A non-uniform hydrological simulation and prediction method based on multi-dimensional dependence analysis and mother wavelet optimization

Abstract

The application discloses a non-uniform hydrological simulation and prediction method based on multi-dimensional dependence analysis and mother wavelet optimization, and belongs to the technical field of hydrology and water resources engineering. The method first collects multi-source hydrological and meteorological sequences, completes pretreatment through detrended pre-whitening and modified Mann-Kendall test, and eliminates autocorrelation and trend interference; then adopts a moving window full correlation method based on matrix Renyi entropy to identify the physical mutation year of the nonlinear dependence relationship between multivariate hydrological sequences; a mother wavelet optimization framework based on K-S test is constructed to objectively select the optimal mother wavelet and extract sequence multi-scale features; finally, the sequence is divided into stages according to the comprehensive mutation year, and the prediction is completed by adopting segmented parameter calibration of the hydrological physical model. The application solves the problems of high-dimensional nonlinear dependence mutation detection difficulty and strong subjectivity of mother wavelet selection in the prior art, significantly improves the hydrological prediction accuracy under the non-uniform environment, and is suitable for the scenes of basin water resources management, flood control, drought resistance and disaster reduction.

Description

Technical Field

[0001] This invention belongs to the field of hydrology and water resources engineering technology, specifically involving non-consistent hydrological sequence mutation detection, multi-scale feature extraction and hydrological simulation and forecasting technology, which can be widely applied to scenarios such as watershed water resources planning and management, flood control and drought relief, water ecological environment protection, and water conservancy project scheduling and operation. Background Technology

[0002] Hydrological simulation and forecasting are core technical supports for ensuring watershed water security. Under the dual impact of global climate change and strong human activities, the evolution patterns of key hydrological elements such as rainfall, runoff, and evaporation in watersheds have undergone significant changes. Hydrological sequences exhibit strong randomness, nonlinearity, and nonstationarity, directly undermining the core fundamental assumption of "independent and identically distributed sequences" in traditional hydrological simulation. This has led to a significant decrease in the accuracy and stability of traditional hydrological forecasting methods, making them unable to meet the needs of watershed water security under non-uniform environments.

[0003] Currently, the relevant technologies for handling and simulating hydrological series inconsistencies, both domestically and internationally, mainly suffer from the following technical shortcomings: (1) Univariate inconsistency detection is severely affected by autocorrelation. Traditional trend and mutation tests are represented by the Mann-Kendall (MK) test, which assumes that the sequence is autocorrelation-free. However, measured hydrological sequences generally have significant autocorrelation. Directly using traditional methods will lead to an underestimation of the variance of the test statistic, falsely reporting the trend in trendless sequences, and causing the detection results to be distorted. Most existing correction methods do not combine detrending and pre-whitening processes simultaneously, and cannot eliminate the dual interference of trend and autocorrelation terms on mutation detection at the same time.

[0004] (2) Insufficient ability to detect abrupt changes in high-dimensional multivariate nonlinear dependencies. Existing multivariate hydrological dependency detection methods are mostly based on linear correlation coefficients or Copula functions. Linear correlation coefficients cannot capture nonlinear dependencies between hydrological variables. In three-dimensional and higher-dimensional scenarios, Copula functions face the "curse of dimensionality" problem, which is difficult to construct joint distribution functions, has high computational complexity, and is difficult to calibrate parameters. It is difficult to effectively identify abrupt changes in nonlinear dependencies between high-dimensional hydrological variables and cannot accurately quantify the variation characteristics of multi-factor co-evolution and the key time points of human activity interference.

[0005] (3) The selection of the mother wavelet in wavelet feature extraction is highly subjective. Wavelet analysis is the mainstream method for multi-scale spatiotemporal feature extraction of hydrological sequences, but its feature extraction results are highly dependent on the selection of the mother wavelet. In the existing technology, the selection of the mother wavelet mostly depends on the researcher's subjective experience and lacks objective and quantitative selection criteria. This leads to significant differences in the feature extraction results obtained by using different mother wavelets for the same sequence. The feature extraction results lack uniqueness and reliability, which directly affects the accuracy of subsequent hydrological simulation and forecasting.

[0006] (4) Hydrological models have poor adaptability and stability in non-consistent environments. Most traditional hydrological models are built based on the assumption of sequence consistency and adopt a unified parameter calibration mode for the entire sequence. When the underlying surface conditions of the watershed change abruptly, the physical mechanism of the watershed hydrological cycle changes fundamentally. The uniformly calibrated model parameters cannot adapt to the different hydrological processes before and after the abrupt change, resulting in a significant decrease in the model simulation accuracy and instability of forecast results. Summary of the Invention

[0007] The purpose of this invention is to address the aforementioned deficiencies in existing technologies by providing a method for detecting and extracting abrupt changes in non-consistent hydrological sequences based on multidimensional dependency analysis and mother wavelet optimization. This method solves the technical problems in existing technologies, such as incomplete elimination of autocorrelation interference, difficulty in detecting abrupt changes in high-dimensional nonlinear dependency, lack of objective basis for mother wavelet selection, and poor model forecast stability under non-consistent environments. It enables high-precision and high-stability simulation and forecasting of hydrological processes under climate change and strong human activity interference.

[0008] To achieve the above-mentioned objectives, this invention provides a non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization, comprising the following steps: Step 1: Data Acquisition and Preprocessing: Obtain multi-source hydrological and meteorological sequences of the watershed to be measured, preprocess the sequences to eliminate interference from trend terms and autocorrelation components, and simultaneously complete sequence trend identification and preliminary abrupt change detection; Step 2: Multivariate Dependency Abrupt Detection: Full correlation is introduced to quantify the total linear and nonlinear dependency strength between multivariate hydrological sequences. The full correlation value is estimated using a matrix-based Renyi α-order entropy functional. A moving window full correlation sequence is constructed using moving window technology. The physical abrupt change year of the dependency relationship between multivariate hydrological sequences is identified through a segmentation algorithm. Step 3: Mother wavelet optimization and multi-scale feature extraction: The results of mutation detection by multiple methods are fused to construct a set of potential mutation points. The Kolmogorov-Smirnov test is used to calculate the degree of sequence variation corresponding to each potential mutation point. Based on the preset quantitative judgment criteria, the optimal mother wavelet is selected from the candidate mother wavelet set. The multi-scale spatiotemporal features of the hydrological sequence are extracted through the optimal mother wavelet. Step 4: Inconsistent segmented hydrological simulation and forecasting: Based on the comprehensive physical abrupt change years determined in Step 2 and Step 3, the research sequence is divided into at least two hydrological periods. The parameters of the hydrological physical model are calibrated for different hydrological periods to complete the hydrological forecasting under inconsistent conditions.

[0009] Preferably, in step 1, the preprocessing adopts the detrended pre-whitening TFPW method, and at the same time, the modified Mann-Kendall test is used to complete trend identification and preliminary mutation point detection. The modified Mann-Kendall test method corrects the variance of the test statistic S by introducing an autocorrelation correction factor based on the sequence rank; the corrected variance is the product of the theoretical variance of the traditional Mann-Kendall test statistic and the autocorrelation correction factor based on the sequence rank. The autocorrelation correction factor is calculated using an empirical approximation formula based on the autocorrelation functions of the rank of hydrological sequence observations and the total number of sequence observations.

[0010] Preferably, the detrended pre-whitening TFPW method specifically includes the following steps: Step 1.1: The linear trend slope of the hydrological series is extracted using Sen's slope method. The linear trend slope is the median of the ratio of the difference between all observations with later time numbers and observations with earlier time numbers in the series to the difference of the corresponding time step. Step 1.2: Remove the linear trend term from the sequence to obtain the detrended sequence; Step 1.3: Calculate the first-order autocorrelation coefficient of the detrended sequence, remove the first-order autocorrelation component from the detrended sequence, and obtain the pre-whitened residual sequence; Step 1.4: Restore the linear trend term to the pre-whitened residual sequence to obtain the final pre-whitened sequence.

[0011] Preferably, in step 2, the total correlation is used to quantify the total dependence strength among multivariate hydrological sequences, and its value is the sum of the marginal entropies of all univariate hydrological sequences minus the joint entropy of the multivariate hydrological sequences; the matrix-based Renyi α-order entropy is calculated from the eigenvalues ​​of the Gram matrix after normalization of the multivariate hydrological sequences, and is used to estimate the univariate marginal entropy and the multivariate joint entropy.

[0012] Preferably, in step 2, the window width of the moving window technique is set according to the sequence time scale, and the step size is 1 time unit sliding along the time axis. The total correlation value is calculated window by window to construct the moving window total correlation sequence. The segmentation algorithm adopts the Bernaola-Galván BG segmentation algorithm to identify the years of significant physical abrupt changes in the sequence.

[0013] Preferably, in step 3, the potential mutation point set is constructed by fusing the cumulative anomaly method, the modified Mann-Kendall test, and the multivariate dependent mutation detection results from step 2, and all significant mutation points are merged to form the potential mutation point set; The degree of sequence variation is the maximum absolute difference of the empirical cumulative distribution function of the two subsequences before and after the potential mutation point over the entire range; when the Kolmogorov-Smirnov test shows asymptotic significance... pWhen the value is less than 0.01, the potential mutation point is determined to be a strong significant mutation point.

[0014] Preferably, in step 3, the preset quantitative judgment criteria include the following four items: Criterion 1: Significance level of Kolmogorov-Smirnov test for sequences before and after potential mutation points p ≤0.05; Criterion 2: Potential mutation points can achieve a continuous, non-overlapping division of the hydrological sequence from start to end; Criterion 3: The mutation trajectory corresponding to the selected mother wavelet contains the largest number of strongly significant mutation points; Criterion 4: Before the initial segment in the mutation trajectory m The degree of variation at each point is minimal. m This represents the number of sequence points corresponding to the step size of the moving window.

[0015] Preferably, in step 3, the candidate mother wavelet set includes db series, sym series, coif series, fk series, and morlet series wavelet basis functions; multi-scale spatiotemporal feature extraction of hydrological sequences is completed through continuous wavelet transform; the continuous wavelet transform adjusts the time scale of the optimal mother wavelet through a scaling factor and adjusts the time position of the optimal mother wavelet through a translation factor, and performs an inner product operation between the hydrological sequence and the complex conjugate function of the translated and scaled optimal mother wavelet to obtain wavelet transform coefficients at different scales and time positions.

[0016] Preferably, in step 4, the hydrological period is divided into natural periods and periods of human activity disturbance. The natural period is the time when the watershed hydrological cycle mechanism is not significantly disturbed by human activities, and the period of human activity disturbance is the time when the watershed hydrological cycle mechanism undergoes significant changes. The hydrological physical model adopts a hydrological model based on the principle of water balance, with runoff as the core forecast target.

[0017] Preferably, in step 4, the Nash-Sutcliffe efficiency coefficient and relative error are used to evaluate the model's simulation and forecasting performance. The Nash-Sutcliffe efficiency coefficient is calculated as follows: 1 minus the sum of squares of the differences between measured and simulated flow rates, and the ratio of the sum of squares of the differences between measured flow rates and their series mean. The closer the value is to 1, the higher the model's simulation accuracy. The relative error is calculated as follows: the ratio of the sum of the differences between simulated and measured flow rates to the sum of measured flow rates, expressed as a percentage. The smaller the absolute value, the smaller the overall simulation error of the model.

[0018] The present invention has the following beneficial effects: 1. This invention optimizes the variance of the Mann-Kendall test statistic by using a rank-based autocorrelation correction factor, combined with TFPW detrending pre-whitening processing, simultaneously eliminating the dual interference of hydrological series autocorrelation and trend term on inconsistency detection, significantly reducing the trend false alarm rate, and solving the problem of severe autocorrelation interference in traditional univariate detection methods.

[0019] 2. The moving window fully correlated mutation detection method based on matrix entropy proposed in this invention directly estimates the fully correlated value of multiple variables through matrix Renyi entropy, avoiding the dimensionality curse of high-dimensional probability density estimation. It can effectively capture the linear and nonlinear co-variable characteristics among multiple variables such as rainfall, runoff, and evaporation, accurately locate the key time points of human activities' interference with hydrological processes, and solve the problem of insufficient detection capability of high-dimensional nonlinear dependent mutations in existing technologies.

[0020] 3. This invention constructs a mother wavelet optimization framework based on the KS test. Through four clear quantitative judgment criteria, it automatically selects the mother wavelet that best matches the physical characteristics of the hydrological sequence from the candidate wavelet set. This completely eliminates the subjective randomness of mother wavelet selection in traditional wavelet analysis and ensures the uniqueness, reliability and repeatability of the multi-scale periodic feature extraction results of the hydrological sequence.

[0021] 4. This invention divides the sequence into stages based on the results of multivariate dependent mutation detection, and uses a physical model based on the principle of water balance for segmented parameter calibration. This allows the model parameters to be adapted to different hydrological and physical mechanisms before and after the mutation, as well as under strong human activity interference. This fundamentally solves the problem of decreased simulation accuracy and unstable forecast results of traditional models after environmental mutations. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0024] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0025] Example 1: Reference Figure 1 This embodiment provides a non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization, including the following steps: Step 1: Data Acquisition and Preprocessing: Obtain multi-source hydro-meteorological sequences of the watershed to be measured, use the detrended pre-whitening (TFPW) method to eliminate the trend term and autocorrelation components of the sequence, and at the same time use the modified Mann-Kendall test method to introduce an autocorrelation correction factor based on the sequence rank to correct the variance of the test statistic, and identify the trend and preliminary abrupt change points of the hydrological sequence. The detrended prewhitening (TFPW) method can remove the influence of the dominant trend in the original data series on the estimation of the autocorrelation coefficient, so as to more accurately perform the MK test on the data series.

[0026] The Mann-Kendall (MK) trend test is a nonparametric rank test that does not require the original data to follow a certain distribution and is not affected by a few outliers or missing data. However, it requires the original sequence to be independent. If the original sequence has autocorrelation, it will significantly amplify the trend of the sequence.

[0027] The detrended pre-whitening (TFPW) method specifically includes the following steps: Step 1.1: Extract the linear trend slope of the hydrological series using Sen's slope method. The slope of the linear trend is the median of the ratios of the differences between all observations with later time numbers and those with earlier time numbers in the sequence, to the differences at corresponding time steps. The formula is as follows: ; In the formula, , These are the hydrological sequence numbers. , One observation value; The median; Because extreme values ​​often exist in hydrological series, the median depends only on the sorting position of the slope estimates. Even if there are a few extreme values, the median is difficult to be skewed. Therefore, the median is less susceptible to interference than the mean, ensuring the reliability of trend extraction.

[0028] Step 1.2: Remove the trend term from the sequence to obtain the detrended sequence. : ; In the formula, For the hydrological sequence number One original observation value, For time step; Step 1.3: Remove the first-order autocorrelation component from the detrended sequence to obtain the pre-whitened residual sequence. : ; In the formula, Detrended sequence The first-order autocorrelation coefficient; Step 1.4: Restore the trend term to obtain the final pre-whitening sequence. : ; The modified Mann-Kendall test method corrects the variance of the test statistic S by introducing an autocorrelation correction factor based on series rank. The corrected variance is the product of the theoretical variance of the traditional Mann-Kendall test statistic and the autocorrelation correction factor based on series rank. The corresponding variance correction formula for the modified Mann-Kendall test method is as follows: ; In the formula, The corrected test statistic variance The theoretical variance of the traditional Mann-Kendall test statistic. The number of observations in the hydrological sequence. This is a rank-based autocorrelation correction factor; The autocorrelation correction factor is calculated based on the autocorrelation functions of each order of the rank of the hydrological sequence observations, combined with the total number of sequence observations, using an empirical approximation formula. The empirical approximation formula for the corresponding autocorrelation correction factor is as follows: ; In the formula, The rank of the hydrological series observations Order autocorrelation function; Step 2: Multivariate Dependency Abrupt Change Detection: Total Correlation (TC) is introduced to quantify the strength of linear and nonlinear total dependence among multivariate hydrological sequences, using a matrix-based approach. The entropy functional estimates the total correlation value, and the moving window total correlation (MCTC) sequence is constructed by combining the moving window technique. The Bernaola-Galván (BG) segmentation algorithm is used to identify the physical abrupt change year of the dependency relationship between multivariate hydrological sequences. The total correlation is used to quantify the overall dependence strength among multivariate hydrological sequences. Its value is the sum of the marginal entropies of all univariate hydrological sequences minus the joint entropy of the multivariate hydrological sequences. The definition formula for the total correlation is: ; In the formula, For the dimensions of hydrological variables, Single variable marginal entropy, for Joint entropy of hydrological variables; The matrix-based Renyi α-order entropy is calculated using the eigenvalues ​​of the Gram matrix after normalization of the multivariate hydrological sequence. It is used to estimate the univariate marginal entropy and the multivariate joint entropy. The formula for calculating the matrix-based Renyi α-order entropy is as follows: ; In the formula, for Gram matrix after normalization of hydrological sequence Gram matrix The 1 eigenvalue, for The order of entropy and .

[0029] Renyi α-order entropy theory defines entropy on the normalized eigenspectrum of the Gram matrix, where the Gram matrix is ​​the Hermitian matrix of the projected data in the reproducing Hilbert space. Matrix Renyi α-order entropy theory can directly estimate the marginal and joint entropies of variables from high-dimensional data without simulating the probability distribution of the variables.

[0030] The moving window technique sets the window width according to the sequence time scale, slides along the time axis with a step size of 1 time unit, and calculates the full correlation value window by window to construct the moving window full correlation sequence; the segmentation algorithm adopts the Bernaola-Galván BG segmentation algorithm to identify the years of significant physical abrupt changes in the sequence.

[0031] Compared with traditional methods, the BG segmentation algorithm uses a t-test to segment a non-stationary sequence into multiple stationary subsequences with different means. Each subsequence represents a different physical background, and the scale of each mean segment obtained by the decomposition is variable and not limited by the method itself.

[0032] For a nonlinear time series {x(t)} {t=1,2,.....,N} with N observations, the calculation steps of the BG segmentation algorithm are as follows: (1) Calculate the average value of the two segments to the left and right of point i, and denote them as follows: and (i=2, 3,...,N-1); (2) To measure the difference between UL and UR, the following statistic is calculated: ; ; In the formula: For joint variance, and as well as and These are the standard deviation and sample size of the left and right segments, respectively, of the split point.

[0033] (3) Determine The maximum value in And calculate its statistical significance. : ; According to Monte Carlo simulations: ; In the formula: γ = 4.19lnN - 11.54, δ = 0.40, N is the length of the time series x(t), v = N - 2, Incomplete The significance level for this function is typically set to 0.95.

[0034] (4) If step (3) If the significance test is passed, the sequence is divided into two subsequences at that point, and steps (1)-(3) are repeated to detect all mutation points.

[0035] Step 3: Construction of the mother wavelet optimization framework: By integrating the cumulative anomaly method, the modified Mann-Kendall test, and the wavelet mutation detection results, a set of potential mutation points is constructed; the Kolmogorov-Smirnov (KS) test is used to calculate the degree of sequence variation corresponding to each potential mutation point; based on the preset quantitative judgment criteria, the optimal mother wavelet with the highest matching degree with the physical characteristics of the hydrological sequence is selected from the candidate mother wavelet set; and the multi-scale spatiotemporal features of the hydrological sequence are extracted through the optimal mother wavelet. The formula for calculating the degree of sequence variation based on the KS test is as follows: ; In the formula, This represents the degree of variation. , These are the empirical cumulative distribution functions of the two subsequences before and after the potential mutation point; when the asymptotic significance of the KS test... When the value is less than 0.01, the potential mutation point is determined to be a strong significant mutation point.

[0036] The preset quantitative judgment criteria include the following four items: Criterion 1: Significance level of KS test for sequences before and after potential mutation points p ≤0.05; Criterion 2: Potential mutation points can achieve a continuous, non-overlapping division of the hydrological sequence from start to end; Criterion 3: The mutation trajectory corresponding to the selected mother wavelet contains the largest number of strongly significant mutation points; Criterion 4: Before the initial segment in the mutation trajectory m The degree of variation at each point is minimal. m This represents the number of sequence points corresponding to the step size of the moving window.

[0037] The candidate mother wavelet set includes wavelet basis functions of the db series, sym series, coif series, fk series, and morlet series. Multi-scale spatiotemporal feature extraction of hydrological sequences is completed through continuous wavelet transform. The continuous wavelet transform adjusts the time scale of the optimal mother wavelet through a scaling factor and adjusts the time position of the optimal mother wavelet through a translation factor. The hydrological sequence is then subjected to an inner product operation with the complex conjugate function of the translated and scaled optimal mother wavelet to obtain wavelet transform coefficients at different scales and time positions.

[0038] Step 4: Inconsistent segmented simulation and forecasting: Based on the comprehensive physical abrupt change years determined in Step 2 and Step 3, the research sequence is divided into natural periods and periods of human activity disturbance. A hydrophysical model based on the principle of water balance is used to calibrate the parameters for different periods.

[0039] The hydrophysical model based on the principle of water balance adopts the RCCC-WBM monthly-scale hydrological model, with monthly runoff as the core forecast target; the natural period refers to the sequence of time when the watershed is less disturbed by human activities and the hydrological cycle mechanism remains in its natural state; the human activity disturbance period refers to the sequence of time when the watershed is affected by strong human activities such as water conservancy project construction, land use change, and groundwater extraction, and the hydrological cycle mechanism undergoes significant changes.

[0040] The Nash-Sutcliffe efficiency coefficient and relative error were used to evaluate the model's simulation and forecasting performance. The Nash-Sutcliffe efficiency coefficient is calculated as follows: 1 minus the sum of squares of the differences between measured and simulated flow rates, divided by the sum of squares of the differences between measured flow rates and their series mean. The closer the value is to 1, the higher the model simulation accuracy. The formula for calculating the Nash-Sutcliffe efficiency coefficient (NSE) is: ; The relative error is calculated as the ratio of the sum of the differences between simulated and measured flow rates to the sum of the measured flow rates, expressed as a percentage. The formula for calculating the relative error (RE) is: ; In the formula, To measure the actual flow rate, To simulate traffic, The mean; Number of observations in the sequence; The closer the value is to 1, the higher the accuracy of the model simulation. The smaller the absolute value, the smaller the simulation error of the total model.

[0041] Example 2: See Figure 1 This embodiment provides a method for detecting and extracting features from abrupt changes in non-consistent hydrological sequences based on multidimensional dependency analysis and mother wavelet optimization, specifically including the following steps: Step 1: Data Acquisition and Preprocessing 1.1 Data Acquisition: Obtain long-term continuous multi-source hydro-meteorological sequences of the watershed to be measured, including daily / monthly rainfall and evaporation data from meteorological stations within the watershed, as well as daily / monthly runoff data from hydrological control stations. Perform quality control on the raw data, such as interpolation of missing values ​​and removal of outliers, to ensure the integrity and reliability of the sequences.

[0042] 1.2 Modified Mann-Kendall Trend Test: For the processed hydrological series, an autocorrelation correction factor based on the series rank is introduced to adjust the test statistic. The variance is corrected; the standardized test statistic is calculated using the corrected variance. ,when When, determine the sequence in A significant trend was observed at the confidence level, completing the sequence trend identification and preliminary mutation point detection.

[0043] 1.3 Detrending Pre-whitening (TFPW) processing: The hydrological sequence is subjected to detrending pre-whitening processing to simultaneously eliminate the trend term and autocorrelation component of the sequence, so as to obtain a pre-processed stationary sequence and eliminate the interference of autocorrelation on subsequent mutation detection.

[0044] Step 2: Multivariate-dependent mutation detection (BMCTC method) 2.1 Multivariate Sequence Normalization: The preprocessed multivariate hydrological sequences of rainfall, runoff, and evaporation were normalized. Normalization eliminates the influence of differences in the dimensions of different variables.

[0045] 2.2 Calculation of Total Correlation Value: Total correlation is introduced to quantify the overall dependency strength among multidimensional variables, using a matrix-based approach. Entropy functionals estimate univariate marginal entropy and multivariate joint entropy, where... order of entropy If we set the value to 2, we construct the normalized Gram matrix and calculate its eigenvalues. We can then directly estimate the total correlation value using the eigenvalues ​​without needing to perform high-dimensional probability density function estimation.

[0046] 2.3 Construction of Moving Window Total Correlation (MCTC) Series: Set the width of the moving window (e.g., 120 months for a monthly scale series, i.e., 10 years), slide the window along the time axis with a step size of 1, calculate the total correlation value of the multidimensional series within each window, construct the MCTC time series, and characterize the dynamic change process of the multivariate dependence strength.

[0047] 2.4 Mutation point identification: The BG segmentation algorithm is used to segment the MCTC sequence, identify all significant mutation points in the sequence, obtain the physical mutation years of the multidimensional hydrological variable dependencies, and accurately locate the key time points of human activities affecting the watershed hydrological process.

[0048] Step 3: Mother wavelet optimization and multi-scale feature extraction 3.1 Construction of Potential Mutation Point Set: The mutation detection results of the cumulative anomaly test, the modified MK test in step 1, and the BMCTC method in step 2 are combined to construct a potential mutation point set.

[0049] 3.2 Quantification of Variation: For each mutation point in the potential mutation point set, the KS test is used to calculate the difference in the empirical cumulative distribution function of the two subsequences before and after the mutation point, obtaining the variation value D and significance. Value; when When the mutation point is identified as a strongly significant mutation point, it is determined to be a significant mutation point.

[0050] 3.3 Optimal Mother Wavelet Selection: Constructing a candidate mother wavelet set, including Wavelet; Based on four quantitative judgment criteria, the mutation detection and feature extraction results of each candidate mother wavelet are scored, and the mother wavelet with the highest score is selected as the optimal mother wavelet.

[0051] 3.4 Multi-scale Feature Extraction: The optimal mother wavelet obtained through screening is used to perform continuous wavelet transform (CWT) on the hydrological sequence. The complete formula is as follows: ; In the formula, It is the complex conjugate function of the optimal mother wavelet function. As a scale factor, The time shift factor is used; multi-scale periodic features and trend evolution features of hydrological sequences are extracted through continuous wavelet transform, thus achieving accurate extraction of the spatiotemporal features of the sequences.

[0052] Step 4: Simulation of Inconsistent Segmentation 4.1 Sequence Periodization: Combining the multivariate dependent physical mutation years obtained in step 2 with the strongly significant mutation points obtained in step 3, the comprehensive mutation years of the watershed hydrological sequence are determined; using the comprehensive mutation years as the dividing point, the research sequence is divided into the natural period (natural state, hydrological cycle mechanism is not significantly disturbed by human activities) and the period of human activity disturbance (hydrological cycle mechanism undergoes significant changes).

[0053] 4.2 Physical Model Construction: The RCCC-WBM monthly hydrological model based on the water balance principle is adopted. With rainfall and evaporation as inputs and monthly runoff as the forecast target, a watershed hydrological physical model is constructed. The core of the model is based on the watershed water coupling balance principle, the physical mechanism is clear, and it is suitable for watershed hydrological simulation under non-uniform environments.

[0054] 4.3 Segmented Parameter Calibration: For the series during natural periods and periods of human activity disturbance, the SCE-UA optimization algorithm was used for model parameter calibration and validation, respectively, to adapt the model parameters to the different hydrophysical mechanisms of the two periods. The Nash-Sutcliffe efficiency coefficient (NSE) and relative error (RE) were used to evaluate the model performance during the calibration period. ≥0.8 Absolute value ≤ 10%, verification period , An absolute value ≤ 15% is the standard for model qualification.

[0055] Example 3: This embodiment uses monthly hydrometeorological data from China from 1992 to 2018 as an example to implement the method. The specific implementation method is as follows: Step 1: Data Acquisition and Preprocessing 1.1 Data Acquisition and Quality Control Precipitation data within the basin were obtained from the CN05.1 gridded dataset (https: / / data.cma.cn / ) of the China Meteorological Administration's Open Laboratory for Climate Research; potential evapotranspiration data were obtained from the "China 1km Monthly Potential Evapotranspiration Dataset" (https: / / data.tpdc.ac.cn); and runoff data were obtained from the China Natural Runoff Gridded Dataset CNRDv1.0 (ChinaNaturalRunoffDatasetversion1.0). Outlier detection was performed on the raw data (3 The criteria were used to remove outliers and impute missing values ​​(linear interpolation), and the precipitation unit was converted from mm / day to mm / month (multiplied by the number of days in the month). Finally, a continuous series of 324 months from January 1992 to December 2018 was obtained, including three variables: precipitation, PET, and runoff.

[0056] 1.2 Detrended Pre-Whitening (TFPW) Processing To eliminate the interference of trend terms and autocorrelation on subsequent mutation detection, runoff sequences were processed according to the following steps: The slope of the linear trend was calculated using Sen's slope method; Remove trend items ; calculate The first-order autocorrelation coefficient r is used to remove the autocorrelation to obtain the pre-whitened residual; The trend term is restored to obtain the processed sequence. .

[0057] 1.3 Modified Mann-Kendall Trend Test For the preprocessed runoff series, an autocorrelation correction factor based on the series rank is introduced, and the variance of the test statistic is corrected according to the formula in claim 2. The standardized test statistic Z = -2.61 (|Z|>1.96) is calculated, indicating that the series has a significant downward trend at the 95% confidence level.

[0058] Step 2: Multivariate-dependent mutation detection (BMCTC method) 2.1 Multivariate Sequence Normalization Min-max normalization was performed on precipitation, PET, and runoff sequences to eliminate dimensional differences.

[0059] 2.2 Calculation of the total correlation value Using matrix-based Renyi α-order entropy ( =2) Estimate the total correlation. First, construct the normalized Gram matrix and calculate its eigenvalues. Then, calculate the univariate marginal entropy and multivariate joint entropy using the formula in Example 1, and finally obtain the total correlation value TC.

[0060] 2.3 Construction of Moving Window Fully Associative (MCTC) Sequences The moving window width is set to 120 months (10 years), and the step size is 1 month. The total correlation value of the multidimensional series is calculated window by window to obtain the MCTC time series, which characterizes the dynamic change of the multivariate dependence strength.

[0061] 2.4 Mutation point identification The Bernaola-Galván (BG) segmentation algorithm was used to segment the MCTC sequence: traversing all possible segmentation points, calculating the t-statistics of the left and right segments, and identifying the position corresponding to the largest t-statistic as the mutation point. In this embodiment, the mutation point was identified as being located in the 132nd month (corresponding to 2003), meaning that the physical mutation year of the multivariate dependency was 2003.

[0062] Step 3: Mother wavelet optimization and multi-scale feature extraction 3.1 Construction of Potential Mutation Point Set By combining the results of the cumulative anomaly test, the modified MK test, and the BMCTC method in step 2, a set of potential mutation points (including years such as 1998, 2003, and 2010) is obtained.

[0063] 3.2 Quantification of Variation For each potential mutation point, a KS test was performed to calculate the difference D in the empirical cumulative distribution function of the preceding and following subsequences and the significance p-value. The 2003 mutation point had a D of 0.32 and a p-value of 0.008, and was therefore identified as a strongly significant mutation point.

[0064] 3.3 Optimal Mother Wavelet Selection Construct a candidate mother wavelet set (db1~db20, sym2~sym20, coif1~coif5, fk4~fk22, morlet). Score each wavelet based on the following four criteria: Criterion 1: KS test before and after the mutation point: p ≤ 0.05; Criterion 2: Mutation points can achieve continuous, non-overlapping sequence partitioning; Criterion 3: The wavelet transform-detected abrupt trajectory contains the most strongly significant abrupt change points; Rule 4: The degree of variation of the first m points of the initial segment of the mutation trajectory is the minimum value (m = number of points corresponding to the window step size).

[0065] In this embodiment, the Morlet wavelet scored the highest on criteria 1 and 3 and was selected as the optimal mother wavelet.

[0066] 3.4 Multi-scale feature extraction Continuous wavelet transform (CWT) was performed on the runoff series using Morlet wavelets, with a scale range of 1–128. Quasi-periodic features of 2–4 years, 6–8 years, and 12–16 years were extracted from the runoff series, as well as the energy center band from 1998 to 2005.

[0067] Step 4: Simulation of Inconsistent Segmentation 4.1 Sequence Periodization Combining the physical mutation year (2003) from step 2 with the strongly significant mutation point from step 3, the comprehensive mutation year is determined to be 2003. The period from 1992 to 2000 is divided into a natural period (considering the mutation transition buffer), and the period from 2001 to 2018 is divided into a period of human activity interference. The period from 1992 to 2000 is used for model calibration, and the period from 2001 to 2018 is used for validation.

[0068] 4.2 Hydrological Model Construction The RCCC-WBM monthly-scale hydrological model, based on the water balance principle, was adopted, with precipitation and potential evapotranspiration as inputs and monthly runoff as the forecast target. Model parameters included: maximum soil moisture content. Shape parameters Evaporation threshold coefficient Surface runoff coefficient Interflow coefficient of soil Base current coefficient Maximum groundwater storage capacity .

[0069] 4.3 Piecewise parameter calibration The model parameters for the natural period and the disturbance period were calibrated using the differential evolution algorithm. The parameter boundaries were set as follows: [50,500], [0.5, 5.0] [0.1, 0.9] [0.01, 0.8], [0.01, 0.5], [0.001, 0.2], [50,300]mm. The calibration objective is to maximize the Nash-Sutcliffe efficiency coefficient (NSE).

[0070] Calibration results: Natural period (1992–2000): NSE = 0.55, RE = -7.2%; Interference period (2001–2018): NSE = 0.61, RE = -6.4%; If natural period parameters are used to directly simulate runoff during disturbance periods, NSE decreases to 0.52 and RE expands to -23.5%, indicating that segmentation calibration significantly improves model adaptability.

[0071] The above embodiments verify the effectiveness of the present invention in autocorrelation elimination, high-dimensional dependent mutation detection, objective optimization of mother wavelet, and non-consistent segmented simulation forecasting. In this embodiment, the natural period calibration NSE is 0.55, lower than the ideal value of 0.8. The main reason is that the selected watershed is strongly disturbed by human activities, and the 1992-2000 sequence length is relatively short (9 years). In practical applications, it is recommended that the sequence length be no less than 15 years, and global optimization algorithms such as SCE-UA can be used to improve calibration efficiency. The core innovation of the present invention lies in the multivariate dependent mutation detection and segmented calibration strategy, rather than pursuing a high NSE value for a single model.

[0072] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization, characterized in that, Includes the following steps: Step 1: Data Acquisition and Preprocessing: Obtain multi-source hydrological and meteorological sequences of the watershed to be measured, preprocess the sequences to eliminate interference from trend terms and autocorrelation components, and simultaneously complete sequence trend identification and preliminary abrupt change detection; Step 2: Multivariate Dependency Abrupt Detection: Full correlation is introduced to quantify the total linear and nonlinear dependency strength between multivariate hydrological sequences. The full correlation value is estimated using a matrix-based Renyi α-order entropy functional. A moving window full correlation sequence is constructed using moving window technology. The physical abrupt change year of the dependency relationship between multivariate hydrological sequences is identified through a segmentation algorithm. Step 3: Mother wavelet optimization and multi-scale feature extraction: The results of mutation detection by multiple methods are fused to construct a set of potential mutation points. The Kolmogorov-Smirnov test is used to calculate the degree of sequence variation corresponding to each potential mutation point. Based on the preset quantitative judgment criteria, the optimal mother wavelet is selected from the candidate mother wavelet set. The multi-scale spatiotemporal features of the hydrological sequence are extracted through the optimal mother wavelet. Step 4: Inconsistent segmented hydrological simulation and forecasting: Based on the comprehensive physical abrupt change years determined in Step 2 and Step 3, the research sequence is divided into at least two hydrological periods. The parameters of the hydrological physical model are calibrated for different hydrological periods to complete the hydrological forecasting under inconsistent conditions.

2. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 1, the preprocessing adopts the detrended pre-whitening TFPW method, and at the same time, the modified Mann-Kendall test is used to complete trend identification and preliminary mutation point detection. The modified Mann-Kendall test method corrects the variance of the test statistic S by introducing an autocorrelation correction factor based on the sequence rank; the corrected variance is the product of the theoretical variance of the traditional Mann-Kendall test statistic and the autocorrelation correction factor based on the sequence rank. The autocorrelation correction factor is calculated using an empirical approximation formula based on the autocorrelation functions of the rank of hydrological sequence observations and the total number of sequence observations.

3. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 2, characterized in that, The detrended pre-whitening TFPW method specifically includes the following steps: Step 1.1: The linear trend slope of the hydrological series is extracted using Sen's slope method. The linear trend slope is the median of the ratio of the difference between all observations with later time numbers and observations with earlier time numbers in the series to the difference of the corresponding time step. Step 1.2: Remove the linear trend term from the sequence to obtain the detrended sequence; Step 1.3: Calculate the first-order autocorrelation coefficient of the detrended sequence, remove the first-order autocorrelation component from the detrended sequence, and obtain the pre-whitened residual sequence; Step 1.4: Restore the linear trend term to the pre-whitened residual sequence to obtain the final pre-whitened sequence.

4. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 2, the total correlation is used to quantify the overall dependence strength among multivariate hydrological sequences. Its value is the sum of the marginal entropies of all univariate hydrological sequences minus the joint entropy of the multivariate hydrological sequences. The matrix-based Renyi α-order entropy is calculated from the eigenvalues ​​of the Gram matrix after normalization of the multivariate hydrological sequences and is used to estimate the univariate marginal entropy and the multivariate joint entropy.

5. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 2, the window width of the moving window technique is set according to the sequence time scale, and the step size is 1 time unit to slide along the time axis. The total correlation value is calculated window by window to construct the moving window total correlation sequence. The segmentation algorithm adopts the Bernaola-Galván BG segmentation algorithm to identify the years of significant physical abrupt changes in the sequence.

6. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 3, the potential mutation point set is constructed by fusing the cumulative anomaly method, the modified Mann-Kendall test, and the multivariate dependent mutation detection results from step 2, and all significant mutation points are merged to form the potential mutation point set; The degree of sequence variation is the maximum absolute difference of the empirical cumulative distribution function of the two subsequences before and after the potential mutation point over the entire range; when the Kolmogorov-Smirnov test shows asymptotic significance... p When the value is less than 0.01, the potential mutation point is determined to be a strong significant mutation point.

7. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 3, the preset quantitative judgment criteria Includes the following four items: Criterion 1: Significance level of Kolmogorov-Smirnov test for sequences before and after potential mutation points p ≤0.05; Criterion 2: Potential mutation points can achieve a continuous, non-overlapping division of the hydrological sequence from start to end; Criterion 3: The mutation trajectory corresponding to the selected mother wavelet contains the largest number of strongly significant mutation points; Criterion 4: Before the initial segment in the mutation trajectory m The degree of variation at each point is minimal. m This represents the number of sequence points corresponding to the step size of the moving window.

8. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 3, the candidate mother wavelet set includes db series, sym series, coif series, fk series, and morlet series wavelet basis functions; multi-scale spatiotemporal feature extraction of hydrological sequences is completed through continuous wavelet transform; The continuous wavelet transform adjusts the time scale of the optimal mother wavelet by a scaling factor and adjusts the time position of the optimal mother wavelet by a translation factor. The hydrological sequence is then multiplied by the complex conjugate function of the translated and scaled optimal mother wavelet to obtain wavelet transform coefficients at different scales and time positions.

9. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 4, the hydrological period is divided into natural periods and periods of human activity disturbance. Natural periods are the time when the watershed hydrological cycle mechanism is not significantly disturbed by human activities, while periods of human activity disturbance are the time when the watershed hydrological cycle mechanism undergoes significant changes. The hydrological physical model adopts a hydrological model based on the principle of water balance, with runoff as the core forecast target.

10. The non-consistent hydrological simulation and forecasting method based on multidimensional dependency analysis and mother wavelet optimization according to claim 1, characterized in that, In step 4, the Nash-Sutcliffe efficiency coefficient and relative error are used to evaluate the model's simulation and forecasting performance. The Nash-Sutcliffe efficiency coefficient is calculated as the ratio of 1 minus the sum of squares of the differences between measured and simulated flow rates to the sum of squares of the differences between measured flow rates and their series mean. The closer the value is to 1, the higher the model's simulation accuracy. The relative error is calculated as the ratio of the sum of the differences between simulated and measured flow rates to the sum of measured flow rates, expressed as a percentage. The smaller the absolute value, the smaller the overall simulation error of the model.

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