A method for improving the effectiveness of hydrological data-driven model calibration

Abstract

The application provides a method for improving the effectiveness of a hydrological data driven model, and the steps are as follows: S1: clustering of an original observation data set D is realized by a self-organizing neural network SOM according to steps S11-S15; S2: data preliminarily clustered in each node in the SOM network is distributed into a checking set C and a verifying set E according to steps S21-S27 by using a traditional DUPLEX method; and S3: the checking set C and the verifying set E are used to check and verify a hydrological data driven model. The application effectively combines the traditional SOM clustering method and the DUPLEX sampling method, reasonably divides the observation data into the checking and verifying data sets, and ensures that the data in the two data sets have good distribution consistency, so that the effectiveness of the hydrological data driven model is improved.

Description

Technical Field

[0001] This invention belongs to the field of hydrological model verification, specifically involving technologies to improve the effectiveness of hydrological data-driven model verification. Background Technology

[0002] Hydrological models have a wide range of applications, including watershed runoff prediction, flood and drought forecasting, and assessing the impacts of climate change. Hydrological models are mainly divided into data-driven models and mechanistic models. Data-driven models fully explore the inherent evolutionary patterns of observational data to establish a mathematical model between input conditions and output information, thereby enabling the prediction of future events. Data-driven models do not require a complete understanding of the actual physical processes in hydrology, making the modeling process very simple. In recent decades, data-driven modeling methods have proven to provide good predictive performance and have been successfully applied to practical hydrological forecasting.

[0003] Before application, hydrological models must undergo independent model calibration and validation. Calibration primarily determines the relevant parameter values ​​of the data-driven model, while validation verifies the effectiveness of these parameters in simulating new scenarios. Therefore, observational data typically needs to be divided into two independent datasets: calibration and validation datasets. Previous research has found that the structural parameters obtained during the calibration period can usually reproduce the hydrological behavior of the calibration dataset well. However, if the validation dataset has a significant distributional difference from the calibration dataset, the model validation performance will decline significantly. For example, if the calibration data consists of drought-related hydrological events, while the validation data consists of high-water-season hydrological data, the model's validation performance is usually poor, thus affecting its practical engineering applications. The main reason for this problem is the lack of statistical distribution consistency between the calibration and validation datasets, leading to overly optimistic or pessimistic estimates of the model's performance and reducing the reliability of the model's predictions.

[0004] A direct approach to solving this problem is to ensure that the observed data, after being allocated to the verification and validation datasets, have similar statistical distributions. This guarantees that the model learns as much effective information within the watershed as possible, covering hydrological events of varying degrees, thereby determining appropriate model structure parameters and correctly evaluating model performance. To achieve this, previous researchers have established various data sampling methods, mainly including the SBSS-N method based on Self-Organizing Neural Networks (SOM) and the Neyman Allocation Principle, and the DUPLEX method based on Euclidean distance and single-linkage distance clustering algorithms. The SBSS-N method is a stochastic method, and the data allocation results vary to some extent each time, while DUPLEX is a deterministic method, and the data allocation results are consistent each time. Through extensive watershed sample testing, the results demonstrate that these two traditional data allocation strategies significantly outperform completely random sampling methods, greatly improving the verification effectiveness of the model; that is, the difference between the verification and validation results of the model is reduced compared to random sampling methods. However, both methods also have significant drawbacks: the SBSS-N method tends to overestimate the model's true predictive ability, while the DUPLEX method tends to underestimate the model's true predictive ability. These shortcomings significantly affect the practical engineering applications of hydrological data-driven models.

[0005] To address the aforementioned challenges, this invention proposes a method for verifying the effectiveness of hydrological data-driven models. By rationally analyzing the characteristics and shortcomings of SOM clustering and DUPLEX methods, and effectively combining the advantages of both methods, a novel data allocation method, which we name SOMPLEX, is proposed. This method is then applied to 717 different hydrological observation datasets for modeling tests. The results show that the SOMPLEX method is a data allocation method with significant advantages, which can significantly improve the verification effectiveness of hydrological data-driven models, thereby enhancing the reliability of the models in engineering applications. Summary of the Invention

[0006] The technical problem to be solved by this invention is to propose a method to improve the effectiveness of hydrological data-driven model verification. This method effectively combines the traditional SOM clustering method and DUPLEX sampling method, reasonably divides the observation data into verification and validation datasets, and ensures that the data in the two datasets have good distribution consistency, thereby improving the effectiveness of hydrological data-driven model.

[0007] The specific technical solution adopted in this invention is as follows:

[0008] A method for improving the effectiveness of hydrological data-driven model verification includes the following steps:

[0009] S1: Clustering of the original observation dataset D is achieved through the self-organizing neural network SOM in steps S11-S13;

[0010] S11: Calculate the amount of data N in the original observation dataset D, determine the number of nodes M of the SOM according to empirical formula 1-1, and determine the number of rows r and columns c of the network according to empirical formula 1-2, thereby determining the topology of the SOM neural network. The specific formulas are as follows:

[0011]

[0012] M = r × c, r = 1.6c 1-2

[0013] S12: Randomly initialize the weights of each node in the SOM network, generally selecting values ​​in the range of -0.5 to 0.5; simultaneously, perform z-score standardization on the data in the original observation dataset D.

[0014] S13: The standardized original observation dataset D is put into the SOM network for multiple rounds of training until convergence. At this time, the nodes in the SOM network have a different number of data clusters. The data features within the same node are similar, while the data features of different nodes are significantly different. Thus, the preliminary clustering of the data is completed.

[0015] S2: Using the traditional DUPLEX method, the data that has been initially clustered in each node of the SOM network is allocated to the check set C and the validation set E according to steps S21-27;

[0016] S21: Determine the total amount of data required for the verification and validation datasets based on the proportion specified by the user, denoted as n. C and n E For each node in the SOM network, determine the amount of data to be allocated to C and E in that node proportionally, denoted as n respectively. C (m) and n E (m) The specific calculation formula is as follows:

[0017]

[0018] Similarly, n can be calculated. E (m) Among them, |U (m) | represents the amount of data aggregated within that node;

[0019] S22: Initialize the local subset for the current SOM node m. Data sampling for the current node;

[0020] S23: Find a pair of data x within the current SOM node m.i ,x j ∈U (m) Make the Euclidean distance ||x i -x j Maximize the allocation of this pair of data to C. (m) ;

[0021] S24: Repeat S23 to assign data to E (m) ;

[0022] S25: Find the next pair of data within the current SOM node m, where the first data is related to C. (m) The single-linkage distance is the largest, followed by the second largest. These two data points are then assigned to C. (m) ;

[0023] S26: Repeat S25 to allocate data at E (m) Then S25 is repeated continuously, and data is allocated to the verification and validation datasets in turn until one of the local subsets reaches the set number of samples, and the remaining data is directly allocated to the other local subset;

[0024] S27: C (m) Merge into C, E (m) Merge into E;

[0025] S3: Use the check set C and the validation set E to check and validate the hydrological data-driven model.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] (1) This invention proposes a novel dataset partitioning method for verification and validation of hydrological data-driven models, which is more advantageous than traditional sampling methods and can significantly improve the validation effectiveness of hydrological data-driven models.

[0028] (2) This invention is an important contribution to the field of hydrological data-driven models. It provides a new data preprocessing approach for hydrological modelers, effectively ensuring the accuracy of evaluating the predictive performance of the model and has broad practical engineering application value.

[0029] (3) Although the novel data partitioning method proposed in this invention has only been tested in hydrological data-driven models, it has great application potential and can be reasonably extended to other types of hydrological models, such as machine learning models. Attached Figure Description

[0030] Figure 1 This is a roadmap for the specific implementation of the present invention.

[0031] Figure 2This is a schematic diagram showing the locations of the 717 watersheds in the embodiment.

[0032] Figure 3 This is the result of random initialization of network nodes after the implementation of SOM in watershed 50.

[0033] Figure 4 This is the SOM clustering result of the example in watershed number 50.

[0034] Figure 5 This is a skewness distribution map of watershed runoff data in an example.

[0035] Figure 6 This is a diagram showing the relative deviation distribution of the three methods across the entire watershed in the embodiment.

[0036] Figure 7 This is a diagram showing the relative deviation distribution of the three methods under different runoff data skewnesses in the embodiments.

[0037] Figure 8 This is a comparison chart of the relationship between the average ranking of the three methods and the skewness of runoff data across the entire watershed in the embodiment. Detailed Implementation

[0038] The present invention will now be described in detail with reference to the accompanying drawings and embodiments, so that those skilled in the art can better understand the essence of the present invention.

[0039] See Figure 1 This invention provides a method for improving the effectiveness of hydrological data-driven model verification, the steps of which are as follows:

[0040] A method for improving the effectiveness of hydrological data-driven model verification includes the following steps:

[0041] S1: Clustering of the original observation dataset D is achieved through the self-organizing neural network SOM in steps S11-S13;

[0042] S11: Calculate the amount of data N in the original observation dataset D, determine the number of nodes M of the SOM according to empirical formula 1-1, and determine the number of rows r and columns c of the network according to empirical formula 1-2, thereby determining the topology of the SOM neural network. The specific formulas are as follows:

[0043]

[0044] M = r × c, r = 1.6c 1-2

[0045] S12: Randomly initialize the weights of each node in the SOM network, generally selecting values ​​in the range of -0.5 to 0.5; simultaneously, perform z-score standardization on the data in the original observation dataset D.

[0046] S13: The standardized original observation dataset D is put into the SOM network for multiple rounds of training until convergence. At this time, the nodes in the SOM network have a different number of data clusters. The data features within the same node are similar, while the data features of different nodes are significantly different. Thus, the preliminary clustering of the data is completed.

[0047] S2: Using the traditional DUPLEX method, the data that has been initially clustered in each node of the SOM network is allocated to the check set C and the validation set E according to steps S21-27;

[0048] S21: Determine the total amount of data required for the verification and validation datasets based on the proportion specified by the user, denoted as n. C and n E For each node in the SOM network, determine the amount of data to be allocated to C and E in that node proportionally, denoted as n respectively. C (m) and n E (m) The specific calculation formula is as follows:

[0049]

[0050] Similarly, n can be calculated. E (m) Among them, |U (m) | represents the amount of data aggregated within that node;

[0051] S22: Initialize the local subset for the current SOM node m. Data sampling for the current node;

[0052] S23: Find a pair of data x within the current SOM node m. i ,x j ∈U (m) Make the Euclidean distance ||x i -x j Maximize the allocation of this pair of data to C. (m) ;

[0053] S24: Repeat S23 to assign data to E (m) ;

[0054] S25: Find the next pair of data within the current SOM node m, where the first data is related to C. (m) The single-linkage distance is the largest, followed by the second largest. These two data points are then assigned to C. (m) ;

[0055] S26: Repeat S25 to allocate data at E (m)Then S25 is repeated continuously, and data is allocated to the verification and validation datasets in turn until one of the local subsets reaches the set number of samples, and the remaining data is directly allocated to the other local subset;

[0056] S27: C (m) Merge into C, E (m) Merge into E;

[0057] S3: Use the check set C and the validation set E to check and validate the hydrological data-driven model.

[0058] The following description of the method of the present invention is combined with specific implementation examples to demonstrate its specific technical effects. The specific steps of the method will not be repeated.

[0059] An application example

[0060] The proposed SOMPLEX method has been tested on rainfall-runoff datasets from 717 watersheds. The watershed locations are distributed as follows: Figure 2 As shown, 315 of these watersheds are located in Australia, and another 402 are located in the United States. These watersheds vary significantly in area, rainfall, runoff skewness, and evapotranspiration characteristics, sufficiently covering most hydrological features under real-world conditions. The distribution range of runoff data skewness is shown in the figure. Figure 3 As shown, the runoff data of the watershed are unevenly distributed, with a large number concentrated within 10, and the number of watersheds with larger skewness is relatively small.

[0061] Data from watershed number 50 was selected to illustrate the operation of the SOMPLEX method:

[0062] (1) Determine the length of the watershed dataset as N = 3650, and perform z-score standardization on the data. Determine the SOM network topology according to step S1, where the number of network nodes M = 121 is calculated using formula 1-1, the number of rows r = 14, and the number of columns c = 9 are calculated using formula 1-2. The weights of each node are randomly initialized as follows: Figure 4 As shown.

[0063] (2) After the SOM network is trained, the amount of data contained in each node is as follows: Figure 5 As shown.

[0064] (3) Set the allocation ratio of calibration set C to validation set E to 80% / 20%, therefore the required data amounts are n respectively. C =2930, n E =720.

[0065] (4) Distribute the data to each node in sequence, for example Figure 4 The first node U (1)If the node contains 97 data points, then the amount of data that needs to be allocated to C and E in this node can be calculated using formula 1-3, n. C (m) =78, n E (m) =19.

[0066] (5) Distribute the data within this node to two local subsets C according to the method in step S2. (m) and E (m) After the allocation is completed, the two local subsets will be merged into C and E respectively.

[0067] (6) Once all nodes have completed data allocation, the SOMPLEX data allocation process is complete.

[0068] The novel method proposed in this invention will be implemented in 717 watersheds, and hydrological data-driven models will be established using the divided data. The performance of the method of this invention and the traditional data allocation method in verifying the effectiveness of hydrological data-driven models will be compared from a statistical perspective.

[0069] The General Regression Neural Network (GRNN) was chosen as the data-driven model for testing because GRNN has a simple structure, and the error between the output data and the training samples is determined only by the smoothing factor in the kernel function. Therefore, it has a very simple performance control method and does not require training a large number of parameters. This ensures that the training result of the neural network is determined only by the data, making it easy to compare the impact of various data allocation methods on the model training result.

[0070] The validation dataset C is used for training and parameter selection of the GRNN, where the model's performance is evaluated using the root mean square error (RMSE). The trained GRNN is then evaluated using the validation dataset E to assess its performance on unseen data.

[0071] For each watershed, the SOMPLEX method of this invention and the two traditional methods, DUPLEX and SBSS-N, were each run 100 times randomly. Each method yielded 100 data allocation results (each result consisted of two datasets, C and E). The model was then trained using each allocation result, resulting in a total of 215,100 (717 × 3 × 100) data-driven models. For each watershed, the average RMSE of the model obtained from running each method 100 times was calculated by comparing it with the baseline value. Calculations are performed, including baseline values ​​for each watershed. This has been obtained through extensive experimental research by predecessors, allowing for the calculation of the relative bias (RB,%) of the model's predictive performance. The calculation formula is as follows:

[0072]

[0073] 717 watersheds may yield 717 RBs, thus allowing for a statistical comparison of the effectiveness of various methods in verifying data-driven models.

[0074] Figure 6 The figure shows the RB distribution of the three methods across the entire watershed. As can be seen from the figure, the SOMPLEX method proposed in this invention is significantly better than the traditional DUPLEX and SBSS-N in evaluating model performance. Traditional methods tend to overestimate or underestimate the model's predictive performance, while SOMPLEX's evaluation results are closer to the model's true performance, i.e., the RB value is very small.

[0075] Figure 7 This is a comparison of the RB distribution plots for the three methods under different runoff data skewnesses, showing the performance of the three methods under different data characteristics. Figure 7 It can be seen that, under various runoff data skewness conditions, the RB distribution of SOMPLEX proposed in this invention is significantly better than the traditional data allocation method, which further confirms the superiority of the SOMPLEX method.

[0076] Figure 8 This is a comparison chart showing the relationship between the average ranking of the three methods and the skewness of runoff data across the entire watershed. The steps for calculating the average ranking of each method are as follows: First, calculate the absolute values ​​of RB (|RB|) for the three methods in each watershed, and sort them in ascending order. Then, based on... Figure 6 The skewness classification of runoff data is used to calculate the average ranking of each method in this classification.

[0077] from Figure 8 As can be seen, under various runoff data skewnesses, the average ranking of SOMPLEX is significantly better than the other two methods, which once again demonstrates the significant advantage of this method in model performance evaluation.

[0078] Therefore, the novel data allocation method proposed in this invention can effectively improve the effectiveness of hydrological data-driven model verification and provide a reasonable evaluation of model performance. Thus, this invention has broad application prospects, providing a systematic data optimization allocation strategy for hydrological model establishment, thereby improving the reliability of model application and possessing significant promotional and practical application value.

Claims

1. A method for improving the effectiveness of hydrological data-driven model verification, characterized in that, The steps are as follows: S1: Clustering of the original observation dataset D is achieved through the self-organizing neural network SOM in steps S11-S13; S11: Calculate the amount of data N in the original observation dataset D, determine the number of nodes M of the SOM according to empirical formula 1-1, and determine the number of rows r and columns c of the network according to empirical formula 1-2, thereby determining the topology of the SOM neural network. The specific formulas are as follows: M = r × c, r = 1.6c 1-2 S12: Randomly initialize the weights of each node in the SOM network, selecting a range from -0.5 to 0.5; simultaneously, perform z-score standardization on the data in the original observation dataset D; S13: The standardized original observation dataset D is put into the SOM network for multiple rounds of training until convergence. At this time, the SOM network has a different amount of data in each node. The data features in the same node are similar, while the data features in different nodes are significantly different. This completes the initial clustering of the data; S2: Using the traditional DUPLEX method, the data that has been initially clustered in each node of the SOM network is allocated to the check set C and the validation set E according to steps S21-27; S21: Determine the total amount of data required for the verification and validation datasets based on the proportion specified by the user, denoted as n. C and n E For each node in the SOM network, determine the amount of data to be allocated to C and E in that node proportionally, denoted as n respectively. C (m) and n E (m) The specific calculation formula is as follows: Similarly, n can be calculated. E (m) Among them, |U (m) | represents the amount of data aggregated within that node; S22: Initialize the local subset for the current SOM node m. Data sampling for the current node; S23: Find a pair of data x within the current SOM node m. i ,x j ∈U (m) Make the Euclidean distance ||x i -x j Maximize the allocation of this pair of data to C. (m) ; S24: Repeat S23 to assign data to E (m) ; S25: Find the next pair of data within the current SOM node m, where the first data is related to C. (m) The single-linkage distance is the largest, followed by the second largest. These two data points are then assigned to C. (m) ; S26: Repeat S25 to allocate data at E (m) Then S25 is repeated continuously, and data is allocated to the verification and validation datasets in turn until one of the local subsets reaches the set number of samples, and the remaining data is directly allocated to the other local subset; S27: C (m) Merge into C, E (m) Merge into E; S3: Use the check set C and the validation set E to check and validate the hydrological data-driven model.

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