that the model can deeply learn the complex features in the dataset;

[0074] The number of iterations is 400, which ensures sufficient parameter updates in each training cycle and helps find the optimal weight configuration;

[0075] The dropout rate was set to 0.15 to prevent the model from being overly sensitive to any single feature or pattern in the training data;

[0076] The number of heads of the multi-head attention mechanism is set to 2 to maintain the generalization ability of the model;

[0077] The series length is 365 days, which enables the model to identify seasonal variations and long-term dependencies over the course of a year.

[0078] The above mentioned variables are used as input data to train the prediction model for predicting SM. All input data are standardized.

[0079] To test the prediction model presented in this study, three indicators were calculated, including R 2 , Kling-Gupta efficiency coefficient (KGE) and root mean square (RMSE) were used to evaluate the performance of the forecast model at a 1-day lead time. 2 It can accurately measure the degree to which the model captures data changes. RMSE can be a good measure of the accuracy of the model's prediction of volatility. KGE can be a good assessment of the similarity between the model's predicted distribution and the actual observed distribution. The three criteria are calculated as follows:

[0080]

[0081]

[0082]

[0083]

[0084] in is from the ERA5-Land dataset at time Soil moisture observations at .

[0085] It is based on the DL model in time The predicted soil moisture value.

[0086] is the mean of the soil moisture observations.

[0087] is the average of the predicted soil moisture values.

[0088] is the standard deviation of the soil moisture observations.

[0089] The standard deviation of the soil moisture predictions.

[0090] By comparing the R 2 , KGE, RMSE and other indicators are used to compare the performance of the two sampling methods in experimental results to judge the effect of the sampling method, and the performance of cluster average sampling is analyzed through the experimental result graph.

[0091] In this experimental example, the number of groups in cluster average sampling and the selection of static variables affect the performance of the model. Based on the LSTM model, the effects of these different parameters on the model performance are tested.

[0092] The CAS-LSTM(SWC), CAS-LSTM(LT), CAS-LSTM(SSD), CAS-LSTM(SC), CAS-LSTM(SST), and CAS-LSTM(DEM) models, each consisting of six static variables (soil water capacity, landtype, soil sand, soilclay, soil silt, and DEM), were tested. The number of groups k in each model was set to 3, 4, 6, and 8, respectively.

[0093] First, the above DL model is trained. Except for the number of groups and the static variables used in clustering, all other hyperparameters of the CAS-LSTM model are set to the same as those of the LSTM model.

[0094] Figure 2 Density scatter plots of the predicted and observed SMs for the CAS-LSTM model using all different numbers of groups and different static variables.

[0095] The regression line between the predicted soil moisture value and the observed soil moisture value for the next day of the CAS-LSTM model is closer to the ideal line (y = x) than that of other DL models.

[0096] It can be seen that k=3 is the best number of groups for CAS-LSTM (SC) model to predict SM, which is better than that when k is 4, 6, and 8. 2 It increased by about 2.7%-16%; KGE increased by about 1.2%-11.3%; and RMSE decreased by about 0.1%-0.9%.

[0097] For CAS-LSTM (LT), compared with k=3, when the number of groups k is 4, 6, and 8, the overall deviation between the predicted value and the true value is larger, and it cannot fit well near the regression line.

[0098] Therefore, when landtype is used to characterize the soil moisture change characteristics, k=3 is selected as the hyperparameter of the clustering algorithm in the CAS architecture.

[0099] If the number of groups is too small, different actual groups may be merged into larger clusters, thereby losing some important information in the data; if the number of groups is too large, there will be very few data points in each cluster, which may cause the clustering to be too sensitive to noise and outliers and prone to overfitting.

[0100] That is, when the number of groups k is 6 or 8, the CAS-LSTM model performs slightly worse than the traditional LSTM model. When the number of groups k is 4, all CAS-LSTM models outperform the randomly sampled LSTM model in all aspects. When the number of groups k is 3, except for the CAS-LSTM(SWC) model, all other phenomena are similar to those when k=4. Based on the above analysis, it can be concluded that CAS-LSTM(SWC), CAS-LSTM(SSD), and CAS-LSTM(DEM) perform best when the number of groups is 4, while CAS-LSTM(SC), CAS-LSTM(SST), and CAS-LSTM(LT) perform best when the number of groups is 3.

[0101] Figure 2 The optimal number of groups for different CAS-LSTM models is determined. Compared with LSTM without cluster average sampling, R 2 The results show that the KGE increased by about 2.2% to 5.3%, and the RMSE decreased by about 0.2% to 0.5%. The best improvement results came from the CAS-LSTM (SC) model.

[0102] Figure 3 CDF plots for different models are indicated.

[0103] CDF is a probability function that describes the probability that a random variable will have a value less than or equal to a certain value. Figure 3 (a) The CDF curve of LSTM is higher than that of all CAS-LSTM models when the KGE value is around 0.65-0.85, indicating that more than 60% of the LSTM models have a KGE value below 0.85.

[0104] exist Figure 3 In (b), we can see that when KGE is close to 1, CAS-LSTM (SSD), CAS-LSTM (SST), and CAS-LSTM (DEM) extend farther than the LSTM model, indicating that these models have higher KGE values ​​in the test of some samples.

[0105] Figure 3 (d) Yes Figure 3 (c) A partial zoom of the cumulative distribution of RMSE shows that the probability of the LSTM model's error being extremely low is higher than that of all CAS-LSTM models. However, as the RMSE increases, the slope of the CDF curve increases, indicating that the proportion of samples with lower errors in the LSTM model is actually lower than that of the CAS-LSTM model. It is worth noting that

[0106] Figure 3(a) shows that as the KGE value increases from 0 to 0.6, the cumulative probability of the CAS-LSTM (SC) model increases relatively slowly, which means that the KGE values ​​of most data points are concentrated in the higher SC value area. When the SC value increases from 0.8 to 1.0, the yellow dotted line shows a faster rise, indicating that most of the high scores are concentrated in the range of 0.8 to 1.0. The RMSE also shows the same trend. Figure 5 The conclusions are similar. When SC is used as the basis for constructing the cluster average sampling of the CAS-LSTM model, the CAS-LSTM model performs best.

[0107] In addition to the above-mentioned evaluation of the global prediction indicators of different hyperparameters of the CAS model, this experimental example also tested the local performance of the model in different regions. From the scatter plot, the k value with the best performance of each variable was selected. Based on the selection of different variables, a box plot was designed to show the model effect in different climate regions, as shown below. Figure 4 As shown,

[0108] Observation shows that the model prediction performance obtained by cluster averaging different static variables varies, indicating that selecting an appropriate variable as the basis for cluster averaging sampling is crucial. Based on the first letter of the 1 km resolution Köppen-Geiger climate classification map (present and future), the 30 climate zones originally proposed by Hylke E. Beck et al. were divided into five. Due to the lack of soil moisture in the Arctic, the EF region is not considered. The classification method is described below.

[0109] The following table shows the partitions of R1-R5 corresponding to AE.

[0110]

[0111] R1 is a tropical climate; R2 is an arid zone; R3 is a mild zone; R4 is a snowy area and R5 is an extremely low area;

[0112] comprehensive Figure 4 Judging from the median of the boxes in (a, b), the CAS-LSTM model has improved R2, R4, and R5 compared to the LSTM model, but the R2 of the CAS-LSTM (DEM) is lower than that of the LSTM in the R4 region;

[0113] Depend on Figure 4(c) As can be seen, the CAS-LSTM model's error in region R4 is lower than that of the LSTM model. R5 is an extremely low region, and its error is not shown. Observing the individual models in each region, we find that in the rainforest region of R1, the CAS-LSTM (LT) model performs significantly worse than the other models. In regions R4 and R5, the CAS-LSTM (DEM) model's KGE improves by 1%-11% compared to the LSTM model. This is because polar regions are rich in glaciers and cold regions are rich in mountain ranges. Compared to other variables, DEMs can better characterize the differences between these regions and other regions, helping the CAS model achieve better prediction results in these areas. In the tropical region of R3, with the exception of the CAS-LSTM (SC) model, all other CAS-LSTM models perform slightly worse than the LSTM model. This is because soil properties in tropical regions (such as sand and clay content) can vary significantly at smaller spatial scales, complicating model prediction. Compared to sandy soils, clay soils have a more uniform texture, which helps the prediction model better understand and simulate the dynamics of soil moisture.

[0114] In the cold regions (R4) and polar regions (R5), the median RMSE of the CAS-LSTM model in the cold regions was approximately 0.02, which was an improvement of approximately 33.3% compared to the LSTM model. In the cold regions (R4) and polar regions (R5), the CAS-LSTM model showed a significant improvement in performance. The improvement in the minimum value indicates that the R 2 In the R2 region, the performance improvement over the LSTM model was significant, reaching 40%. KGE achieved a nearly 60% improvement. Overall, CAS-LSTM (SC) outperformed the LSTM model in all metrics across all regions. Therefore, subsequent experiments used CAS-LSTM (SC) for comparison and analysis.

[0115] Combining box plot analysis with consideration of climate zoning, we observe that the CAS-LSTM model demonstrates improved performance in soil moisture prediction for arid (R2) and cold (R4) climate regions. Given that these regions encompass the arid zone extending from northern Africa to northwestern China, as well as the cold zone encompassing Canada, Russia, eastern Europe, and northeastern China, the CAS-LSTM model's improvement in soil moisture prediction is likely to be even more significant in these climate regions.

[0116] In order to verify the generalization of the cluster average sampling method on different models, the CAS-LSTM (SC), CAS-EDLSTM (SC), and CAS-AttLSTM (SC) models were selected to compare the R of the corresponding three LSTM-based models. 2 ,KGE,RMSE on a global scale.

[0117] Among the satisfactory predictions of soil moisture by all models, soil moisture is higher in southern China, northern Brazil, southeastern United States, and south-central Africa, while soil moisture is relatively lower in northwestern China, northern Africa, southern Brazil, and southwestern United States.

[0118] These results show that the CAS-LSTM (SC)-based model outperforms other LSTM-based models in forecasting 1-day lead time. In eastern Canada, northern Russia, and northwestern China, the CAS-LSTM-based model outperforms the LSTM-based model R 2 Improvement of about 50%, RMSE improvement of about 30%, KGE improvement of about 30%;

[0119] There was also some improvement in other mid- and high-latitude regions. However, the improvement was less pronounced in some areas of the Southern Hemisphere, with indicators in southern Australia decreasing by approximately 0% to 30%. This also demonstrates that the CAS-LSTM-based model performs better in cold regions.

[0120] The forecast performance of the CAS-AttLSTM model with 365 time steps is compared, and it outperforms the randomly sampled AttLSTM model. To evaluate the temporal variation of the forecast, the one-year time series forecast of the AttLSTM model with 365 time steps and the CAS-AttLSTM model are compared with the true value with a lead time of 1 day.

[0121] Among the satisfactory soil moisture predictions of all models, soil moisture is higher in southern China, northern Brazil, southeastern United States, and south-central Africa, while soil moisture is relatively lower in northwestern China, northern Africa, southern Brazil, and southwestern United States.

[0122] These results show that the CAS-LSTM (SC)-based model outperforms other LSTM-based models for one-day lead time forecasts. In eastern Canada, northern Russia, and northwestern China, the CAS-LSTM-based model improves R² by approximately 50%, RMSE by approximately 30%, and KGE by approximately 30% compared to the LSTM-based model.

[0123] There was also some improvement in other mid- and high-latitude regions. However, the improvement was slightly less pronounced in some areas of the Southern Hemisphere, with indicators decreasing by approximately 0% to 30% in southern Australia. This also demonstrates that the CAS-LSTM-based model performs better in cold regions.

[0124] like Figure 5The following graph shows a time series of soil moisture. The horizontal axis represents the time series from 0 to 365 days, and the vertical axis represents the soil moisture value. Soil moisture values ​​are roughly distributed between 0 and 0.5. Each of the six graphs has three lines. The black line represents the observed value; the red line represents the predicted value using AttLSTM; and the blue line represents the predicted value using CAS-AttLSTM.

[0125] Six points corresponding to different longitudes and latitudes around the world were selected for image analysis. The following is an analysis of them.

[0126] Figure 5(a) shows 33S and 120E in Western Australia, Australia, a state with diverse topography and climates, including arid, semi-arid, and temperate climates. The soil types are also diverse, making them suitable for different ecosystems and agricultural production. The blue box shows that when predicting soil moisture 145-175 days out, the group sampling method consistently underestimates the actual soil moisture, and the prediction performance deviates from the LSTM method.

[0127] Figure 5 (b) is located in central California, USA, at 40°N, 121°W. It is adjacent to higher elevations and features valleys, mountains, and canyons. The climate is warm and dry.

[0128] Figure 5 (c) is located at 67N, 115W in northern Canada, within the Canadian Arctic Circle. The climate is extremely cold, and the soil type is likely mainly glacial soil and rocky gravel. Vegetation growth is limited by climate and topography.

[0129] Figure 5 (d) is 76N, 105E, located in northern Siberia, Russia, near the Taimyr Peninsula. The terrain is complex, the climate is extremely cold, and the soil types are likely primarily glacial and gravelly. Vegetation growth is restricted by the climate and terrain.

[0130] Figure 5 (e) is 60N, 82E, located in southern Siberia, near the southern extension of the Carpathian Mountains. The climate is temperate continental, and soil types primarily include black soil, forest soil, and riverine soil, making it suitable for various ecosystems and agricultural production.

[0131] Figure 5 (f) is an area at 6N, 35E located in South Sudan. Its topography may be mainly plains and hills, the climate may be tropical, and the soil types may include black soil, sandy soil and riverine soil, which are suitable for different types of ecosystems and agricultural production.

[0132] Figure 5 (b)-(f) show that when soil moisture changes slowly, the CAS-AttLSTM model is relatively close to the observed values, even matching them. When soil moisture changes rapidly, the CAS-AttLSTM model is closer to the true value than the LSTM model (as shown in the small figure on the right).

[0133] Figure 5 The results show that the CAS-AttLSTM model predicts soil moisture for 365 time steps better than the AttLSTM in capturing the changing trend. These results indicate that the CAS-AttLSTM model has its own advantages and its proper use will improve the prediction.

[0134] Overall, soil moisture prediction in the Northern Hemisphere is better than in the Southern Hemisphere. CAS-AttLSTM is an AttLSTM model that optimizes sampling and is much more complex than traditional LSTM models that use random sampling.

[0135] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0136] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A global soil moisture prediction method based on an average cluster sampling strategy, characterized by: The following steps are involved: First, six key variables were selected as the basis for distinguishing soil characteristics: soil water capacity, land type, soil sand, soil clay, soil silt, and digital elevation model (DEM). These variables were clustered using the K-means clustering algorithm, and the classification results were visualized. A batch size of k samples was uniformly sampled from each region and passed to an LSTM-based model. The idea of ​​cluster average sampling was incorporated into three models: the LSTM model, the Encoder-Decoder LSTM, and the Attention LSTM. The prediction model was trained and finally evaluated. Among them, the K-means clustering algorithm clusters a static variable. First, it is necessary to pre-specify the number of initial clusters, that is, the number of defined soil moisture change characteristic categories; Then randomly initialize the cluster centers in the cluster. Secondly, for each sample x in the static variable j , calculate it to each cluster center The distance between two points is calculated using the Euclidean distance. The formula is: ； Afterwards, for each cluster, the cluster center is recalculated to make it the mean of all points in the cluster. The cluster center update formula is: ； Among them, C i represents the set of all samples in the i-th cluster, | C i | is cluster C i Repeat until the cluster center no longer changes, and assign a corresponding label to each sample in the corresponding static variable to mark the cluster to which the sample belongs; Then, in the area corresponding to the samples in each cluster, the input corresponding to the area is uniformly extracted and placed in the model for training. The formula is as follows: ； Indicates the number of clusters; Indicates the size of each batch, that is, the number of samples entering the model training; int represents the rounding function; represents the kth sample belonging to the i-th cluster; C i represents the set of all samples in the i-th cluster; Finally, each batch of Input into the model for training; Experimental setup for the LSTM model: The input data consists of 15 variables from day T-365 to day T-1, and the batch size is set to 64. The input size of the prediction model is 64×365×15. The output is the predicted soil moisture for the next day, the same size as the input. For the LSTM-based prediction model, the hidden layer size is set to 128, which is fed into the dropout layer. Finally, a fully connected layer based on the LSTM output on day T-1 is used to obtain the predicted SM for the next day. The number of iterations is empirically set to 400, the batch size is set to 128, and the Adam optimizer is used for training. The encoder in the EncoderDecoder LSTM uses an LSTM model and fully connected layers to extract input data features related to soil moisture and capture the key factors affecting soil moisture changes. The fully connected layer mainly integrates the extracted features and maps the output of the LSTM layer to the output dimension. The decoder processes the encoder's output features through the LSTM layer, which helps the model further refine its analysis of time series features related to soil moisture. By analyzing current data and soil moisture change trends, the EncoderDecoder LSTM model effectively captures the dynamic changes in time series data, thereby improving the accuracy of predicting future soil moisture changes. The experimental setup of the AttentionLSTM prediction model uses the same input data as the LSTM model. Through parallel processing, the multi-head attention mechanism effectively distinguishes and quantifies the specific impact of each prediction variable on soil moisture at different time scales. Finally, a fully connected layer is used to convert the last day's data into a prediction result.

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