Method and system for quantifying unsteady response of water level and water quality of Tongjiang lake

Abstract

The invention discloses a method and a system for quantifying water level and water quality unsteady-state response of a Tongjiang lake. The system comprises a time sequence multi-scale decomposition module, an interannual scale unsteady-state response quantification module, a water level change seasonal item grouping module and a seasonal scale unsteady-state response quantification module. The time sequence multi-scale decomposition module is used for decomposing a water level monthly scale time sequence into a trend term, a season term and an error term based on a seasonal trend decomposition method; the interannual scale unsteady state response quantification module calculates the time-varying dryness of the water level and the water quality in the interannual scale by using wavelet coherence analysis based on the trend term of the interannual scale, generates a time-frequency coherence map, and reveals the unsteady state response coherence intensity between variables; the water level change seasonal item grouping module groups the long-time sequences according to water level change seasonal items; and the seasonal scale unsteady state response quantification module performs wavelet cross transform on the grouped seasonal items, calculates a cross wavelet spectrum between the water level and the water quality, extracts an instantaneous phase difference of the seasonal scale, and quantitatively reveals a leading-lagging response rule between seasonal scale variables. According to the method, the complex interaction between the water level and the water quality can be effectively clarified, and the unsteady state response relation between the water level and the water quality is quantitatively analyzed through seasonal trend analysis, wavelet coherence analysis and wavelet cross transformation.

Description

Technical Field

[0001] The present invention relates to the field of quantitative technology for identifying the interaction between water level and water quality, and in particular to a method and system for quantifying the non-steady-state response of water level and water quality in lakes connected to rivers. Background Art

[0002] River-connected lakes are influenced by the rivers they flow into, often experiencing extremely complex hydrological and hydrodynamic interactions. This in turn leads to nonlinear responses between water level and water quality, making the river-lake interactions in river-connected lakes extremely complex. Therefore, scientifically quantifying the non-steady-state responses of water level and water quality in river-connected lakes on interannual and seasonal scales has become a pressing technical challenge in current research on hydrological variability, and is of great significance for water resource management under the influence of human activities. The existence of a state-dependent nonlinear coupling mechanism between hydrological driving forces and water quality responses, and the dynamic phase shifts in the lead-lag relationship, pose a challenge to the traditional stationary modeling paradigm.

[0003] Wavelet analysis and wavelet cross transforms have become core methods for detecting periodic changes in hydrological and water quality time series. By decomposing signals in the time and frequency domains, this method effectively captures temporal evolutionary characteristics and interactions at specific scales. The coupled analysis of seasonal trend decomposition and wavelet coherence overcomes the key limitation of traditional correlation analysis, which assumes data stationarity, and addresses the inherent noise interference in long-term monitoring data, providing a quantitative approach for quantifying the coupling of hydrological and biogeochemical data at specific scales.

[0004] In view of this, in view of the complex interactive response relationship between water level and water quality in Tongjiang lakes, it is necessary to propose a method to quantify the non-steady-state response of water level and water quality in Tongjiang lakes, so as to directly reflect the changes in the response relationship between water level and water quality under the influence of climate change and human activities, and serve water resources management and engineering scheduling decisions. Summary of the Invention

[0005] Purpose of the invention: The present invention provides a method and system for quantifying the non-steady-state response of water level and water quality in lakes connected to rivers, which can effectively clarify the complex interaction between water level and water quality, and quantitatively analyze the relationship between the non-steady-state response of water level and water quality through seasonal trend analysis, wavelet coherence analysis, and wavelet cross transform.

[0006] Technical solution: The method of quantifying the non-steady-state response of water level and water quality in lakes connected to rivers in the present invention comprises the following steps:

[0007] Step 1: Multi-scale decomposition of time series. Based on the seasonal trend decomposition method, the monthly water level time series is decomposed into trend term, seasonal term and error term.

[0008] Step 2: Quantify the interannual scale non-stationary response. Based on the interannual scale trend term, wavelet coherence analysis is used to calculate the time-varying coherence of water level and water quality at the interannual scale, generate a time-frequency coherence map, and reveal the coherence strength of the non-stationary response between variables.

[0009] Step 3: Group the long time series according to the seasonal terms of water level changes;

[0010] Step 4: Quantify the seasonal scale non-steady-state response. Perform wavelet cross transform on the grouped seasonal items, calculate the cross wavelet spectrum between water level and water quality, extract the instantaneous phase difference on the seasonal scale, and quantitatively reveal the lead-lag response law between seasonal scale variables.

[0011] Furthermore, in step 1, the time series is decomposed at multiple scales. Based on the seasonal trend decomposition method, the monthly water level time series is decomposed into trend terms, seasonal terms, and error terms. Specifically,

[0012] Y t =T t +S t +R t (t=1,2,3,…,T)

[0013] Among them, in the observation time series Y t , decomposed into three components: T t Represents the potential trend item, reflecting the long-term evolution process or systematic law of the data; S t represents the seasonal term, which describes the periodic fluctuations and patterns that repeat on a monthly or annual basis; R t is the error term, reflecting random noise or short-term fluctuations not explained by trend and seasonal factors.

[0014] Furthermore, in step 2, the wavelet coherence analysis specifically includes the following steps:

[0015] Step 21: In the data processing of the wavelet coherence analysis, ensure that the time series of the water level trend term and the water quality trend term are of equal length and complete the preprocessing of outlier correction and missing value filling;

[0016] Step 22: Specify the sampling frequency fs=1 month for the trend item of water level and the trend item of water quality to achieve scale-frequency conversion;

[0017] Step 23: Decomposition is performed using the Morlet wavelet basis function. By scaling and translating the decomposed signal, the time and frequency localization characteristics are utilized to adaptively balance the time and frequency resolution at the interannual scale (with a period of one year).

[0018] Step 24: The calculated modulus distribution of the complex coefficients characterizes the energy density in the time-frequency domain (reflecting the contribution intensity of a specific frequency in a local time period): the modulus peak corresponds to the main period of the signal (1 year), and the proportion of the modulus at each scale reveals the contribution weight of the periodic component;

[0019] Step 25. Perform significance tests through Monte Carlo simulation to verify the statistical reliability of the time-frequency domain correlation: first, construct a null hypothesis data set, randomize the phase or shuffle the order of the original data to destroy the true phase relationship between the variables; then repeat the wavelet coherence analysis 1000 times to generate the null hypothesis coherence sample distribution; extract the upper bound of the distribution as the significance threshold based on the 95% confidence level; finally, by comparing the measured coherence with the threshold, eliminate random noise interference, extract and retain the effective signal, and focus on analyzing the time-frequency region with a coherence greater than 0.6.

[0020] Furthermore, in step 2, based on the interannual trend term, wavelet coherence analysis is used to calculate the time-varying coherence of water level and water quality at the interannual scale, and a time-frequency coherence map is generated, revealing the coherence strength of the non-steady-state response between the variables:

[0021]

[0022] in, Represents the cross wavelet spectrum, which is used to evaluate the temporal similarity and phase change of two sequences at multiple time scales. The phase angle range is ([-π,π]), and the lead-lag relationship is determined by the phase angle.

[0023] Furthermore, in step 3, the long time series are grouped according to the seasonal variation of water levels. Combined with the natural properties of the hydrological system (such as precipitation cycle, seasonal differences in evaporation, river water inflow patterns, etc.), the continuous time series data are divided into seasonal units with significant hydrological significance (such as flood season, receding water season, dry season, and rising water season), so that the water level fluctuations in each group show a unified trend characteristic or periodic pattern, while highlighting the differences between different seasons.

[0024] Furthermore, in step 4, the phase difference of the two variables on the seasonal scale in different seasons is quantified by using the cross-wavelet spectrum to further determine the lead-lag relationship between the two variables.

[0025] Furthermore, in step 4, the wavelet cross transform specifically includes the following steps:

[0026] Step 41: First, perform continuous wavelet transform on the seasonal data of water level and water quality in different seasonal periods, and then perform cross wavelet transform by complex multiplication:

[0027] Step 42: Adopting the complex Morlet wavelet basis function, adaptively balancing time and frequency on a monthly scale; setting the time interval dt to 1 month to represent the sampling interval of the time series;

[0028] Step 43: Multiply the wavelet coefficient of the water level seasonal term by the conjugate of the wavelet coefficient of the water quality seasonal term to obtain a cross-wavelet spectrum. This result reveals the common power distribution and relative phase relationship of the two signals in the time-frequency domain. The complex wavelet coefficients represent the energy distribution of the signal on a one-month scale. The modulus (amplitude) of the coefficients reflects the energy intensity of the corresponding time-frequency point. The larger the modulus, the more significant the energy contribution of the frequency component at the current time point.

[0029] Step 44: Smoothing: suppressing noise interference in the time-frequency domain and enhancing the continuity of the significant correlation pattern through Gaussian smoothing;

[0030] Step 45: Extract phase information from the cross-spectral density of the wavelet coefficients of the two signals, and determine the signal relationship from the phase difference: 0° indicates an in-phase change, 180° corresponds to an anti-phase change, and ±90° indicates a 1 / 4 cycle lag or lead.

[0031] Correspondingly, a system for quantifying the non-steady-state response of water level and water quality in Tongjiang lakes includes: a time series multi-scale decomposition module, an interannual scale non-steady-state response quantification module, a water level change seasonal term grouping module and a seasonal scale non-steady-state response quantification module; the time series multi-scale decomposition module decomposes the water level monthly scale time series into trend term, seasonal term and error term based on the seasonal trend decomposition method; the interannual scale non-steady-state response quantification module calculates the time-varying coherence of water level and water quality at the interannual scale based on the interannual scale trend term using wavelet coherence analysis, generates a time-frequency coherence map, and reveals the non-steady-state response coherence strength between variables; the water level change seasonal term grouping module groups long time series according to the water level change seasonal term; the seasonal scale non-steady-state response quantification module performs wavelet cross transform on the grouped seasonal terms, calculates the cross wavelet spectrum between water level and water quality, extracts the instantaneous phase difference at the seasonal scale, and quantitatively reveals the lead-lag response law between seasonal scale variables.

[0032] Beneficial effects: Compared with the existing technology, the present invention has the following significant advantages: (1) Effectively handle nonlinear and non-stationary data. The observed water level and water quality data often have nonlinear and non-stationary characteristics. The seasonal trend decomposition method can adaptively handle nonlinear trends and seasonal changes during the decomposition process, and has good robustness to outliers and noise; (2) It can quantitatively analyze multi-time scale relationships. The seasonal trend decomposition method is coupled with wavelet correlation analysis. The data is first decomposed by the seasonal trend decomposition method to obtain trend and seasonal components, and then wavelet correlation analysis is performed. The relationship between water level and water quality can be quantitatively evaluated on multiple time scales; (3) Nonlinear and time-varying characteristics are revealed. The wavelet cross transform method can effectively reveal the nonlinear and time-varying characteristics between water level and water quality; (4) Enhance explanatory power and provide early warning signals. The seasonal trend decomposition method is coupled with wavelet correlation analysis and wavelet cross transform to enhance the explanatory power of the relationship between water level and water quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the method of the present invention.

[0034] Figure 2 This is a seasonal trend analysis diagram of water level in the present invention.

[0035] Figure 3 Schematic diagram of wavelet coherence analysis of water level and water quality at the inter-annual scale in the present invention.

[0036] Figure 4 Schematic diagram of wavelet cross-transformation of water level and total nitrogen concentration on a seasonal scale in the present invention.

[0037] Figure 5 Schematic diagram of wavelet cross-transformation of water level and total phosphorus concentration on a seasonal scale in the present invention. DETAILED DESCRIPTION

[0038] like Figure 1 As shown, a method for quantifying the non-steady-state response of water level and water quality in lakes connected to the river includes the following steps:

[0039] Step 1: Multi-scale decomposition of time series. Based on the seasonal trend decomposition method, the monthly water level time series is decomposed into trend term, seasonal term and error term.

[0040] Step 2: Quantify the interannual scale non-stationary response. Based on the interannual scale trend term, wavelet coherence analysis is used to calculate the time-varying coherence of water level and water quality at the interannual scale, generate a time-frequency coherence map, and reveal the coherence strength of the non-stationary response between variables.

[0041] Step 3: Group the long time series according to the seasonal terms of water level changes;

[0042] Step 4: Quantify the seasonal scale non-steady-state response. Perform wavelet cross transform on the grouped seasonal items, calculate the cross wavelet spectrum between water level and water quality, extract the instantaneous phase difference on the seasonal scale, and quantitatively reveal the lead-lag response law between seasonal scale variables.

[0043] Taking the water level and water quality of Poyang Lake, a large lake connected to the middle reaches of the Yangtze River, as an example, this plan includes the following steps:

[0044] S1. Seasonal trend analysis was conducted on the monthly average water level at Xingzi Station from 1988 to 2019, and the monthly average concentration series data of total nitrogen and total phosphorus in the lake.

[0045] S2. Calculate the non-steady-state response relationship between water level and water quality at the interannual scale using wavelet coherence analysis based on trend data;

[0046] The method is as follows: Based on the trend item data, the Morlet wavelet function is used to decompose the dual variables (water level and the monthly average concentrations of total nitrogen and total phosphorus) in the time-frequency domain to obtain the amplitude and phase information of each frequency component on the interannual scale.

[0047]

[0048] Among them, Rn 2 represents the wavelet correlation coefficient, ranging from 0 to 1. The degree of coherence between two sequences is positively correlated with their numerical values, reaching a value of 1 when synchronization is maximized. S represents the scale and time domain smoothing operators, and W(s) represents the weight function of the variables.

[0049] S3. Seasonal grouping of water level data according to hydrological rhythms. The core goal is to capture and reflect the cyclical fluctuation patterns of water level changes to the greatest extent possible through refined time dimension division. This process requires combining the natural properties of the hydrological system and dividing continuous time series data into seasonal units with significant hydrological significance (such as flood season, receding water season, dry season, and rising water season). This allows the water level fluctuations within each group to exhibit a unified trend characteristic or cyclical pattern, while highlighting the differences between different seasons (such as the surge characteristics during the flood peak period and the slow decline trend during the dry season). Seasonal item data is extracted based on the seasonal trend decomposition method and grouped accordingly.

[0050] S4. Wavelet coherence analysis and wavelet cross transform are performed on the grouped seasonal terms to quantitatively explain the non-steady-state response of seasonal water quality to water level fluctuations. Wavelet cross transform is used to analyze the phase relationship (lead-lag relationship) between the two time series in the time-frequency domain.

[0051]

[0052] in, Represents a cross-wavelet spectrum, used to assess temporal similarity and phase variation between two sequences at multiple time scales. The phase angle range is ([-π,π]), and the phase angle can be used to determine lead-lag relationships (e.g., a phase angle of π / 2 indicates that x leads y by 90°, corresponding to a periodic signal where x leads y by 1 / 4 period).

[0053] Morlet wavelet functions were used to decompose the dual variables in the time-frequency domain, obtaining amplitude and phase information for each frequency component. Wavelet coherence spectra were used to quantify the strength of synchronization between the dual variables at specific time scales within different seasons (coherence coefficients ranged from 0–1). The lead-lag relationship between the dual variables was determined based on phase angles (0°–360°). While traditional global analysis cannot distinguish dynamic differences between seasons, grouped wavelet coherence analysis can pinpoint the dominant cycle within a specific season, revealing the physical driving mechanisms of the coupled patterns across seasons. Phase shifts can be captured, and seasonal phase angle differences directly reflect seasonal reversals of causal relationships.

[0054] Figure 2 This is an analysis of the seasonal trend of water levels. The water level trend shows a significant downward trend, and the amplitude of seasonal fluctuations also shows a decreasing trend. The trend curve shows a relatively gentle downward trend before 2003, indicating that while the water level was declining overall during this period, the rate of decline was relatively steady, with no significant acceleration or sudden changes. The observed value curve also roughly follows this relatively gentle downward trend in its fluctuations, indicating that short-term fluctuations in the water level did not alter the overall slow downward trend. After 2003, the downward trend in the trend curve has intensified significantly, with an increased slope, indicating that the rate of water level decline has accelerated since 2003, possibly due to the impact of the Three Gorges Dam. The observed value curve also shows a more pronounced downward trend in its fluctuations, with the low points of the fluctuations gradually decreasing, indicating not only an accelerating long-term decline but also overall lower short-term water level fluctuations. The seasonal curve shows relatively large fluctuations before 2003, indicating a more pronounced seasonal variation in water levels and large differences between seasons. After 2003, the amplitude of the seasonal curve has decreased, and the seasonal variation of water levels has weakened. This may be due to changes in the regulatory role of water conservancy projects, which have gradually reduced the water level differences between seasons and made seasonal changes less significant than before. At the same time, the fluctuation pattern of the seasonal term curve may also have changed, and the originally regular fluctuations may become more gentle or irregular.

[0055] Figure 3 This is the wavelet coherence analysis diagram of water level and water quality in a 1-year cycle. Figure 3 a indicates that the correlation between water level and total nitrogen concentration was low before 2003, but increased after 2003. This suggests that changes in water level and total nitrogen concentration became more closely related after 2003, possibly indicating an increased interaction between the two. Figure 3 b mainly shows the changes in the coherence between total phosphorus concentration and water level, with a low value around 2003. This may be because the construction of the Three Gorges Dam has weakened the coherence between water level and total phosphorus concentration on the interannual scale, and more attention should be paid to its changes on the seasonal scale.

[0056] Figure 4 Wavelet coherence analysis of water level and total nitrogen concentration on a seasonal scale. Figure 4 a indicates that during the water receding period, the phase angle between the two is concentrated between 0° and 60°, indicating that water level leads changes in total nitrogen concentration by approximately 0-5 days. This means that as water levels drop during the receding period, water flow velocity and direction change. These changes affect the diffusion and transport of pollutants. For example, if water flow velocity decreases during the receding period, nitrogen-containing pollutants, which diffuse rapidly during high water levels, diffuse more slowly at lower flow rates, accumulating in localized areas. This causes water level to change before total nitrogen concentration. Figure 4 b During the flood season, the coherence before 2003 was higher than that after 2003, indicating that the effect of water level on total nitrogen concentration during the flood season has weakened after the completion of the Three Gorges Dam.

[0057] Figure 5 Wavelet coherence analysis of water level and total phosphorus concentration on a seasonal scale (one-month cycle). Figure 5 a represents the dry season. The coherence after 2003 is higher than before 2003, and after 2003, it presents an opposite phase (0°--60°), indicating that changes in total phosphorus concentration lead changes in water level by approximately 0-5 days. When the water level of Poyang Lake drops during the dry season, the water in some areas becomes shallower, and the bottom mud, which was originally in a reducing environment, gradually becomes exposed or approaches the water surface, beginning to undergo a transition from anaerobic to aerobic conditions. During this transition process, when the water level first begins to drop, the bottom mud still maintains a certain degree of anaerobic state. In this anaerobic environment, the activity of microorganisms (such as denitrifying bacteria) in the bottom mud releases bound phosphorus, causing the total phosphorus concentration to increase. Figure 5 During the receding water period (b), the phase angle between the two is primarily concentrated at 50°, indicating that total phosphorus concentration lags behind water level changes by approximately four days. During the receding water period, the drop in water level and the increase in water velocity enhance the scouring of surrounding pollution sources, accelerating the entry of phosphorus-containing pollutants from shorelines (such as residual phosphorus in farmland and phosphorus-containing substances in garbage dumps) into the water body, leading to an increase in total phosphorus concentration.

[0058] Correspondingly, a system for quantifying the non-steady-state response of water level and water quality in Tongjiang lakes includes: a time series multi-scale decomposition module, an interannual scale non-steady-state response quantification module, a water level change seasonal term grouping module and a seasonal scale non-steady-state response quantification module; the time series multi-scale decomposition module decomposes the water level monthly scale time series into trend term, seasonal term and error term based on the seasonal trend decomposition method; the interannual scale non-steady-state response quantification module calculates the time-varying coherence of water level and water quality at the interannual scale based on the interannual scale trend term using wavelet coherence analysis, generates a time-frequency coherence map, and reveals the non-steady-state response coherence strength between variables; the water level change seasonal term grouping module groups long time series according to the water level change seasonal term; the seasonal scale non-steady-state response quantification module performs wavelet cross transform on the grouped seasonal terms, calculates the cross wavelet spectrum between water level and water quality, extracts the instantaneous phase difference at the seasonal scale, and quantitatively reveals the lead-lag response law between seasonal scale variables.

[0059] The present invention can effectively process nonlinear and non-stationary data. The observed water level and water quality data often have nonlinear and non-stationary characteristics. The seasonal trend decomposition method can adaptively process nonlinear trends and seasonal changes during the decomposition process, and also has good robustness to outliers and noise. Directly performing wavelet coherence analysis, although wavelet coherence analysis itself has a certain processing capability for non-stationary signals, when faced with complex nonlinear and non-stationary data, if there is no seasonal trend decomposition method to pre-process the data and remove the interference of trend and seasonal components, its analysis results may be affected and cannot accurately reflect the true characteristics and intrinsic relationships of the data. The seasonal trend decomposition method can effectively separate long-term trends and seasonal changes, retain the nonlinear characteristics of the data, avoid random interference, have high computational efficiency, and do not require complex feature recognition models. For example, when analyzing the water level and water quality data of Poyang Lake, its long-term and seasonal change trends can be clearly obtained, laying the foundation for subsequent analysis.

[0060] Wavelet correlation analysis can quantitatively analyze relationships across multiple time scales. It analyzes correlations between non-stationary time series variables in the time-frequency domain and can identify changes in resonance intensity and relative phase relationships across different time scales. However, using wavelet correlation analysis alone has limitations when processing data with significant seasonal variation. By coupling seasonal trend decomposition with wavelet correlation analysis, first decomposing the data using seasonal trend decomposition to obtain trend and seasonal components, and then performing wavelet correlation analysis, it is possible to quantitatively assess the relationship between water level and water quality across multiple time scales. For example, the analysis of 32 years of data from Poyang Lake in this study comprehensively revealed changes in the relationship between the two at both long-term and seasonal scales.

[0061] Wavelet cross-transformation can effectively reveal nonlinear and time-varying characteristics between water level and water quality. For example, studies have found that the correlation between Poyang Lake water level and water quality exhibits complex variations across time scales and seasons, shifting from a negative correlation to a positive correlation, with varying responses across seasons.

[0062] To enhance explanatory power and provide early warning signals, seasonal trend decomposition methods coupled with wavelet correlation analysis and wavelet cross-transformation can enhance the explanatory power of the relationship between water level and water quality. This analysis reveals how water quality responds to changes in water level fluctuation patterns, which can serve as early warning signals of water quality changes. Combined with climate change models, this has important implications for early warning of future lake water level fluctuations and water quality changes, providing guidance for water environment management.

[0063] The present invention can effectively clarify the non-steady-state response relationship between water level and water quality. Through seasonal trend analysis and wavelet coherence calculation, it overcomes the noise interference problem inherent in long-term monitoring data and quantifies the non-steady-state response relationship between water level and water quality at interannual and seasonal scales. The operation is relatively simple and the required cost is low.

Claims

1. A method for quantifying the non-steady-state response of water level and water quality in lakes connected to rivers, characterized in that: The steps include: Step 1: Multi-scale decomposition of time series. Based on the seasonal trend decomposition method, the monthly water level time series is decomposed into trend term, seasonal term and error term. Step 2: Quantify the interannual scale non-stationary response. Based on the interannual scale trend term, wavelet coherence analysis is used to calculate the time-varying coherence of water level and water quality at the interannual scale, generate a time-frequency coherence map, and reveal the coherence strength of the non-stationary response between variables. Step 3: Group the long time series according to the seasonal terms of water level changes; Step 4: Quantify the seasonal scale non-steady-state response. Perform wavelet cross transform on the grouped seasonal items, calculate the cross wavelet spectrum between water level and water quality, extract the instantaneous phase difference on the seasonal scale, and quantitatively reveal the lead-lag response law between seasonal scale variables.

2. The method for quantifying the non-steady-state response of water level and water quality of lakes connected to rivers as claimed in claim 1, characterized in that: In step 1, the time series is decomposed at multiple scales. Based on the seasonal trend decomposition method, the monthly water level time series is decomposed into trend term, seasonal term and error term. Specifically: Y t =T t +S t +R t (t=1,2,3,…,T) Among them, in the observation time series Y t , decomposed into three components: T t Represents the potential trend item, reflecting the long-term evolution process or systematic law of the data; S t represents the seasonal term, which describes the periodic fluctuations and patterns that repeat on a monthly or annual basis; R t is the error term, reflecting random noise or short-term fluctuations not explained by trend and seasonal factors.

3. The method for quantifying the non-steady-state response of water level and water quality of lakes connected to rivers as claimed in claim 1, characterized in that: In step 2, the wavelet coherence analysis specifically includes the following steps: Step 21: In the data processing of the wavelet coherence analysis, ensure that the time series of the water level trend term and the water quality trend term are of equal length and complete the preprocessing of outlier correction and missing value filling; Step 22: Specify the sampling frequency fs=1 month for the trend item of water level and the trend item of water quality to achieve scale-frequency conversion; Step 23: Use Morlet wavelet basis function for decomposition, and use the time-frequency localization characteristics of the decomposed signal by scaling and translating it to adaptively balance the time and frequency resolution on an interannual scale. Step 24: The calculated modulus distribution of the complex coefficients characterizes the energy density in the time-frequency domain: the modulus peak corresponds to the main period of the signal, and the proportion of the modulus at each scale reveals the contribution weight of the periodic component; Step 25. Perform significance tests through Monte Carlo simulation to verify the statistical reliability of the time-frequency domain correlation: first, construct a null hypothesis data set, randomize the phase or shuffle the order of the original data to destroy the true phase relationship between the variables; then repeat the wavelet coherence analysis 1000 times to generate the null hypothesis coherence sample distribution; extract the upper bound of the distribution as the significance threshold based on the 95% confidence level; finally, by comparing the measured coherence with the threshold, eliminate random noise interference, extract and retain the effective signal, and focus on analyzing the time-frequency region with a coherence greater than 0.

6.

4. The method for quantifying the non-steady-state response of water level and water quality in lakes connected to rivers as claimed in claim 1, characterized in that: In step 2, based on the interannual trend term, wavelet coherence analysis is used to calculate the time-varying coherence of water level and water quality at the interannual scale, and a time-frequency coherence map is generated to reveal the coherence strength of the non-steady-state response between the variables: in, Represents the cross wavelet spectrum, which is used to evaluate the temporal similarity and phase change of two sequences at multiple time scales. The phase angle range is ([-π,π]), and the lead-lag relationship is determined by the phase angle.

5. The method for quantifying the non-steady-state response of water level and water quality of lakes connected to rivers as claimed in claim 1, characterized in that: In step 3, the long time series are grouped according to the seasonal variation of water levels. Combined with the natural properties of the hydrological system, the continuous time series data are divided into seasonal units with significant hydrological significance, so that the water level fluctuations in each group show a unified trend characteristic or periodic pattern, while highlighting the differences between different seasons.

6. The method for quantifying the non-steady-state response of water level and water quality in lakes connected to rivers as claimed in claim 1, characterized in that: In step 4, the phase difference of the two variables on the seasonal scale in different seasons is quantified through the cross-wavelet spectrum, and the lead-lag relationship between the two variables is further determined.

7. The method for quantifying the non-steady-state response of water level and water quality in lakes connected to rivers as claimed in claim 1, characterized in that: In step 4, the wavelet cross transform specifically includes the following steps: Step 41: First, perform continuous wavelet transform on the seasonal data of water level and water quality in different seasonal periods, and then perform cross wavelet transform by complex multiplication: Step 42: Adopting the complex Morlet wavelet basis function, adaptively balancing time and frequency on a monthly scale; setting the time interval dt to 1 month to represent the sampling interval of the time series; Step 43: Multiply the wavelet coefficient of the water level seasonal term by the conjugate of the wavelet coefficient of the water quality seasonal term to obtain a cross-wavelet spectrum. This result reveals the common power distribution and relative phase relationship of the two signals in the time-frequency domain. The complex wavelet coefficients represent the energy distribution of the signal on a one-month scale, and the modulus of the coefficients reflects the energy intensity of the corresponding time-frequency point. The larger the modulus, the more significant the energy contribution of the frequency component at the current time point. Step 44: Smoothing: suppressing noise interference in the time-frequency domain and enhancing the continuity of the significant correlation pattern through Gaussian smoothing; Step 45: Extract phase information from the cross-spectral density of the wavelet coefficients of the two signals, and determine the signal relationship from the phase difference: 0° indicates an in-phase change, 180° corresponds to an anti-phase change, and ±90° indicates a 1 / 4 cycle lag or lead.

8. A system for implementing the method for quantifying the non-steady-state response of water level and water quality in lakes connected to rivers as claimed in claim 1, characterized in that: include: Time series multi-scale decomposition module, interannual scale non-stationary response quantification module, water level change seasonal term grouping module and seasonal scale non-stationary response quantification module; The time series multi-scale decomposition module decomposes the monthly water level time series into trend terms, seasonal terms and error terms based on the seasonal trend decomposition method; The interannual scale non-stationary response quantification module calculates the time-varying coherence of water level and water quality at the interannual scale based on the interannual scale trend term using wavelet coherence analysis, generates a time-frequency coherence map, and reveals the non-stationary response coherence strength between variables; the water level change seasonal term grouping module groups long time series according to the water level change seasonal term; the seasonal scale non-stationary response quantification module performs wavelet cross transform on the grouped seasonal terms, calculates the cross wavelet spectrum between water level and water quality, extracts the instantaneous phase difference at the seasonal scale, and quantitatively reveals the lead-lag response law between seasonal scale variables.

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