A method and system for quantifying non-steady-state response of water level and water quality of rivers and lakes

Abstract

The application discloses a kind of quantification methods and systems of non-steady-state response of river lake water level and water quality, comprising: time series multiscale decomposition module, interannual scale non-steady-state response quantification module, water level change seasonal term grouping module and seasonal scale non-steady-state response quantification module;Time series multiscale decomposition module is based on seasonal trend decomposition method, and water level month scale time series is decomposed into trend term, seasonal term and error term;Interannual scale non-steady-state response quantification module is based on the trend term of interannual scale and uses wavelet coherence analysis to calculate the time-varying coherence of water level and water quality in interannual scale, generates time-frequency coherence atlas, reveals the non-steady-state response coherence intensity between variables;Water level change seasonal term grouping module is grouped according to water level change seasonal term according to long time series;Seasonal scale non-steady-state response quantification module carries out wavelet cross transform to the seasonal term after grouping, calculates the cross wavelet spectrum between water level and water quality, extracts seasonal scale instantaneous phase difference, and quantitatively reveals the leading-lag response law between seasonal scale variables.The application can effectively clarify the complex interaction between water level and water quality, and quantitatively analyze the relationship between non-steady-state response of water level and water quality through seasonal trend analysis, wavelet coherence analysis and wavelet cross transform.

Description

Technical Field

[0001] This 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 unsteady-state response of water level and water quality in lakes connected to rivers. Background Technology

[0002] Lakes connected to rivers often exhibit extremely complex hydrological and hydrodynamic interactions due to the influence of the rivers they flow into, leading to nonlinear characteristics in the response relationship between water level and water quality. The river-lake interaction in these lakes is exceptionally complex. Therefore, scientifically quantifying the unsteady-state responses of water level and water quality in connected lakes at interannual and seasonal scales has become a pressing technical problem in the field of hydrological change research, and is of great significance for water resource management under the influence of human activities. A state-dependent nonlinear coupling mechanism exists between hydrological driving forces and water quality responses, and the dynamic phase shift of their lead-lag relationship challenges traditional stationarity modeling paradigms.

[0003] Wavelet analysis and wavelet cross-transform have become core methods for detecting periodic changes in hydrological and water quality time series. Based on signal decomposition in the time and frequency domains, this method can effectively capture temporal evolution characteristics and interactions at specific scales. The coupling analysis of seasonal trend decomposition and wavelet coherence overcomes the key limitation of traditional correlation analysis's assumption of data stationarity, solves the inherent noise interference problem in long-term monitoring data, and provides a quantitative method for quantifying hydrological and biogeochemical coupling at specific scales.

[0004] In view of this, given the complex interactive response relationship between water level and water quality in lakes connected to the Yangtze River, it is necessary to propose a method to quantify the unsteady-state response of water level and water quality in these lakes. This method can 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 resource management and engineering scheduling decisions. Summary of the Invention

[0005] Purpose of the invention: This invention provides a method and system for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers. It can effectively clarify the complex interaction between water level and water quality. Through seasonal trend analysis, wavelet coherence analysis, and wavelet cross transform, it quantitatively analyzes the relationship between the unsteady-state response of water level and water quality.

[0006] Technical solution: The present invention provides a method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers, comprising 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, seasonal and error terms.

[0008] Step 2: Quantification of interannual scale nonsteady-state 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, generating a time-frequency coherence spectrum to reveal the nonsteady-state response coherence intensity between variables.

[0009] Step 3: Group the long-term series according to the seasonal component of water level changes;

[0010] Step 4: Quantification of seasonal-scale unsteady-state response. Perform wavelet cross-transform on the grouped seasonal terms, calculate the cross-wavelet spectrum between water level and water quality, extract the instantaneous phase difference at the seasonal scale, and quantitatively reveal the leading-lag response law between seasonal-scale variables.

[0011] Furthermore, in step 1, the time series multi-scale decomposition, based on the seasonal trend decomposition method, decomposes the monthly water level time series into a trend term, a seasonal term, and an error term, specifically as follows:

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

[0013] Among them, in the observed time series Y t In the middle, it decomposes into three components: T t This represents the potential trend term, reflecting the long-term evolution or systematic pattern of the data; S t Representing seasonality, it describes periodic fluctuations and patterns that repeat in monthly or yearly cycles; R t This is the error term, reflecting short-term fluctuations that are not explained by random noise or trends 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 wavelet coherence analysis, ensure that the trend terms of water level and water quality are of equal length and complete outlier correction and missing value filling preprocessing.

[0016] Step 22: Determine the sampling frequency fs = 1 month for the trend terms of water level and water quality, in order to achieve scale-frequency conversion;

[0017] Step 23: Select Morlet wavelet basis function for decomposition. By scaling and translating the decomposed signal, utilize its time-frequency localization characteristics to adaptively balance time and frequency resolution on an interannual scale (with a period of 1 year).

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

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

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

[0021]

[0022] in, The cross wavelet spectrum is used to evaluate the temporal similarity and phase changes of two sequences across 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-term series is grouped according to the seasonal variation pattern of water level. Combining the natural attributes of the hydrological system (such as precipitation cycle, seasonal differences in evaporation, and river inflow patterns), the continuous time series data is divided into seasonal units with significant hydrological significance (such as high water period, low water period, dry water period, and rising water period). This ensures that the water level fluctuations within each group exhibit a unified trend 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 is quantified by cross-wavelet spectrograms 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 for different seasonal periods, and then perform cross wavelet transform using complex multiplication:

[0027] Step 42: Use complex Morlet wavelet basis functions to adaptively balance time and frequency on a monthly scale; set the time interval dt to 1 month to represent the sampling interval of the time series;

[0028] Step 43: Multiply the wavelet coefficients of the seasonal water level term and the conjugate of the seasonal water quality term wavelet coefficients to obtain the 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 characterize the energy distribution of the signal on a one-month scale. The magnitude (amplitude) of the coefficients reflects the energy intensity at the corresponding time-frequency point—the larger the magnitude, the more significant the energy contribution of the frequency component at the current time point.

[0029] Step 44: Smoothing process. Gaussian smoothing is used to suppress noise interference in the time-frequency domain and enhance the continuity of significantly correlated patterns.

[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 in-phase change, 180° corresponds to out-of-phase change, and ±90° indicates a 1 / 4 period lag or lead.

[0031] Correspondingly, a system for quantifying the unsteady-state response of water level and water quality in lakes connected to the Yangtze River includes: a time series multi-scale decomposition module, an interannual scale unsteady-state response quantification module, a water level change seasonal term grouping module, and a seasonal scale unsteady-state response quantification module. The time series multi-scale decomposition module, based on the seasonal trend decomposition method, decomposes the monthly water level time series into a trend term, a seasonal term, and an error term. The interannual scale unsteady-state response quantification module, based on the interannual scale trend term, uses wavelet coherence analysis to calculate the time-varying coherence of water level and water quality at the interannual scale, generating a time-frequency coherence spectrum to reveal the unsteady-state response coherence intensity between variables. The water level change seasonal term grouping module groups the long-term series according to the water level change seasonal term. The seasonal scale unsteady-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 leading-lag response law between seasonal scale variables.

[0032] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) It effectively handles 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 the relationship between multiple time scales. By coupling the seasonal trend decomposition method with wavelet correlation analysis, the trend and seasonal components are obtained by decomposing the data through the seasonal trend decomposition method, and then wavelet correlation analysis is performed. The relationship between water level and water quality can be quantitatively evaluated at multiple time scales; (3) It reveals nonlinear and time-varying characteristics. The wavelet cross-transform method can effectively reveal the nonlinear and time-varying characteristics between water level and water quality; (4) It enhances explanatory power and provides early warning signals. The seasonal trend decomposition method coupled with wavelet correlation analysis and wavelet cross-transform can enhance the explanatory power of the relationship between water level and water quality. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0034] Figure 2 This is a seasonal trend analysis chart of water level in this invention.

[0035] Figure 3 This is a schematic diagram of wavelet coherence analysis of water level and water quality on an interannual scale in this invention.

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

[0037] Figure 5 This is a schematic diagram of the wavelet cross-transformation of water level and total phosphorus concentration on a seasonal scale in this invention. Detailed Implementation

[0038] like Figure 1 As shown, a method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers 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, seasonal and error terms.

[0040] Step 2: Quantification of interannual scale nonsteady-state 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, generating a time-frequency coherence spectrum to reveal the nonsteady-state response coherence intensity between variables.

[0041] Step 3: Group the long-term series according to the seasonal component of water level changes;

[0042] Step 4: Quantification of seasonal-scale unsteady-state response. Perform wavelet cross-transform on the grouped seasonal terms, calculate the cross-wavelet spectrum between water level and water quality, extract the instantaneous phase difference at the seasonal scale, and quantitatively reveal the leading-lag response law between seasonal-scale variables.

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

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

[0045] S2. Based on trend data, wavelet coherence analysis was used to calculate the non-steady-state response relationship between water level and water quality on an interannual scale;

[0046] The method is as follows: Based on the trend data, Morlet wavelet and other functions are used to perform time-frequency domain decomposition on the bivariate (water level and monthly average concentrations of total nitrogen and total phosphorus) to obtain the amplitude and phase information of each frequency component at the interannual scale.

[0047]

[0048] Among them, Rn 2 represents the wavelet correlation coefficient, ranging from 0 to 1. The coherence of two sequences is positively correlated with its value, reaching a value of 1 when synchronicity is maximized. S represents the scaling and time-domain smoothing operators, and W(s) are the weight functions of the variables, respectively.

[0049] S3. Seasonally grouping water level data according to hydrological rhythms aims to capture and reflect the periodic fluctuations in water level changes to the greatest extent possible through refined time-dimensional division. This process requires combining the natural attributes of the hydrological system to divide continuous time-series data into seasonal units with significant hydrological meaning (such as high-water season, low-water season, dry season, and rising-water season), ensuring that water level fluctuations within each group exhibit a unified trend or periodic pattern, while highlighting the differences between different seasons (such as the surge characteristics of flood peaks and the gradual decline trend during dry seasons). Seasonal data are extracted based on the seasonal trend decomposition method and grouped accordingly.

[0050] S4. Perform wavelet coherence analysis and wavelet cross-transform on the grouped seasonal terms to quantitatively interpret the non-steady-state response of water quality with water level fluctuations at the seasonal scale. Use wavelet cross-transform to analyze the phase relationship (lead-lag relationship) of the two time series in the time-frequency domain.

[0051]

[0052] in, This represents the cross wavelet spectrum, used to evaluate the temporal similarity and phase changes of two sequences across multiple time scales. The phase angle range is ([-π,π]), and the lead-lag relationship can be determined by the phase angle (e.g., a phase angle of π / 2 indicates that x leads y by 90°, corresponding to x leading y by 1 / 4 period in a periodic signal).

[0053] Morlet wavelet function is used to decompose the bivariate variables in the time-frequency domain to obtain the amplitude and phase information of each frequency component. Wavelet coherence spectrum is used to quantify the synchronicity strength of the bivariate variables at specific time scales within different seasons (coherence coefficient values ​​range from 0 to 1). The lead-lag relationship of the bivariate variables is determined based on the phase angle (0°–360°). Traditional global analysis cannot distinguish the dynamic differences between different seasons, while grouped wavelet coherence analysis can pinpoint the dominant cycle within a specific season, revealing the physical driving mechanism of coupling modes under different seasons. Phase shifts can be captured; the phase angle differences in different seasons can directly reflect the seasonal reversal of causal relationships.

[0054] Figure 2 This analysis focuses on the seasonal trend of water levels. The water level trend shows a significant decline, and the amplitude of seasonal fluctuations also shows a decreasing trend. Before 2003, the downward trend of the trend curve was relatively gentle, indicating that although the water level was generally declining during this period, the rate of decline was relatively stable, without any significant acceleration or abrupt changes. The observed value curve also roughly followed this relatively gentle downward trend during fluctuations, indicating that short-term fluctuations did not change the overall slow downward trend. After 2003, the downward trend of the trend curve intensified significantly, with a larger slope, indicating that the rate of water level decline accelerated after 2003, possibly influenced by the Three Gorges Dam project. The observed value curve also showed a more pronounced downward trend during fluctuations, and the low points of the fluctuations gradually decreased, indicating that not only was the long-term trend accelerating, but short-term water level fluctuations were also generally at a lower level. Before 2003, the amplitude of fluctuations in the seasonal curve was relatively large, indicating that the seasonal changes in water levels were quite obvious, with significant differences in water levels between different seasons. After 2003, the amplitude of fluctuations in the seasonal curve decreased, and the seasonal variation characteristics of water levels weakened. This may be due to changes in the regulatory role of water conservancy projects, causing the differences in water levels between different seasons to gradually narrow, and seasonal variations to become less pronounced than before. At the same time, the fluctuation pattern of the seasonal term curve may also have changed, with previously more regular fluctuations becoming smoother or more irregular.

[0055] Figure 3 This is a wavelet coherence analysis diagram of water level and water quality over a one-year period. Figure 3 The study indicates that the correlation between water level and total nitrogen concentration was low before 2003, but increased after 2003. This suggests that the relationship between water level changes and total nitrogen concentration changes became stronger after 2003, potentially implying an enhanced interaction between the two.Figure 3 b mainly shows the correlation between total phosphorus concentration and water level. The value was low around 2003, possibly because the construction of the Three Gorges Dam had a weaker correlation between water level and total phosphorus concentration on an interannual scale. More attention needs to be paid to its changes on a 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 receding water period, the phase angle between the two is concentrated between 0° and 60°, suggesting that water level leads changes in total nitrogen concentration by approximately 0-5 days. This means that as water level drops during the receding water period, water flow velocity and direction change. These changes affect the diffusion and transport of pollutants. For example, if the water flow velocity decreases during the receding water period, nitrogenous pollutants that diffused rapidly at high water levels diffuse more slowly at lower flow velocities, accumulating in localized areas, causing water level changes to precede changes in total nitrogen concentration. Figure 4 b. During the flood season, the coherence before 2003 was higher than that after 2003, indicating that the influence of water level on total nitrogen concentration during the flood season has weakened since the Three Gorges Dam was built.

[0057] Figure 5 Wavelet coherence analysis of water level and total phosphorus concentration on a seasonal scale (1-month cycle). Figure 5 'a' represents the dry season. The coherence after 2003 is higher than before 2003, and there is an out-of-phase relationship (0°-60°) after 2003, indicating that changes in total phosphorus concentration precede changes in water level, with a lead time of approximately 0-5 days. During the dry season in Poyang Lake, as water levels drop, some areas become shallower, and the sediment, originally in a reducing environment, gradually becomes exposed or approaches the surface, beginning a transition from an anaerobic to an aerobic environment. At the very beginning of this transition, the sediment maintains a certain degree of anaerobic conditions. Under anaerobic conditions, the activity of microorganisms in the sediment (such as denitrifying bacteria) releases bound phosphorus, causing the total phosphorus concentration to increase. Figure 5 During the receding water period, the phase angle between the two is mainly concentrated at 50°, indicating that the total phosphorus concentration lags behind the water level change, and the lag time is about 4 days. During the receding water period, the water level drops and the water flow speed increases, which enhances the scouring of surrounding pollution sources, causing phosphorus-containing pollutants on the shore (such as residual phosphorus in farmland and phosphorus-containing substances in garbage dumps) to enter the water body more quickly, resulting in an increase in the total phosphorus concentration.

[0058] Correspondingly, a system for quantifying the unsteady-state response of water level and water quality in lakes connected to the Yangtze River includes: a time series multi-scale decomposition module, an interannual scale unsteady-state response quantification module, a water level change seasonal term grouping module, and a seasonal scale unsteady-state response quantification module. The time series multi-scale decomposition module, based on the seasonal trend decomposition method, decomposes the monthly water level time series into a trend term, a seasonal term, and an error term. The interannual scale unsteady-state response quantification module, based on the interannual scale trend term, uses wavelet coherence analysis to calculate the time-varying coherence of water level and water quality at the interannual scale, generating a time-frequency coherence spectrum to reveal the unsteady-state response coherence intensity between variables. The water level change seasonal term grouping module groups the long-term series according to the water level change seasonal term. The seasonal scale unsteady-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 leading-lag response law between seasonal scale variables.

[0059] This invention effectively handles nonlinear and non-stationary data, as observed water level and water quality data often exhibit nonlinear and non-stationary characteristics. The seasonal trend decomposition method adaptively handles nonlinear trends and seasonal variations during the decomposition process and also demonstrates good robustness to outliers and noise. While wavelet coherence analysis itself has some processing capabilities for non-stationary signals, when faced with complex nonlinear and non-stationary data, the analysis results may be affected without preprocessing the data using the seasonal trend decomposition method to remove interference from trend and seasonal components, failing to accurately reflect the true characteristics and intrinsic relationships of the data. The seasonal trend decomposition method, however, effectively separates long-term trends and seasonal variations, preserves the nonlinear characteristics of the data, avoids random interference, has high computational efficiency, and does not require complex feature recognition models. For example, in analyzing the water level and water quality data of Poyang Lake, its long-term and seasonal trends can be clearly obtained, laying the foundation for subsequent analysis.

[0060] Wavelet correlation analysis can quantitatively analyze relationships across multiple time scales. It can analyze the correlation between non-stationary time series variables in the time-frequency domain, identifying changes in resonance intensity and relative phase relationships at different time scales. However, wavelet correlation analysis alone has limitations when dealing with data exhibiting significant seasonal variations. Coupled with seasonal trend decomposition, which first decomposes the data to obtain trend and seasonal components, and then performs wavelet correlation analysis, the relationship between water level and water quality can be quantitatively assessed across multiple time scales. For example, the analysis of 32 years of data from Poyang Lake in this study comprehensively revealed the changes in their relationship at both long-term and seasonal scales.

[0061] By revealing nonlinear and time-varying characteristics, the wavelet cross-transform method can effectively reveal the nonlinear and time-varying features between water level and water quality. For example, studies have found that the correlation between water level and water quality in Poyang Lake exhibits complex changes across different time scales and seasons, shifting from a negative correlation to a positive correlation, and showing different responses in different seasons.

[0062] Enhancing explanatory power and providing early warning signals, the seasonal trend decomposition method coupled with wavelet correlation analysis and wavelet cross-transform can improve the explanatory power of the relationship between water level and water quality. Analysis reveals how water quality responds to changes in water level fluctuation patterns, which can serve as an early warning signal for water quality changes. Combined with climate change models, this has significant implications for early warning of future lake water level fluctuations and water quality changes, providing guidance for water environment management.

[0063] This 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 inherent noise interference problem in long-term monitoring data and quantifies the non-steady-state response relationship between water level and water quality on interannual and seasonal scales. It is relatively simple to operate and has low cost.

Claims

1. A method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers, characterized in that, Includes the following steps: 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, seasonal and error terms. Step 2: Quantification of interannual scale nonsteady-state 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, generating a time-frequency coherence spectrum to reveal the nonsteady-state response coherence intensity between variables. Step 3: Group the long-term series according to the seasonal component of water level changes; Step 4: Quantification of seasonal-scale unsteady-state response. For the grouped seasonal terms, perform wavelet cross-transform to calculate the cross-wavelet spectrum between water level and water quality, extract the instantaneous phase difference at the seasonal scale, and quantitatively reveal the leading-lag response pattern between seasonal-scale variables. 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 for different seasonal periods, and then perform cross wavelet transform using complex multiplication: Step 42: Use complex Morlet wavelet basis functions to adaptively balance time and frequency on a monthly scale; set the time interval dt to 1 month to represent the sampling interval of the time series; Step 43: Multiply the wavelet coefficients of the seasonal water level term and the conjugate of the seasonal water quality term wavelet coefficients to obtain the 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 characterize the energy distribution of the signal on a one-month scale. The magnitude of the coefficients reflects the energy intensity at the corresponding time-frequency point. The larger the magnitude, the more significant the energy contribution of the frequency component at the current time point. Step 44: Smoothing process. Gaussian smoothing is used to suppress noise interference in the time-frequency domain and enhance the continuity of significantly correlated patterns. 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 in-phase change, 180° corresponds to out-of-phase change, and ±90° indicates a 1 / 4 period lag or lead.

2. The method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers as described in claim 1, characterized in that, In step 1, the time series multi-scale decomposition, based on the seasonal trend decomposition method, decomposes the monthly water level time series into a trend term, a seasonal term, and an error term, specifically as follows: Y t = T t + S t + R t (t = 1, 2, 3,…,T) Among them, in the observed time series Y t In the middle, it decomposes into three components: T t This represents the potential trend term, reflecting the long-term evolution or systematic pattern of the data; S t Representing seasonality, it describes periodic fluctuations and patterns that repeat in monthly or yearly cycles; R t This is the error term, reflecting short-term fluctuations that are not explained by random noise or trends and seasonal factors.

3. The method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers as described in claim 1, characterized in that, Step 2, wavelet coherence analysis specifically includes the following steps: Step 21: In the data processing of wavelet coherence analysis, ensure that the trend terms of water level and water quality are of equal length and complete outlier correction and missing value filling preprocessing. Step 22: Determine the sampling frequency fs = 1 month for the trend terms of water level and water quality, in order to achieve scale-frequency conversion; Step 23: Select Morlet wavelet basis functions for decomposition. By scaling and translating the decomposed signal, utilize its time-frequency localization characteristics to adaptively balance time and frequency resolution on an interannual scale. Step 24: The calculated distribution of the complex coefficient modulus represents the energy density in the time-frequency domain: the peak value of the modulus 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 a significance test using Monte Carlo simulation to verify the statistical reliability of the time-frequency domain correlation: First, construct a null hypothesis dataset and randomize or shuffle the phase of the original data to destroy the true phase relationship between variables; then repeat wavelet coherence analysis 1000 times to generate a null hypothesis coherence sample distribution; extract the upper bound of the distribution as a significance threshold based on a 95% confidence level; finally, by comparing the measured coherence with the threshold, remove random noise interference, extract and retain the effective signal, and focus on analyzing the time-frequency region with coherence greater than 0.

6.

4. The method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers as described in claim 1, characterized in that, In step 2, wavelet coherence analysis is used to calculate the time-varying coherence of water level and water quality at the interannual scale based on the interannual trend term, generating a time-frequency coherence spectrum to reveal the specific non-steady-state response coherence intensity between variables: in, The cross wavelet spectrum is used to evaluate the temporal similarity and phase changes of two sequences across 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 unsteady-state response of water level and water quality in lakes connected to rivers as described in claim 1, characterized in that, In step 3, the long-term series is grouped according to the seasonal variation pattern of water level. Combined with the natural attributes of the hydrological system, the continuous time series data is divided into seasonal units with significant hydrological significance, so that the water level fluctuations in each group show a unified trend or periodic pattern, while highlighting the differences between different seasons.

6. The method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers as described in claim 1, characterized in that, In step 4, the phase difference of the two variables on the seasonal scale is quantified by cross-wavelet spectrograms to further determine the lead-lag relationship between the two variables.

7. A system for implementing the method for quantifying the unsteady-state response of water level and water quality in lakes connected to rivers as described in claim 1, characterized in that, include: The module includes a time series multi-scale decomposition module, an interannual scale unsteady-state response quantification module, a water level change seasonal term grouping module, and a seasonal scale unsteady-state response quantification module. The time series multi-scale decomposition module is based on the seasonal trend decomposition method, which decomposes the monthly water level time series into trend, seasonal and error terms. The interannual-scale unsteady-state response quantification module uses wavelet coherence analysis based on the interannual-scale trend term to calculate the time-varying coherence of water level and water quality at the interannual scale, generating a time-frequency coherence spectrum to reveal the unsteady-state response coherence intensity between variables. The water level change seasonal term grouping module groups the long-term series according to the water level change seasonal term. The seasonal-scale unsteady-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 leading-lag response law between seasonal-scale variables.

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