A method for assimilating multi-source soil moisture data based on dynamic interval analysis and EnKF

Abstract

This invention discloses a method for assimilating multi-source soil moisture data based on dynamic interval analysis and EnKF. The method includes five steps: data preprocessing, state prediction, dynamic interval analysis, dynamic weight adjustment, and data assimilation update. This invention introduces dynamic interval analysis and dynamic weight optimization mechanisms into traditional methods, significantly improving the accuracy and robustness of data fusion. Combined with Newton's iteration method, it dynamically analyzes the uncertainty intervals of data sources and adjusts the weights, further enhancing the accuracy of data fusion. Based on an improved covariance matrix, it optimizes the Kalman gain matrix, achieving efficient assimilation of multi-source data and enhancing the robustness of data assimilation.

Description

Technical Field

[0001] This invention relates to the technical field of hydrological multi-source data processing methods, specifically to a method for assimilating multi-source soil moisture data based on dynamic interval analysis and EnKF. Background Technology

[0002] Soil moisture is a key variable in hydrological, agricultural, and meteorological models, and the accuracy of its estimation is crucial for drought monitoring, irrigation management, and climate prediction. However, traditional soil moisture estimation methods have several problems:

[0003] (1) It is difficult to dynamically adjust the weights of multi-source data to reflect changes in uncertainty. In practical applications, the reliability of soil moisture data provided by different data sources varies with factors such as time and space. Traditional methods cannot reasonably adjust the weights of each data source in the data fusion process according to the real-time changes in the uncertainty of the data sources, resulting in the data fusion results not accurately reflecting the true soil moisture situation.

[0004] (2) The lack of effective interval analysis methods makes it difficult to accurately characterize the error range of different data sources. Due to the lack of effective interval analysis tools, it is impossible to accurately determine the error range of each data source. This makes it impossible to fully consider the uncertainty of the data during data fusion, thus affecting the accuracy of soil moisture estimation.

[0005] Ensemble Kalman Filtering (EnKF) is an optimization method for assimilating nonlinear and high-dimensional data. It approximates the state distribution of a system by introducing a set of "ensemble" states, thereby enabling data fusion in complex systems. This makes it particularly suitable for problems involving high-dimensional and complex nonlinear variations, such as soil moisture. EnKF overcomes the limitations of traditional Kalman Filtering (KF) in handling nonlinear problems and high-dimensional data. By using multiple sets of predictions as state estimates, it significantly improves the model's adaptability to observed data and computational efficiency. In terms of data processing, EnKF can effectively process and fuse data from multiple sources, especially in situations with significant uncertainty or noise. Summary of the Invention

[0006] To address the problems of traditional soil moisture estimation methods, such as difficulty in dynamically adjusting the weights of multi-source data and the lack of effective interval analysis methods, this invention proposes a multi-source data assimilation method based on dynamic interval analysis and EnKF. This method aims to optimize data weight allocation and covariance adjustment mechanisms to improve the accuracy of data fusion.

[0007] This invention is implemented as follows: a method for assimilating multi-source soil moisture data based on dynamic interval analysis and EnKF, the method comprising the following steps:

[0008] Step 1, Data Preprocessing: Acquire multi-source data, including measured soil moisture data and ERA-5 reanalysis data. Standardize the acquired multi-source data to eliminate dimensional differences between different data sources, so that the multi-source data are consistent in time and space, thereby providing consistent data input for Step 2.

[0009] Step 2, State Prediction: The distributed soil hydrological model generates an initial humidity state prediction set for the target area, including the initial humidity state and its uncertainty estimate, to capture soil humidity changes within the target area;

[0010] Step 3, Dynamic Interval Analysis: Using Newton's iteration, the upper and lower bounds of the uncertainty interval of each data source in the multi-source data in Step 1 are calculated, and the error interval of each predicted value is generated by combining the simulation error propagation mechanism, thereby adjusting the interval range of the initial humidity state prediction set.

[0011] Step 4, Dynamic Weight Adjustment: Optimize the weight allocation function according to the dynamic range, and use a non-linear function to dynamically adjust the weights of multi-source data fusion;

[0012] Step 5, Data Assimilation and Update: Using the dynamically improved covariance matrix and weights, calculate the Kalman gain matrix and update the initial humidity state prediction set to generate the optimal humidity estimate after multi-source data fusion.

[0013] Furthermore, the standardization process described in step 1 includes time alignment, spatial resolution matching, and normalization. The formula for normalization is:

[0014]

[0015] In the formula, x i " x represents the normalized measured soil moisture value. i x represents the original measured soil moisture value. min x represents the minimum humidity among all measured values. max This represents the maximum humidity among all measured values.

[0016] Furthermore, the distributed soil hydrological model mentioned in step 2 is the GBHM geomorphological-based hydrological model.

[0017] Furthermore, the expression for the initial humidity state prediction set mentioned in step 2 is:

[0018] x t+1 =f(x) t +u t )+∈ t (2)

[0019] In the formula, xt+1 x is the predicted value of soil moisture in the next state. t As the current soil moisture status, u t To control the input, f(x) t +u t The function represents the evolution of soil moisture from its current state to its next state. t It is Gaussian white noise.

[0020] Furthermore, the Newton iteration formula mentioned in step 3 is as follows:

[0021]

[0022] In the formula, x n+1 x is an approximation of the (n+1)th iteration. n f(x) is an approximation of the nth iteration. n ) represents the uncertainty of soil moisture, f"(x n ) is a function in x n The derivative value at that point;

[0023] For the i-th data source, the upper and lower bounds of the interval are [L i U i The formulas for calculating the upper and lower bounds of the dynamic interval are:

[0024] L i =x-α i U i =x-β i (4)

[0025] In the formula, x is the initial predicted value of soil moisture, and α i β i These are the upper and lower boundaries of the error interval of the data source, calculated using Newton's iteration method.

[0026] Furthermore, the dynamic adjustment of the multi-source data fusion weights described in step 4 involves assigning higher weights to data sources with smaller uncertainty intervals and correspondingly lower weights to data sources with larger uncertainties. This ensures that different data sources contribute reasonably during the fusion process, improving the accuracy of the data assimilation results. For N data sources, the weight w... i The calculation formula is:

[0027]

[0028] In the formula, i and j are the indices of the data source, Δ i Let Δ be the interval range of the i-th data source. i =U i -L i Δ j Let Δ be the interval range of the j-th data source.j =U j -L j .

[0029] Furthermore, for data sources with smaller uncertainty intervals, the weight range is 0.7–1.0; for data sources with larger uncertainty intervals, the weight range is 0.1–0.3.

[0030] Furthermore, to ensure that the sum of all weights is 1, each weight is normalized. The formula for weight normalization is:

[0031]

[0032] In the formula, w i " The weights after normalization, w i The weights are calculated using formula (5).

[0033] Furthermore, in step 5, the Kalman gain matrix is ​​optimized, the soil moisture state formula is updated, and the error covariance matrix is ​​updated:

[0034] Optimization of the Kalman gain matrix: The formula for calculating the Kalman matrix K is:

[0035] K = PH T (HPH T +R) -1 (7)

[0036] In the formula, P is the error covariance matrix of the predicted state, and H is the measured matrix. T R is the transpose of the measured matrix, and R is the covariance matrix of the measured noise.

[0037] By introducing an improved covariance matrix, the optimized Kalman gain matrix is ​​obtained.

[0038]

[0039] In the formula, The error covariance matrix of the optimized predicted state;

[0040] The updated soil moisture state formula is as follows:

[0041] x t+1 =x t +K(Z t -Hx t (9)

[0042] In the formula, x t+1 For the soil moisture state at the next moment, x t Z represents the current soil moisture state.t This represents the measured soil moisture value at the current moment.

[0043] The formula for updating the covariance matrix is:

[0044] P t+1 =(I-KH)P t (10)

[0045] In the formula, P t+1 Let P be the covariance matrix at the next time step. t Let I be the covariance matrix at the current time, and let I be the identity matrix.

[0046] The beneficial effects of this invention are: by introducing dynamic interval analysis and dynamic weight optimization mechanisms into traditional methods, the accuracy and robustness of data fusion are significantly improved. By combining Newton's iteration method, the uncertainty interval of the data source is dynamically analyzed and the weights are adjusted, thus improving the accuracy of data fusion; and by optimizing the Kalman gain matrix based on an improved covariance matrix, efficient assimilation of multi-source data is achieved, enhancing the robustness of data assimilation.

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0048] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0049] Example 1:

[0050] This embodiment provides a method for assimilating multi-source soil moisture data based on dynamic interval analysis and EnKF, such as... Figure 1 As shown, it includes the following steps:

[0051] Step 1, Data Preprocessing:

[0052] Multi-source data were acquired, including measured soil moisture data and ERA-5 reanalysis data. ERA-5 reanalysis data is a fifth-generation global high-resolution meteorological, climate, and environmental information dataset provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), covering data from 1950 to the present. The data was standardized to eliminate dimensional differences between different data sources. Linear interpolation was used to align the time steps, and bilinear interpolation was employed to match the spatial resolution, ensuring consistency of the multi-source data in both time and space.

[0053] Time alignment unifies the time axes of all data sources to the same time step and start and end points. Spatial matching, based on spatial resolution and coordinate axes, unifies the spatial information from different data sources to the same standard. Normalization normalizes the units and quantities from different data sources to a unified range, facilitating subsequent analysis. For multi-source data, normalization can reduce the impact of different units on the assimilation results. The normalization formula is:

[0054]

[0055] In the formula, x i " x represents the normalized measured soil moisture value. i x represents the original measured soil moisture value. min x represents the minimum humidity among all measured values. max This represents the maximum humidity among all measured values.

[0056] Step 2, State Prediction:

[0057] A distributed soil hydrological model was used to generate a predicted ensemble of soil moisture, including initial moisture states and their uncertainty estimates, providing a foundation for subsequent uncertainty analysis and data assimilation. The initial ensemble contains multiple possibilities to capture soil moisture changes within the target area.

[0058] x t+1 =f(x) t +u t )+∈ t (2)

[0059] In the formula, x t+1 x is the predicted value of soil moisture in the next state. t u represents the current soil moisture state (i.e., the predicted soil moisture value). t To control for inputs, hydrological models typically use external influencing factors such as precipitation, temperature, and evaporation, all of which are important factors affecting soil moisture changes. t +u t The function represents the evolution of soil moisture from its current state to its next state. t Gaussian white noise refers to unpredictable random disturbances or uncertainties, and it is used to represent random uncertainties or errors in model predictions.

[0060] The uncertainty interval of the initial state is calculated using the Newton-Raphson iterative method. Combined with the propagation mechanism of simulation errors (i.e., error accumulation over time and error expansion in space), an error interval for each predicted value is generated, including upper and lower bounds, thus generating an adjusted dynamic interval range. Error accumulation over time refers to the fact that, since soil moisture changes dynamically, any initial error will gradually increase or change over time. Simulation errors propagate and accumulate in subsequent simulations through prediction, update, and correction steps at each time step. Error expansion in space means that if the soil moisture prediction is based on a spatial model (such as the moisture distribution of a certain region), the initial error will not only propagate in the time dimension but also affect the moisture estimation of the entire region, especially in areas with insufficient observational data, where the error will extend to adjacent areas. The dynamic interval is used to describe the uncertainty range of each data source under different conditions, thereby improving the robustness of data assimilation.

[0061] Newton's iterative formula: Assume f(x) n The function described describes the uncertainty of soil moisture, so Newton's iteration is used to determine the root. The iteration formula is:

[0062]

[0063] This process is used to continuously adjust the upper and lower bounds of the uncertainty interval until the convergence condition is met.

[0064] Calculation of upper and lower bounds of dynamic intervals:

[0065] Suppose that for the i-th data source, the upper and lower bounds of the interval are [L]. i U i If the value is ], then it will be updated after each iteration:

[0066] L i =x-α i U i =x-β i (4)

[0067] In the formula, x is the initial predicted value of soil moisture, and α i β i These are the dynamic adjustment values ​​(upper and lower boundaries of the error interval of the data source) obtained through Newton's iteration calculation.

[0068] Step 4, Dynamic Weight Adjustment:

[0069] Based on the accuracy and reliability of model prediction data, ERA-5 reanalysis data, and measured data, weights are dynamically allocated to provide optimized weights for data assimilation. A nonlinear optimization function is used to adjust the weights of multi-source data based on the dynamic range. Specifically, data sources with smaller uncertainty ranges are given higher weights, ranging from 0.7 to 1.0; data sources with larger uncertainty ranges are given lower weights, ranging from 0.1 to 0.3. This adjustment mechanism ensures that different data sources contribute reasonably during the fusion process, improving the accuracy of the data assimilation results.

[0070] For N data sources, the weight w i The calculation formula is:

[0071]

[0072] In the formula, i and j are the indices of the data source, Δ i Let Δ be the interval range of the i-th data source. i =U i -L i Δ j Let Δ be the interval range of the j-th data source. j =U j -L j .

[0073] Weight normalization: To ensure that the sum of all weights is 1, each weight is normalized.

[0074]

[0075] Step 5, Data Assimilation and Update:

[0076] Using the improved covariance matrix The Kalman gain matrix K is used to assimilate the multi-source data and update the humidity state set. Through the dual improvement of dynamic weights and the improved covariance matrix, the optimal soil moisture estimate after fusion is obtained, i.e., formula (9).

[0077] Kalman gain matrix calculation: The formula for calculating the Kalman gain matrix K is:

[0078] K = PH T (HPH T +R) -1 (7)

[0079] In the formula, P is the error covariance matrix of the predicted state, H is the measured matrix of soil moisture data and ERA-5 reanalysis data, and R is the covariance matrix of measured Gaussian white noise. An improved covariance matrix is ​​introduced... The optimized Kalman gain matrix is ​​obtained as follows:

[0080]

[0081]

[0082] State update formula: The formula used to update the soil moisture state is:

[0083] x t+1 =x t +K(Z t -Hx t (9)

[0084] In the formula, x t+1 For the soil moisture state at the next moment, x t Z represents the current soil moisture state. t This represents the measured soil moisture value at the current moment.

[0085] The Kalman gain matrix K is used to adjust for the difference between model predictions and measured values.

[0086] Update of the covariance matrix: Error covariance matrix P t The update formula is:

[0087] P t+1 =(I-KH)P t (10)

[0088] In the formula, P t+1 Let P be the covariance matrix at the next time step. t Let I be the covariance matrix at the current time, and let I be the identity matrix.

[0089] In the dynamically optimized assimilation method, the covariance matrix P t Optimized to P t+1 This allows for a better description of the uncertainty in the system's state.

[0090] Example 2:

[0091] This embodiment is an application example of Embodiment 1, as shown in Table 1:

[0092] Table 1 Application Example Data

[0093]

[0094]

[0095]

[0096] In the table, GBHM represents the soil moisture result output by the hydrological model, ERA-5 represents the soil moisture result extracted from the ERA-5 reanalysis data, SVWC represents the measured soil moisture result, and Kalman_Filter_Estimate represents the result after data fusion based on the improved Kalman filter. The RMSE results compared with the measured soil moisture data (SVWC) are as follows: GBHM vs SVWC: RMSE 0.144; ERA-5 vs SVWC: RMSE 0.037; Kalman_Filter_Estimate vs SVWC: RMSE 0.0014. Kalman_Filter_Estimate has the smallest error compared to SVWC, with an RMSE of 0.0014, indicating that the result fused by Kalman filtering is closest to the measured value and has the highest accuracy. According to calculations, the accuracy improvement of the Kalman filtering method (Kalman_Filter_Estimate) compared to GBHM and ERA-5 is as follows: Compared to GBHM, Kalman filtering improves accuracy by 99.06%. Compared to ERA-5, the Kalman filter improves accuracy by 96.32%.

[0097] Finally, it should be noted that the above is only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention.

Claims

1. A method for assimilating multi-source soil moisture data based on dynamic interval analysis and EnKF, characterized in that, The method includes the following steps: Step 1, Data Preprocessing: Acquire multi-source data, including measured soil moisture data and ERA-5 reanalysis data. Standardize the acquired multi-source data to eliminate dimensional differences between different data sources, so that the multi-source data are consistent in time and space, thereby providing consistent data input for Step 2. Step 2, State Prediction: The distributed soil hydrological model generates an initial humidity state prediction set for the target area, including the initial humidity state and its uncertainty estimate, to capture soil humidity changes within the target area; Step 3, Dynamic Interval Analysis: Using Newton's iteration, the upper and lower bounds of the uncertainty interval of each data source in the multi-source data in Step 1 are calculated, and the error interval of each predicted value is generated by combining the simulation error propagation mechanism, thereby adjusting the interval range of the initial humidity state prediction set. Step 4, Dynamic Weight Adjustment: Optimize the weight allocation function based on the dynamic range. Use a non-linear function to dynamically adjust the weights for multi-source data fusion. Data sources with smaller uncertainty ranges are given higher weights (0.7–1.0); data sources with larger uncertainty ranges are given lower weights (0.1–0.3). This ensures that different data sources contribute reasonably during the fusion process, improving the accuracy of the data assimilation results. For N data sources, the weight w... i The calculation formula is: In the formula, i and j are the indices of the data source, Δ i Let Δ be the interval range of the i-th data source. i =U i -L i Δ j Let Δ be the interval range of the j-th data source. j =U j -L j ; Step 5, Data Assimilation and Update: Using the dynamically improved covariance matrix and weights, calculate the Kalman gain matrix and update the initial humidity state prediction set to generate the optimal humidity estimate after multi-source data fusion.

2. The method for assimilation of multi-source soil moisture data based on dynamic interval analysis and EnKF as described in claim 1, characterized in that, The standardization process described in step 1 includes time alignment, spatial resolution matching, and normalization. The formula for normalization is: In the formula, x i ′ x represents the normalized measured soil moisture value. i x represents the original measured soil moisture value. min x represents the minimum humidity among all measured values. max This represents the maximum humidity among all measured values.

3. The method for assimilation of multi-source soil moisture data based on dynamic interval analysis and EnKF as described in claim 1, characterized in that, The distributed soil hydrological model mentioned in step 2 is the GBHM geomorphological-based hydrological model.

4. The method for assimilation of multi-source soil moisture data based on dynamic interval analysis and EnKF as described in claim 1, characterized in that, The initial humidity state prediction set expression mentioned in step 2 is: x t+1 =f(x t +u t )+∈ t (3) In the formula, x t+1 x is the predicted value of soil moisture in the next state. t As the current soil moisture status, u t To control the input, f(x) t +u t The function represents the evolution of soil moisture from its current state to its next state. t It is Gaussian white noise.

5. The method for assimilation of multi-source soil moisture data based on dynamic interval analysis and EnKF according to claim 1, characterized in that, The Newton iteration formula mentioned in step 3 is: In the formula, x n+1 x is an approximation of the (n+1)th iteration. n f(x) is an approximation of the nth iteration. n ) represents the uncertainty of soil moisture, f ′ (x n ) is a function in x n The derivative value at that point; For the i-th data source, the upper and lower bounds of the interval are [L i U i The formulas for calculating the upper and lower bounds of the dynamic interval are: L i =x-α i ,U i =x-β i (5) In the formula, x is the initial predicted value of soil moisture, and α i β i These are the upper and lower boundaries of the error interval of the data source, calculated using Newton's iteration method.

6. The method for assimilation of multi-source soil moisture data based on dynamic interval analysis and EnKF according to claim 1, characterized in that, To ensure that the sum of all weights is 1, each weight is normalized. The formula for weight normalization is: In the formula, w i ′ The weights after normalization, w i The weights are calculated using formula (5).

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