Hydrological element change trend comprehensive analysis system and method

Abstract

The present application relates to the technical field of hydrological data, and more particularly to a system and method for comprehensive analysis of hydrological element change trend. The method comprises the following steps: obtaining time series data of hydrological elements of a target basin, eliminating the influence of upstream reservoir regulation and storage in the time series data of hydrological elements, and obtaining a natural runoff sequence; performing linear trend analysis on the natural runoff sequence under different time scales to obtain a regression slope parameter; when a non-zero trend signal is detected in the regression slope parameter, triggering a non-parametric significance test to generate an effective trend signal; decomposing the natural runoff sequence into multi-level periodic characteristics by time-frequency wavelet; identifying the main oscillation period of the multi-level periodic characteristics, calibrating the dominant period and the average change period, and constructing a periodic oscillation atlas of hydrological elements. The present application integrates trend signals, periodic characteristics and persistence parameters to construct a trend comprehensive identification path, and realizes the characterization of the change characteristics of hydrological elements.

Description

Technical Field

[0001] This invention relates to the field of hydrological data technology, and in particular to a comprehensive analysis system and method for the changing trends of hydrological elements. Background Technology

[0002] The changing trends of hydrological elements refer to the systematic changes in major hydrological elements such as precipitation, evaporation, runoff, groundwater, water level, and soil moisture content over time within a certain temporal and spatial scale. Analyzing and understanding these trends is crucial for watershed management, water resource allocation, flood and drought disaster prevention and control, and ecological environmental protection. Accurate assessment of the long-term changing trends of runoff within a watershed is essential for effectively addressing and managing watershed water resources. Trend analysis of evolutionary patterns not only helps reveal the impacts of past climate and human activities on runoff within the watershed but also provides a scientific basis for future watershed water resource planning and risk management.

[0003] In existing technologies, the linear trend analysis methods (such as linear regression) commonly used in the analysis of hydrological element change trends usually assume that the time series is stationary and the error terms are independent and identically distributed, which cannot effectively capture the non-stationary fluctuations of runoff processes under the influence of climate periodic disturbances and human regulation. While the spectral analysis method based on Fourier transform can reveal certain periodic information, it is difficult to locate the periodic change behavior over time and lacks time-frequency local sensitivity. Summary of the Invention

[0004] Therefore, it is necessary for the present invention to provide a comprehensive analysis system and method for hydrological element change trends in order to solve at least one of the above-mentioned technical problems.

[0005] To achieve the above objectives, a comprehensive analysis method for the changing trends of hydrological elements includes the following steps:

[0006] Step S1: Obtain time series data of hydrological elements in the target watershed and eliminate the influence of upstream reservoir regulation in the time series data of hydrological elements to obtain the natural runoff sequence;

[0007] Step S2: Perform linear trend analysis on the natural runoff sequence at different time scales to obtain the regression slope parameter; when a non-zero trend signal is detected in the regression slope parameter, trigger a non-parametric significance test to generate an effective trend signal;

[0008] Step S3: Decompose the time-frequency wavelet of the natural runoff sequence into multi-level periodic features; identify the main oscillation period of the multi-level periodic features, and mark the dominant period and average variation period to construct the periodic oscillation spectrum of hydrological elements;

[0009] Step S4: The Hurst index calculated using the main oscillation cycle is used as the persistence analysis result; the persistence analysis result is corrected by combining the phase state of the average change cycle and the dominant cycle to obtain the trend state description after cycle correction.

[0010] Step S5: Construct a trend identification model using effective trend signals, periodic oscillation patterns, and trend state descriptions as input variables; use the trend identification model to output the hydrological change trend of the target watershed.

[0011] This invention also provides a comprehensive analysis system for hydrological element change trends, used to execute the above-described comprehensive analysis method for hydrological element change trends, the comprehensive analysis system for hydrological element change trends comprising:

[0012] The data preprocessing module is used to acquire time series data of hydrological elements in the target watershed and eliminate the influence of upstream reservoir regulation in the time series data of hydrological elements to obtain the natural runoff sequence.

[0013] The trend detection module is used to perform linear trend analysis on natural runoff sequences at different time scales to obtain regression slope parameters. When a non-zero trend signal is detected in the regression slope parameter, a non-parametric significance test is triggered to generate a valid trend signal.

[0014] The periodic analysis module is used to decompose the time-frequency wavelet of the natural runoff sequence into multi-level periodic features; identify the main oscillation period of the multi-level periodic features, and mark the dominant period and the average variation period to construct the periodic oscillation spectrum of hydrological elements;

[0015] The persistence assessment module uses the Hurst index, calculated through the main oscillation cycle, as the persistence analysis result; it combines the phase state of the average change cycle and the dominant cycle to correct the persistence analysis result, thus obtaining a cycle-corrected trend state description.

[0016] The comprehensive identification module is used to construct a trend identification model using effective trend signals, periodic oscillation patterns, and trend state descriptions as input variables; and to output the hydrological change trend of the target watershed using the trend identification model.

[0017] This invention integrates trend signals, periodic oscillation characteristics, and trend persistence states from hydrological time series data to construct a highly flexible and adaptable watershed hydrological trend identification technology path. This method is mutually supportive in its theoretical logic and technical implementation, significantly improving the accuracy, dynamic response capability, and spatial applicability of identifying natural runoff change trends, thus possessing strong promotion and practical application value. Through the identification of effective trend signals, it can accurately reflect the linear change direction and significance of runoff sequences across multiple time scales (such as interannual, flood season, and monthly). The use of non-parametric testing methods, such as the Mann-Kendall test, avoids over-assumptions about data distribution, exhibiting good robustness and universality. Simultaneously, setting a trend neutrality interval (e.g., −0.1 to 0.1) effectively shields against misjudgments caused by weak changes. Given the natural volatility and uncertainty of hydrological data, it can more accurately define the true upward or downward trend, avoiding the misinterpretation of random fluctuations as structural trends. By introducing continuous wavelet transform for multi-scale periodic analysis of natural runoff sequences, the dominant period and average variation period can be effectively identified. Combining wavelet variance and the real part characteristics of wavelet coefficients, a periodic oscillation spectrum is constructed. This process not only reveals the implicit dominant periodic variation pattern in the hydrological sequence but also identifies the phase structure and periodic boundaries of the transition between wet and dry seasons, compensating for the shortcomings of traditional trend identification methods in processing nonlinear and non-stationary signals. The periodic oscillation spectrum provides a visual way to understand the intrinsic regulatory mechanism of the hydrological sequence by clearly describing the oscillation amplitude, phase change, and transition frequency at the dominant scale. Persistence analysis using the Hurst exponent can identify whether the trend has long-term continuity, thus determining whether the current change is a short-term anomaly or part of a long-term evolution. Correction by combining the periodic phase state, especially phase adjustment of the Hurst value within the rising or falling phase of the dominant period, helps to correct the apparent persistence bias caused by periodic oscillations, thus obtaining a more realistic description of the trend state. This method achieves a joint representation of trend direction, trend strength, and trend persistence, avoiding potential misinterpretations of trends due to isolated analysis, and enhancing the comprehensiveness and scientific rigor of trend judgment. An adaptive trend identification model is employed to fuse three types of trend information, achieving dynamic weighting of input information, temporal alignment, and unified trend output. This model not only automatically adjusts weights based on information consistency within a time period, improving fusion stability, but also resolves pseudo-conflicts caused by response lag between trend information through a trend transmission delay compensation mechanism, ensuring logical continuity and strong consistency in the fusion results. The output includes not only trend direction but also quantifies trend strength and time-period stability, giving it not only identification capabilities but also interpretation and early warning abilities, greatly enhancing the model's practicality and strategic value.This method is widely applicable to natural runoff time series data with mixed characteristics of periodicity, phases, and trends, and is particularly suitable for complex hydrological systems under the dual influence of climate change and human activities. Its multi-dimensional trend inputs, fusion model design, and phase correction mechanism together form a systematic, robust, and highly operable framework for hydrological trend analysis, providing theoretical basis and data support for watershed water resources management, extreme hydrological event prediction, hydrological model-driven strategies, and ecological regulation. Attached Figure Description

[0018] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0019] Figure 1 This is a schematic diagram of the steps in the comprehensive analysis method for the changing trends of hydrological elements according to the present invention;

[0020] Figure 2 This is a schematic diagram of a comprehensive analysis system for hydrological element change trends according to the present invention;

[0021] Figure 3 This is a multi-year distribution map of annual average runoff and average runoff during the flood season provided in an embodiment of the present invention;

[0022] Figure 4 This is a multi-year monthly average runoff distribution map provided in an embodiment of the present invention;

[0023] Figure 5 A line graph showing the average annual runoff provided in an embodiment of the present invention;

[0024] Figure 6 A line graph showing the average runoff during the flood season provided in an embodiment of the present invention;

[0025] Figure 7 A statistical chart of annual average runoff MK provided in an embodiment of the present invention;

[0026] Figure 8 A statistical chart of average runoff during the flood season (MK) provided in an embodiment of the present invention;

[0027] Figure 9 The wavelet real part variation diagram and corresponding wavelet variance diagram of annual average runoff are provided in an embodiment of the present invention. Detailed Implementation

[0028] The technical method of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0029] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0030] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0031] To achieve the above objectives, please refer to Figures 1 to 9 This invention provides a comprehensive analysis method for the changing trends of hydrological elements, the method comprising the following steps:

[0032] Step S1: Obtain time series data of hydrological elements in the target watershed and eliminate the influence of upstream reservoir regulation in the time series data of hydrological elements to obtain the natural runoff sequence;

[0033] In some embodiments, time series data of hydrological elements in the target watershed are acquired, such as multi-year daily or monthly runoff records. Considering that upstream reservoir regulation behavior can disturb downstream hydrological sequences, numerical corrections are made by inverting and modeling the impact of regulation, analyzing reservoir capacity regulation, or using scheduling data related to regulation behavior to eliminate unnatural disturbances to the sequence and obtain a natural runoff sequence that more accurately reflects the climate-hydrological driving mechanism.

[0034] Step S2: Perform linear trend analysis on the natural runoff sequence at different time scales to obtain the regression slope parameter; when a non-zero trend signal is detected in the regression slope parameter, trigger a non-parametric significance test to generate an effective trend signal;

[0035] In some embodiments, to fully characterize the changes in hydrological variations at different time scales, the natural runoff sequence is divided into sub-scale data segments such as interannual, flood season, and monthly. Linear trend fitting is performed on each sub-sequence, and the regression slope parameter is calculated using the least squares method. If the regression slope parameter falls outside a preset range (e.g., less than -0.1 or greater than 0.1), a significant trend signal is considered to exist. This further triggers non-parametric testing methods such as Mann-Kendall to calculate trend statistics and standardized statistics, and to determine the significance of the trend direction. Finally, a significant upward or downward effective trend signal is output.

[0036] Step S3: Decompose the time-frequency wavelet of the natural runoff sequence into multi-level periodic features; identify the main oscillation period of the multi-level periodic features, and mark the dominant period and average variation period to construct the periodic oscillation spectrum of hydrological elements;

[0037] In some embodiments, to analyze the periodic oscillation characteristics of hydrological elements, wavelet analysis is performed on the standardized natural runoff sequence (eliminating the influence of mean and variance). The Morlet wavelet function is selected as the mother wavelet, and continuous wavelet transform is performed to obtain a two-dimensional wavelet coefficient matrix. In this matrix, wavelet variance indices at each scale are extracted, and the main oscillation period is determined based on its variance peak value. The periods corresponding to the first three variance peak values ​​are constructed as multi-level periodic features. Based on this, the period with the largest wavelet variance is determined as the dominant period. Then, based on the wavelet real part coefficients, the alternation points of adjacent positive and negative phases are extracted, the average period span is calculated, and the average variation period is obtained. Combining the positive and negative characteristics of the wavelet real part sign, different time periods are marked as high-water seasons, low-water seasons, or phase transition points. By plotting a time-period phase distribution map, the oscillation amplitude, periodic structure, and phase switching frequency of the hydrological sequence are visualized, forming a complete periodic oscillation spectrum.

[0038] Step S4: The Hurst index calculated using the main oscillation cycle is used as the persistence analysis result; the persistence analysis result is corrected by combining the phase state of the average change cycle and the dominant cycle to obtain the trend state description after cycle correction.

[0039] In some embodiments, a dynamic sliding window is set based on the length of the dominant cycle, and the Hurst index within each window is calculated to identify the persistence characteristics of the hydrological process. For example, a Hurst index greater than 0.5 indicates that the segment has a long-term memory trend, while a lower Hurst index indicates a short-term or stochastic process. Simultaneously, the phase state of the dominant cycle and the average cycle within each window (e.g., in the rising phase of a peak or the falling phase of a trough) is extracted. This phase state is combined with the Hurst index to correct for the trend direction, ensuring that the final trend description comprehensively considers both the persistence of the trend and the cycle-driven mechanism. For example, if a window has a high Hurst index but is in a falling phase of the cycle, the upward trend assessment needs to be corrected to avoid misjudgment.

[0040] Step S5: Construct a trend identification model using effective trend signals, periodic oscillation patterns, and trend state descriptions as input variables; use the trend identification model to output the hydrological change trend of the target watershed.

[0041] In some embodiments, the three types of outputs mentioned above—significant trend signals (quantitative trend direction), periodic oscillation spectra (time-frequency structure expression), and trend state descriptions (joint correction results of trend and period)—are used as input features to construct a trend identification model. This model can employ a rule-based logical discrimination mechanism or use machine learning methods (such as support vector machines, random forests, etc.) to fuse and model multi-dimensional trend elements, outputting the final hydrological element change trend results, such as "significant increase," "dominantly periodic fluctuations," or "no significant trend."

[0042] It should be noted that this method particularly emphasizes eliminating the influence of reservoir regulation in trend detection to ensure that the analysis object is the natural hydrological response; at the same time, a periodic phase correction mechanism is introduced in the trend persistence judgment process, so that the final trend judgment reflects both linear tendency and nonlinear periodic change characteristics, which is closer to the objective law of the evolution of actual watershed hydrological processes.

[0043] Furthermore, step S2 includes the following steps:

[0044] Step S21: Segment the natural runoff sequence according to interannual, flood season, and monthly scales to generate three independent subsequences for analysis;

[0045] In some embodiments, the natural runoff series is split into three independent analytical subsequences based on interannual scales (e.g., total annual runoff), flood season scales (e.g., the sum of runoff from May to September each year), and monthly scales (e.g., monthly series). This scale division method can effectively capture the variation characteristics of hydrological series at different temporal aggregation levels.

[0046] Step S22: Perform linear fitting on each independent subsequence and use the least squares method to solve the regression slope parameter in the regression equation. When the sign of the regression slope parameter is positive, the hydrological element is judged to be on an upward trend. When the sign of the regression slope parameter is negative, the hydrological element is judged to be on a downward trend.

[0047] In some embodiments, linear fitting is performed on each subsequence, with time as the independent variable and runoff as the dependent variable. A regression equation is constructed, and the regression slope parameter is solved using the least squares method. This slope value reflects the overall trend direction and magnitude of hydrological elements changing over time. If the slope parameter is positive, the runoff is considered to be increasing at that time scale; conversely, if the slope is negative, it is judged to be decreasing.

[0048] Step S23: When a zero-trend signal is detected for the regression slope parameter, a non-significant fluctuation signal is generated, where the zero-trend signal is specifically −0.1 < regression slope parameter < 0.1;

[0049] In some embodiments, to avoid misjudging weak fluctuations as trend signals, if the absolute value of the regression slope parameter is between -0.1 and 0.1 (i.e., -0.1 < slope < 0.1), the trend change is deemed insufficient to reflect significant hydrological changes, defined as a zero-trend signal, and its corresponding trend type is recorded as a non-significant fluctuation signal, not participating in the subsequent significance determination process. This processing mechanism can effectively avoid false trend identification caused by data dispersion, interannual fluctuations, or observation errors.

[0050] Step S24: When a non-zero trend signal is detected in the regression slope parameter, a non-parametric significance test is triggered to generate a valid trend signal.

[0051] In some embodiments, if the regression slope exceeds the zero-trend threshold interval, a nonparametric significance test procedure is triggered. Methods such as the Mann-Kendall test are used to determine the statistical significance of the trend direction. Specifically, a trend statistic is constructed based on the ranking of positive and negative differences in the sequence, and a modified variance calculation is introduced to accommodate possible duplicate values ​​in the data, thereby calculating the standardized statistic Z-value. If the absolute value of the Z-value exceeds a preset critical value (e.g., 1.96 corresponds to a 95% confidence interval), the trend is considered statistically significant and is determined to be a valid trend signal. For example, if the regression slope for a certain monthly subsequence is −0.42 and the standardized statistic Z=−2.13, then the subsequence is judged to have a significant downward trend, and a valid trend signal is output.

[0052] It should be noted that when defining the zero-trend range (e.g., ±0.1), appropriate adjustments can be made based on different watershed characteristics, data fluctuation amplitude, or research objectives to balance false positive rate control and trend sensitivity. In addition, the Mann-Kendall test has non-parametric characteristics and does not depend on the data distribution pattern, making it particularly suitable for non-normal situations in hydrological sequences. This gives the method strong universality and robustness in different regions and sample types.

[0053] The present invention also provides an embodiment:

[0054] Please see Figure 3 This is a multi-year distribution map of average annual runoff and average runoff during the flood season. For example, the multi-year average annual runoff of the Longtan Reservoir basin is 1502 m³. 3 / s, the average annual runoff in 1979 was the highest since 1957, with a maximum average annual runoff of 2283 m³ / s. 3 / s, which is 52.0% less than the same period in previous years; the average annual runoff in 2023 was the lowest since 1957, with a minimum average annual runoff of 656 m³. 3 The average annual runoff was 2418 m³ / s, which is 56.32% less than the same period in previous years, and the ratio of the maximum to minimum annual average runoff extremes was 3.48. The average runoff during the flood season (May-October) in the Longtan Reservoir basin over many years is 2418 m³ / s. 3 / s, the average runoff during the 1979 flood season was the highest since 1957, with the maximum average runoff during the flood season being 4088 m³. 3 / s, which is 69.04% higher than the same period in previous years; the average runoff during the 2011 flood season was the lowest since 1957, with a minimum average runoff of 965 m³ / s. 3 / s, which is 60.10% less than the same period in many years, and the ratio of the maximum and minimum annual average runoff extreme values ​​is 4.24.

[0055] Please see Figure 4 The multi-year monthly average runoff distribution map shows that the multi-year monthly average runoff in the Longtan Reservoir basin from January to December is 495 m³. 3 / s、430m 3 / s、421 m 3 / s、521 m 3 / s、1119 m 3 / s, 29199 m 3 / s、3607 m 3 / s、3089m 3 / s、2259 m 3 / s、1528 m 3 / s、933 m 3 / s and 616 m 3 / s, average monthly runoff over many years Figure 4As shown, July has the highest multi-year average monthly runoff, while March has the lowest, with the ratio of the highest to the lowest monthly average runoff being 8.57 times. Furthermore, February has the highest extreme ratio of monthly average runoff, with an average monthly runoff of 37.5 m³ in February 2010. 3 / s, the average monthly runoff in February 2022 was 1030 m³ / s. 3 / s, with an extreme value ratio of 27.5.

[0056] Please see Figure 5 The annual average runoff is plotted as a line graph. Based on the inflow monitoring data of Longtan Reservoir, the linear trend of annual average runoff is estimated, and the results are as follows: Figure 5 As shown, the regression constant for the annual average runoff of the Longtan Reservoir basin versus time is 10212, and the regression coefficient is -4.3768. The regression coefficient and the fitted curve indicate that the annual average runoff of the Longtan Reservoir basin has generally shown a decreasing trend since 1957.

[0057] Please see Figure 6 The graph shows the average runoff during the flood season. The regression constant for the average runoff during the flood season in the Longtan Reservoir basin versus time is 21303, and the regression coefficient is -9.4899. The regression coefficient and the fitted curve show that the average annual runoff in the Longtan Reservoir basin has generally shown a decreasing trend since 1957. However, the decreasing trend of the average runoff during the flood season is more significant than that of the average annual runoff.

[0058] Furthermore, the nonparametric significance test described in step S24 specifically includes:

[0059] The trend statistics of natural runoff sequences at interannual, flood season, and monthly time scales are calculated using the following formula:

[0060]

[0061]

[0062] In the formula, A trend statistic used to measure the quantitative difference between upward and downward trends in a natural runoff series. This represents the total number of runoff values ​​in the natural runoff sequence. The first in the natural runoff sequence Individual runoff values, The first in the natural runoff sequence Individual runoff values, To judge and The sign function of the size relationship;

[0063] The variance of the trend statistic is calculated using the modified variance formula, which is as follows:

[0064]

[0065] In the formula, The variance of the trend statistic. The first in a repeating group of runoff values ​​with equal values The number of times each duplicate value appears. This represents the total number of runoff values ​​in the natural runoff sequence.

[0066] Calculate standardized statistics based on variance and trend statistics;

[0067] The significance of trend direction is determined by trend statistics and standardized statistics, thus obtaining effective trend signals.

[0068] Furthermore, the calculation of standardized statistics based on variance and trend statistics includes:

[0069] When the trend statistic is positive, the standardized statistic = (trend statistic - 1) / square root of the variance of the statistic;

[0070] When the trend statistic is 0, the standardized statistic = 0;

[0071] When the trend statistic is negative, the standardized statistic = (trend statistic + 1) / square root of the variance of the statistic.

[0072] In some embodiments, to achieve nonparametric discrimination of the significance of trends in natural runoff sequences, the Mann-Kendall method is used to statistically verify the trends. Specifically, the corresponding subsequences are first processed based on three time scales: interannual, flood season, and intermonthly. At each scale, the natural runoff sequence is denoted as a sequence of length *l*. time series The trend statistic is calculated using the following formula. : The symbolic function sgn(·) is used to compare the runoff volume at any two time points, and its definition is:

[0073] This statistic The physical meaning is: traversing any two different time points in the sequence The relationship between runoff values ​​is such that if the latter is greater than the former, it indicates an upward trend, and vice versa. Ultimately... This is the difference between the logarithm of all upward trends and the logarithm of all downward trends. Therefore, The larger the value, the more pronounced the overall upward trend in the sequence. The smaller the value, the more pronounced the downward trend. For example, if in 21 years of runoff data at a certain interannual scale, there are 130 pairs of increasing relationships and 90 pairs of decreasing relationships, then... The initial trend is upward. Considering the possibility of multiple identical values ​​(i.e., "repeated values") in the hydrological series, a modified variance calculation formula needs to be introduced for correction. The standard deviation is used to improve the accuracy of the judgment. Variance of the statistic. The calculation formula is:

[0074]

[0075] Where n is the total length of the sequence, and tᵢ represents the number of repetitions of the same value in the i-th repeating group composed of equal values ​​in the runoff sequence. The introduction of this correction term can reduce the bias caused by repeated values ​​and improve the sensitivity to actual trend changes. For example, if there are 3 runoff points with a "repeated value" of 500 m³ / s in a subsequence at the flood season scale, then t1=3. Substituting this into the formula can accurately reflect the influence of the repeated group on the variance. Next, using the trend statistic S and its variance Var(S), the standardized statistic Z is calculated to determine the significance of the trend. The calculation rules for the standardized statistic are as follows:

[0076]

[0077] After standardization, the Z-value follows an approximately normal distribution. Therefore, the significance of the trend can be judged based on its absolute value and the critical value of the standard normal distribution. For example, when a confidence level of 95% is selected, the critical Z-value is ±1.96. If |Z|>1.96, the trend can be considered significant; otherwise, it is considered random fluctuation.

[0078] Finally, the trend type is classified based on the Z value and the positive or negative direction of S: if Z > 1.96, it indicates a significant upward trend in runoff; if Z < −1.96, it indicates a significant downward trend; if −1.96 ≤ Z ≤ 1.96, it is judged as a non-significant trend, meaning the trend direction cannot be determined by statistical methods, and the output is a random fluctuation signal. Taking the above interannual series as an example, if S = 65 and Var(S) = 180 are calculated, substituting them into the equation yields Z ≈ 4.74, which is much greater than 1.96, indicating a significant upward trend and forming an effective trend signal.

[0079] It should be noted that, to ensure trend judgment can still be made in different watersheds with small data volumes or drastic fluctuations, this method uses a non-parametric approach rather than statistical testing tools based on hypothetical distributions, thereby improving adaptability and robustness. Furthermore, the improved variance calculation formula is particularly important when handling duplicate values. It is recommended to pre-analyze the input data in practical applications to identify all duplicate groups and ensure the accuracy of Var(S) calculation.

[0080] The present invention also provides an embodiment:

[0081] Please see Figure 7 The following is a line graph showing the annual average runoff (MK) trend analysis results for the Longtan Reservoir basin: Figure 7 As shown, the annual average runoff of the Longtan Reservoir basin did not show a significant trend from 1957 to 2023, alternating between insignificant upward and downward trends. Specifically, the annual average runoff showed a non-significant downward trend from 1957 to 1964, a non-significant upward trend from 1964 to 1991, a non-significant downward trend from 1992 to 1994, a non-significant upward trend from 1995 to 2004, and a non-significant downward trend from 1905 to 2023. Combining the annual average runoff data of the Longtan Reservoir basin, the abrupt change points in the trend occurred in 2008 and 2013.

[0082] Please see Figure 8 The following is a line graph showing the annual average runoff. The trend analysis results of the average runoff MK during the flood season in the Longtan Reservoir basin are as follows: Figure 8 As shown, the average runoff during the flood season in the Longtan Reservoir basin did not show a significant trend from 1957 to 2023. This insignificant upward and downward trend is basically consistent with the change in the average annual runoff in the Longtan Reservoir basin. From 1957 to 1960, the average runoff during the flood season in the Longtan Reservoir basin showed a non-significant downward trend; from 1961 to 1962, a non-significant upward trend; in 1963, a non-significant downward trend; from 1964 to 2003, a non-significant upward trend; and from 2004 to 2023, a non-significant downward trend. Combining the data on the average runoff during the flood season in the Longtan Reservoir basin, the abrupt change in the trend occurred in 2008.

[0083] The analysis of the monthly average runoff (MK) trend in the Longtan Reservoir basin from 1957 to 2023 shows that March, April, June, and August exhibit significant increasing or decreasing trends, while the trends for other months are not significant. Specifically, the monthly average runoff in March showed a significant increasing trend from 2003 to 2023; the monthly average runoff in April showed a significant increasing trend from 2020 to 2023; the monthly average runoff in June showed a significant increasing trend from 1984 to 1986; and the monthly average runoff in August showed a significant decreasing trend from 2022 to 2023. Furthermore, the average monthly runoff in the Longtan Reservoir basin showed a non-significant downward trend before 1964, and a non-significant upward trend after 1964; the average monthly runoff in February showed a non-significant upward trend overall; the average monthly runoff in May showed a non-significant upward trend before 1991, and a non-significant downward trend after 1991; the average monthly runoff in July showed an unclear upward or downward trend between 1984 and 1986; the average monthly runoff in September showed a non-significant upward trend before 2002, and a non-significant downward trend after 2002; the average monthly runoff in October... The changes showed a non-significant upward trend before 1992, and a non-significant downward trend after 1998. The monthly average runoff in November showed a non-significant upward trend before 1991, and a non-significant downward trend after 2010. The monthly average runoff in November fluctuated five times: a non-significant downward trend from 1957 to 1962, a non-significant upward trend from 1963 to 1988, a non-significant downward trend from 1989 to 1999, a non-significant upward trend from 2000 to 2021, and a non-significant downward trend from 2022 to 2023.

[0084] Furthermore, the specific steps for determining the significance of the trend direction using trend statistics and standardized statistics to obtain an effective trend signal are as follows:

[0085] When the trend statistic is greater than zero and the absolute value of the standardized statistic is greater than the preset critical value, the natural runoff sequence is judged to have increased significantly over time, and is recorded as a significant upward trend signal.

[0086] When the trend statistic is less than zero and the absolute value of the standardized statistic is greater than the preset critical value, the natural runoff sequence is judged to have decreased significantly over time, and is recorded as a significant downward trend signal.

[0087] When the absolute value of the standardized statistic is less than or equal to the preset critical value, it is determined that the natural runoff sequence has no significant trend over time, and is recorded as a random fluctuation signal, which is an invalid trend signal.

[0088] Significant upward trend signals and significant downward trend signals are combined into effective trend signals.

[0089] In some embodiments, after calculating the trend statistic S and variance Var(S) of the natural runoff sequence, to further identify the significance and direction of the trend, S needs to be standardized to obtain a standardized statistic Z. This standardized statistic Z is then combined with a preset statistical significance threshold to determine the significance of the trend direction, ultimately forming the trend identification result. The standardization process transforms the original trend statistic into a statistical indicator that follows an approximately standard normal distribution, allowing subsequent significance testing methods to determine the reliability of the trend. Based on this, a preset significance threshold is introduced. (A commonly used value is 1.96, corresponding to a 95% confidence level) as the significance threshold. Then, based on the value and sign of the standardized statistic Z, the trend direction and significance of the natural runoff sequence are determined, according to the following rules:

[0090] When S>0 and |Z|> When this occurs, it indicates that the upward trend in the sequence is significantly stronger than the downward trend, and is judged as a significant upward trend signal;

[0091] When S < 0 and |Z| > When this occurs, it indicates that the downward trend in the sequence is significantly stronger than the upward trend, and is judged as a significant downward trend signal;

[0092] When |Z|≤ When the sign of S is unknown, it is judged as having no significant trend and is recorded as a random fluctuation signal. The trend is considered unidentifiable, and the signal is an invalid trend signal.

[0093] For example: If the natural runoff sequence at a monthly scale for a certain watershed yields a trend statistic S=47 and a variance Var(S)=89, then the standardized statistic... The value is approximately 4.88, which is much greater than the critical value of 1.96, and S>0. Therefore, it is determined that the sequence has a significant upward trend on a monthly scale, forming a significant upward trend signal.

[0094] In another example, if a sequence at a flood season scale yields S = −35 and Var(S) = 70, then Since Z ≈−4.06 and S < 0, it can be determined as a significant downward trend signal.

[0095] Conversely, if a sequence yields Z=1.43, although the trend statistic may be positive, its absolute value is less than 1.96, indicating that the trend is not statistically significant. Therefore, the signal is considered a random fluctuation signal and does not have the power to identify trends.

[0096] It should be noted that the preset threshold value The choice of is related to the confidence level, with common values ​​being 1.96 (95% confidence level) or 2.576 (99% confidence level), which can be set according to the actual analytical precision requirements. Furthermore, the non-parametric nature of this method makes it applicable to data with different distribution patterns, exhibiting strong robustness and adaptability, particularly suitable for hydrological sequences exhibiting non-normality, jumps, or abrupt changes. Finally, all significant upward trend signals and significant downward trend signals together constitute the effective trend signal set, used as input variables for subsequent trend identification models.

[0097] Furthermore, step S3 includes the following steps:

[0098] The zero mean and unit variance of the natural runoff series are calculated to eliminate the original trend term and scale effect of the natural runoff series, thus obtaining the standardized natural runoff series.

[0099] Morlet wavelet is selected as the mother function for wavelet analysis. A continuous wavelet transform is performed on the standardized natural runoff sequence to obtain a wavelet coefficient matrix containing different scales and time positions. The wavelet transform can be expressed as:

[0100]

[0101] In the formula, These are continuous wavelet transform coefficients. To control the scale factor of the wavelet period length, Let be the translation factor that moves the wavelet's position on the signal time axis. For time variables, The input is the function value of the natural runoff sequence. This is the conjugate form of the Morlet wavelet function;

[0102] Calculate the wavelet variance in the wavelet coefficient matrix and plot the wavelet variance plot;

[0103] The main periodic components are identified by wavelet variance plots, sorted by wavelet variance size, and the period with the largest variance is taken as the main oscillation period. The three periods with the largest variance are combined to form a multi-level periodic feature.

[0104] The dominant period and average variation period in the multi-level periodic characteristics are identified, and a periodic oscillation pattern of hydrological elements is constructed.

[0105] In some embodiments, to analyze potential periodic oscillation patterns in natural runoff sequences and reveal their non-stationary dynamic characteristics, this method introduces continuous wavelet transform for multi-scale time-frequency analysis. Specifically, the original runoff sequence is first standardized to eliminate interference from the original trend term and scale effects, ensuring the objectivity and comparability of the wavelet analysis results. The natural runoff sequence is then processed with zero mean and unit variance. The Morlet wavelet function is selected as the mother wavelet, and a continuous wavelet transform (CWT) is performed on the standardized runoff sequence to obtain a two-dimensional wavelet coefficient matrix. The Morlet wavelet is a complex-valued wavelet with good time-domain and frequency-domain locality, suitable for analyzing hydrological non-stationary signals. The variance of the wavelet coefficients at each scale is calculated to obtain the wavelet variance spectrum, which is expressed as:

[0106]

[0107] in, Let W(a,b) represent the average wavelet energy (i.e., wavelet variance) at scale *a*, and let W(a,b) be the elements of the wavelet coefficient matrix. By sorting the wavelet variances corresponding to all scales, the energy distribution in the natural runoff sequence at different periodic scales can be clearly identified. Then, the calculation results are plotted as a wavelet variance plot, with the horizontal axis representing the scale or corresponding period length and the vertical axis representing the magnitude of the wavelet variance. The peak value in the plot represents the periodic fluctuation with dominant energy. Based on the wavelet variance plot, the period corresponding to the scale with the largest variance is defined as the main oscillation period. At the same time, the top three periods with the highest wavelet variance are selected as multi-level periodic features, forming a set of periods describing the oscillation characteristics of hydrological changes.

[0108] Furthermore, two key periodic parameters are extracted from the multi-level periodic features:

[0109] Dominant period: the period with the largest wavelet variance, representing the most significant oscillation frequency of the hydrological system;

[0110] Average variation period: the average of the three periods with the highest variance, reflecting the central trend of periodic changes in the hydrological system at different time scales.

[0111] Finally, the multi-level periodic characteristics, dominant period, and average variation period are integrated into a visualization map to construct a periodic oscillation map of hydrological elements, which is used to characterize the periodic structure and dominant rhythm of the natural runoff system.

[0112] It should be noted that, since the Morlet wavelet is a complex mother wavelet, its coefficient matrix contains both amplitude and phase information. If subsequent phase state correction analysis is required (such as introducing phase discrimination in Hurst persistence analysis), the phase trajectory under each dominant period should be further extracted. Furthermore, the conversion between the scaling factor and the actual period needs to be corrected using the wavelet function's center frequency and sampling period. In practice, it is recommended to use built-in wavelet analysis tools (such as MATLAB's cwt function or Python's pywt library) for auxiliary analysis.

[0113] The present invention also provides an embodiment:

[0114] Please see Figure 9 The graph shows the wavelet real part variation of the annual average runoff and the corresponding wavelet variance. As can be seen from the graph, the average runoff during the flood season in the Longtan Reservoir basin exhibits a certain periodicity, with oscillation periods of 4 years, 16 years, and 25 years. The first principal period of fluctuation in the average runoff during the flood season in the Longtan Reservoir basin is consistent with the annual average runoff. The 25-year annual average runoff sequence shows the strongest periodic oscillation, while 16 years and 4 years represent the second and third principal periods, respectively. At the 25-year scale, the trend of the wavelet coefficient of the average runoff during the flood season is consistent with the trend of the annual average runoff. The average runoff sequence during the flood season in the Longtan Reservoir basin mainly exhibits a 16-year average variation period at the first principal period scale. In the years following 2023, the average runoff during the flood season will continue to be relatively low, consistent with the trend of the annual average runoff.

[0115] The wavelet analysis results of the monthly average runoff in the Longtan Reservoir Basin are detailed in the table below. The number of time scales and specific years of the oscillation cycle of the monthly average runoff are basically different for each month, but January, May and December have the same first principal cycle of 52 years, and August, October and November have the same first principal cycle of 25 years.

[0116]

[0117] Furthermore, the specific steps for determining the dominant period and average variation period in the multi-level periodic characteristics and constructing the periodic oscillation spectrum of hydrological elements are as follows:

[0118] The period with the largest wavelet variance in the multi-level periodic features is determined as the dominant period;

[0119] On the dominant period scale, identify the peak and trough positions of the real part curve of the wavelet, calculate the time span of adjacent phase points in the same direction, and take the arithmetic mean of all spans as the average variation period.

[0120] The sign characteristics of the real part values ​​in the wavelet coefficient matrix are extracted. When the real part value is continuously positive, it is marked as the high water season; when the real part value is continuously negative, it is marked as the low water season. The zero-crossing point of the real part value is marked as the phase transition critical point, thus obtaining the wavelet real part sign label.

[0121] A time-period phase distribution diagram is plotted based on wavelet real part notation, with the vertical axis representing the scale range of the dominant period and the average variation period, and the horizontal axis representing the time series;

[0122] Based on the time-period phase distribution map, combined with the oscillation intensity variation of the dominant period and the distribution density of the phase transition critical point, a periodic oscillation spectrum including period length, oscillation amplitude, phase state and transition frequency is constructed.

[0123] In some embodiments, to further extract the periodic evolution characteristics of natural runoff sequences, after obtaining multi-level periodic features, it is necessary to calibrate and perform phase analysis on the three periods with the highest wavelet variance, thereby constructing a complete periodic oscillation map. This process not only identifies the rhythmic structure of periodic changes but also reflects the phase transition behavior in hydrological fluctuations. Among the identified multi-level periodic features, the period with the largest wavelet variance is selected as the dominant period. The dominant period refers to the periodic scale that can concentrate the most energy among all wavelet scales, representing the most important oscillation frequency in natural runoff changes and having significant hydrological interpretation significance. This period is represented by the highest peak position in the wavelet variance map. At the scale corresponding to the dominant period, the real part numerical sequence of the wavelet coefficient matrix is ​​extracted, and the real part curve is plotted. On this curve, the start and end points of each complete oscillation cycle are determined by identifying the positions of local peaks (positive maxima) and troughs (negative minima). A complete periodic unit is defined as the time span between adjacent phase points in the same direction (e.g., the time interval between two adjacent wave crests). The time spans of all complete periodic units are calculated, and their arithmetic mean is taken to obtain the average variation period at this scale. The average variation period reflects the average period length formed by the alternation of wet and dry seasons in actual hydrological changes. Based on the wavelet real part sequence at the dominant periodic scale, its symbol features are further extracted: when the continuous wavelet real part values ​​are positive, the time period is marked as a wet season; when the continuous real part values ​​are negative, it is marked as a dry season; and when the wavelet real part value crosses zero and undergoes a positive-to-negative transformation, that point is considered a phase transition critical point. This labeling process forms a set of "wet-dry-transition" time period labels for subsequent phase map drawing and trend analysis. After completing the symbol labeling, a time-period phase distribution map is drawn on a two-dimensional plane based on the phase state of the wavelet real part. This graph uses the time axis as the horizontal axis and the scale range including the dominant period and the average variation period as the vertical axis, marking the real part sign state at each time point (e.g., positive in red, negative in blue, and a black boundary line at zero). Through color or symbol visualization, it intuitively presents the alternation of wet and dry periods and the phase evolution trend of the hydrological system at different periodic scales. Finally, based on the pattern presented by the time-period phase distribution map, and combined with the following core elements, a complete periodic oscillation map is constructed:

[0124] Period length: The dominant period and the average variation period represent the most significant frequency of change and the average rhythm of the system, respectively;

[0125] Oscillation amplitude: The difference between the peaks and troughs of the real part curve of the wavelet reflects the intensity of the fluctuation within the period, which can be measured by the absolute value of the wavelet coefficients;

[0126] Phase state: The distribution of wet and dry seasons marked by the real part sign constitutes the phase description within the period;

[0127] Conversion frequency: The number of phase transition critical points that occur per unit time, which measures the activity level of periodic changes.

[0128] For example, suppose that in the annual-scale natural runoff analysis of a certain watershed, the dominant period is 12 years, and the average variation period is 8.5 years. At the dominant period scale, the wavelet real part curve exhibits multiple continuous positive and negative fluctuation intervals. The positive segment lasts 3-5 years, corresponding to the high-water season; the negative segment lasts 4-6 years, corresponding to the low-water season; the zero intersection of the real part values ​​occurs on average once every 10 years, corresponding to phase transitions. Therefore, the final periodic oscillation spectrum can be expressed as: dominant period = 12 years, average period = 8.5 years, oscillation intensity range [-0.8, +0.9], and transition frequency once every 10 years. This spectrum can serve as input for hydrological trend modeling and scheduling management.

[0129] It should be noted that although the zero-crossing point of the real part of the wavelet can be regarded as the phase transition point, noise and short-term jitter exist in the actual data. To avoid misidentification, smoothing processing should be applied to the real part sequence or a threshold for the duration of the zero-crossing point should be set. In addition, the calibration of the average variation period should exclude the interference of incomplete oscillation segments (such as incomplete periods at the beginning and end of the sequence) on the average value to improve the stability of the results. The finally constructed periodic oscillation spectrum serves as an important input to the trend identification model, which can significantly improve the sensitivity and robustness of trend identification to periodic fluctuations.

[0130] Furthermore, step S4 includes the following steps:

[0131] Step S41: Determine the size of the dynamic calculation window based on the length of the main oscillation period, and use it as the dynamic calculation window;

[0132] Step S42: The natural runoff sequence is segmented according to the dynamic calculation window. The Hurst index is calculated for the runoff in each dynamic calculation window. The persistence analysis results of each window are obtained by rescaled range analysis.

[0133] Step S43: Extract the phase information of the average change period and the dominant period in each time period, determine whether the period is in an upward phase or a downward phase, and obtain the period phase state;

[0134] Step S44: Match the persistence analysis results of each window with the periodic phase state of the corresponding time period, and correct the persistence characteristic parameters according to the periodic phase state to generate a periodically corrected trend state description.

[0135] In some embodiments, based on the extraction of periodic features and identification of trend significance in natural runoff sequences, to more comprehensively depict the long-term changing trend of the sequence, it is necessary to further combine Hurst index analysis and periodic phase state to periodically correct the persistence of the trend. This process not only analyzes the "presence" of a trend, but also quantifies the "strength of persistence" and "direction of change" of the trend. The specific implementation method is as follows: The size of the dynamic calculation window is determined according to the length of the main oscillation cycle identified in the previous step. For example, if the dominant cycle is 10 years, the length of the dynamic window can be set to 10 years or a multiple thereof (such as 20 years) to ensure that each window can fully cover at least one complete cycle. This window setting method based on periodic features adaptive adjustment can avoid the scaling bias problem that may be caused by a fixed window. The natural runoff sequence is divided into sliding segments according to the set dynamic calculation window, for example, every 10 years is a window, and the analysis is performed by sliding a fixed step size (such as 1 year). Within each dynamic window, the Hurst index of the data segment is calculated using the rescaled range analysis (R / S Analysis) method. The Hurst index is a statistic that measures the long-term dependence and trend persistence of a time series. Its value is usually between (0,1): When H>0.5, it indicates that the series has a positive correlation, that is, the trend is persistent. If the current trend is upward, it may continue to rise in the future. When H<0.5, it indicates that the series has a negative correlation, that is, the trend has a reversal characteristic. The stronger the current trend, the more likely it is to reverse in the future. When H≈0.5, it indicates that the series changes are close to a random process and there is no obvious trend memory.

[0136] To enhance the understanding of trend changes, phase information of the dominant cycle and the average variation cycle is extracted from the previously obtained periodic oscillation spectrum. This involves determining whether each time period is in an upward phase (from dry to wet season) or a downward phase (from wet to dry season). Specifically, in the wavelet real part curve, the direction of the sign change of the real part value is tracked: from negative to positive indicates an upward phase, and from positive to negative indicates a downward phase. The dominant cycle phase trend within each dynamic window is categorized to form a "phase state marker." The Hurst exponent result in each dynamic window is matched and fused with the corresponding periodic phase state to construct a trend state description that better reflects the actual hydrological evolution. The core idea is that trend persistence depends not only on statistical characteristics but also on the influence of periodic phase regulation. The specific correction strategy is as follows: If Hurst > 0.5 within the window and the cycle is in an upward phase, the trend is confirmed to have strong persistence, and the trend status is marked as "strong persistence upward"; if Hurst > 0.5 and the cycle is in a downward phase, the trend direction is opposite to the phase trend, the trend strength level should be lowered, and the trend status is marked as "weak persistence"; if Hurst < 0.5 and the cycle is in a downward phase, the trend will be more likely to reverse, so it is marked as "unstable trend" or "tending to reverse"; if Hurst ≈ 0.5, regardless of the cycle phase, it can be regarded as "random fluctuation trend"; if Hurst > 0.7 and the cycle is in the same phase direction (e.g., continuous upward), it can be marked as "stable trend segment".

[0137] It should be noted that the Hurst exponent is a statistic reflecting long-term memory, while the periodic phase belongs to the transient structure in the dynamic process. Combining the two can compensate for their respective limitations. Compared with the simple trend significance result, the modified trend state description can more accurately reflect the changing trend, stability and potential turning points of the natural runoff system, providing a more forward-looking basis for water resource planning and scheduling.

[0138] Furthermore, step S5 includes the following steps:

[0139] Step S51: Align the effective trend signal, the periodic oscillation spectrum, and the trend state description on the time axis, and calculate the consistency score of the three in pointing to the trend direction in each time period.

[0140] Step S52: Identify the time delay effect between valid trend signals, periodic oscillation patterns, and trend state descriptions, and establish a trend transmission delay compensation mechanism;

[0141] Step S53: Dynamically adjust the fusion weights of effective trend signals, periodic oscillation patterns and trend state descriptions based on the consistency score, and combine the trend transmission delay compensation mechanism to perform time alignment processing on the input variables, and construct an adaptive weight allocation trend identification model;

[0142] Step S54: Run the trend identification model to output the hydrological change trend, which includes the trend direction and intensity of change of the target watershed.

[0143] In some embodiments, to comprehensively consider the changing trend characteristics of natural runoff, periodic oscillation information, and trend persistence status, and further improve the accuracy and timeliness of trend identification, an adaptive trend identification model integrating three types of trend input variables is constructed. This model systematically integrates "effective trend signals," "periodic oscillation spectra," and "trend state descriptions" to achieve the identification of the direction and intensity assessment of hydrological change trends in the target watershed. Alignment of the three types of input variables on the time axis is required. This involves comparing "effective trend signals" (e.g., significant increase or decrease), "periodic oscillation spectra" (dominant periodic phase trends, amplitude changes, etc.), and "trend state descriptions" (e.g., strong and continuous increase, tendency to reverse, etc.) on a time-by-time basis, unifying the time resolution (e.g., by year), and forming a corresponding mapping of the three types of information for each time period. After alignment, a consistency score is calculated by analyzing whether these three types of variables point to the same trend direction (increase or decrease) in the same time period. For example, if in a given year: the effective trend signal is "upward"; the dominant cycle of the cyclical oscillation pattern is in an upward phase; and the trend state is described as "strong and sustained upward," then the three trends are consistent, and the consistency score can be set to 1. If two of the three are consistent, the consistency score is 0.66; if the three contradict each other, the consistency score is lower than 0.5 or even 0. By analyzing the consistency score sequence over the entire time period, the stability and reliability of the trend characteristics can be further assessed. To avoid misjudging trend inconsistencies caused by response lags as conflicting information, it is necessary to identify the time delay effect between the three types of trend information. For example, cyclical oscillations may show a turning signal before the trend significance analysis, or the trend state may have a delayed response after the cyclical change ends. Therefore, by calculating the time lag corresponding to the maximum correlation coefficient between variables (e.g., reaching maximum correlation after a 1-year lag), a "trend transmission delay compensation mechanism" can be established. This involves artificially introducing an appropriate time offset during trend fusion to adjust the variables forward or backward, making their trend signals logically more aligned. This mechanism ensures that trend judgment considers both the essential logical order between variables and avoids misunderstandings caused by short-term lags. Based on the results of the first two steps, an adaptive weighting trend identification model is constructed. The core of the model is to dynamically adjust the weights of the three types of trend variables according to their consistency scores in each time period. For example, in years with high consistency scores, the weights of the three types of variables are close to average (e.g., 0.33:0.33:0.33). When the trend direction of a certain type of variable is inconsistent for a long period or deviates from the overall trend, its weight is automatically reduced (e.g., if the direction of periodic oscillations changes repeatedly, the weight of that type is reduced to 0.2, and the combined weight of the other two types is increased). During fusion, each variable is first processed with time delay compensation, and then a weighted trend score for the current time period is uniformly output. The score can be between -1 and 1, representing the trend strength from a strong downward trend to a strong upward trend.Running the fusion model outputs hydrological change trend results for the target watershed on a time-by-time basis, including: trend direction (rising, falling, no significant change); trend strength (which can be quantitatively expressed as a weighted score value); and trend stability (calculated based on the consistency score time series to determine trend continuity or abrupt change).

[0144] It should be noted that the threshold for consistency scores can be adjusted according to different watershed characteristics. For example, in areas sensitive to hydrological changes, the consistency requirement can be higher (>0.7 is considered effective fusion); while in arid areas or areas with significant water storage impacts, a certain degree of trend inconsistency can be allowed. The trend delay compensation time difference is generally controlled within the range of 0 to 2 time units (year or month) to prevent over-correction leading to information mismatch. This adaptive fusion method can effectively improve the adaptability and interpretability of hydrological trend identification to complex change processes.

[0145] This invention also provides a comprehensive analysis system for hydrological element change trends, used to execute the above-described comprehensive analysis method for hydrological element change trends, the comprehensive analysis system for hydrological element change trends comprising:

[0146] The data preprocessing module is used to acquire time series data of hydrological elements in the target watershed and eliminate the influence of upstream reservoir regulation in the time series data of hydrological elements to obtain the natural runoff sequence.

[0147] The trend detection module is used to perform linear trend analysis on natural runoff sequences at different time scales to obtain regression slope parameters. When a non-zero trend signal is detected in the regression slope parameter, a non-parametric significance test is triggered to generate a valid trend signal.

[0148] The periodic analysis module is used to decompose the time-frequency wavelet of the natural runoff sequence into multi-level periodic features; identify the main oscillation period of the multi-level periodic features, and mark the dominant period and the average variation period to construct the periodic oscillation spectrum of hydrological elements;

[0149] The persistence assessment module uses the Hurst index, calculated through the main oscillation cycle, as the persistence analysis result; it combines the phase state of the average change cycle and the dominant cycle to correct the persistence analysis result, thus obtaining a cycle-corrected trend state description.

[0150] The comprehensive identification module is used to construct a trend identification model using effective trend signals, periodic oscillation patterns, and trend state descriptions as input variables; and to output the hydrological change trend of the target watershed using the trend identification model.

[0151] Therefore, the embodiments should be considered as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the application are intended to be included within the invention.

[0152] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. A comprehensive analysis method for the changing trends of hydrological elements, characterized in that, Includes the following steps: Step S1: Obtain time series data of hydrological elements in the target watershed and eliminate the influence of upstream reservoir regulation on the time series data of hydrological elements to obtain the natural runoff sequence; Step S2: Perform linear trend analysis on the natural runoff sequence at different time scales to obtain the regression slope parameter; when a non-zero trend signal is detected in the regression slope parameter, trigger a non-parametric significance test to generate an effective trend signal; Step S3: Decompose the time-frequency wavelet of the natural runoff sequence into multi-level periodic features; Identify the main oscillation period of multi-level periodic characteristics, label it as the dominant period, and calculate the average variation period to construct a periodic oscillation spectrum of hydrological elements. Step S4: The Hurst index calculated using the main oscillation cycle is used as the persistence analysis result; the persistence analysis result is corrected by combining the phase state of the average change cycle and the dominant cycle to obtain the trend state description after cycle correction. Step S4 is as follows: Step S41: Determine the size of the dynamic calculation window based on the length of the main oscillation period, and use it as the dynamic calculation window; Step S42: The natural runoff sequence is segmented according to the dynamic calculation window. The Hurst index is calculated for the runoff in each dynamic calculation window. The persistence analysis results of each window are obtained by rescaled range analysis. Step S43: Extract the phase information of the average change period and the dominant period in each time period, determine whether the period is in an upward phase or a downward phase, and obtain the period phase state; Step S44: Match the persistence analysis results of each window with the periodic phase state of the corresponding time period, and correct the persistence characteristic parameters according to the periodic phase state to generate a periodically corrected trend state description. Step S5: Construct a trend identification model using effective trend signals, periodic oscillation patterns, and trend state descriptions as input variables; The trend identification model is used to output the hydrological change trend of the target watershed.

2. The comprehensive analysis method for hydrological element change trends according to claim 1, characterized in that, Step S2 includes the following steps: Step S21: Segment the natural runoff sequence according to interannual, flood season, and monthly scales to generate three independent subsequences for analysis; Step S22: Perform linear fitting on each independent subsequence and solve the regression slope parameter in the regression equation using the least squares method. When the sign of the regression slope parameter is positive, the hydrological element is judged to be on an upward trend; when the sign of the regression slope parameter is negative, the hydrological element is judged to be on a downward trend. Step S23: When a zero-trend signal is detected for the regression slope parameter, a non-significant fluctuation signal is generated, where the zero-trend signal is specifically −0.1 < regression slope parameter < 0.1; Step S24: When a non-zero trend signal is detected in the regression slope parameter, a non-parametric significance test is triggered to generate a valid trend signal.

3. The comprehensive analysis method for hydrological element change trends according to claim 2, characterized in that, The nonparametric significance test described in step S24 specifically includes: The trend statistics of natural runoff sequences at interannual, flood season, and monthly time scales are calculated using the following formula: In the formula, A trend statistic used to measure the quantitative difference between upward and downward trends in a natural runoff series. This represents the total number of runoff values ​​in the natural runoff sequence. The first in the natural runoff sequence Individual runoff values, The first in the natural runoff sequence Individual runoff values, To judge and The sign function of the size relationship; The variance of the trend statistic is calculated using the modified variance formula, which is as follows: In the formula, The variance of the trend statistic. The first in a repeating group of runoff values ​​with equal values The number of times each duplicate value appears. This represents the total number of runoff values ​​in the natural runoff sequence. Calculate standardized statistics based on variance and trend statistics; The significance of trend direction is determined by trend statistics and standardized statistics, thus obtaining effective trend signals.

4. The comprehensive analysis method for hydrological element change trends according to claim 3, characterized in that, The calculation of standardized statistics based on variance and trend statistics includes: When the trend statistic is positive, the standardized statistic = (trend statistic - 1) / square root of the variance of the statistic; When the trend statistic is 0, the standardized statistic = 0; When the trend statistic is negative, the standardized statistic = (trend statistic + 1) / square root of the variance of the statistic.

5. The comprehensive analysis method for hydrological element change trends according to claim 4, characterized in that, The method of determining the significance of trend direction using trend statistics and standardized statistics to obtain effective trend signals specifically involves: When the trend statistic is greater than zero and the absolute value of the standardized statistic is greater than the preset critical value, the natural runoff sequence is judged to have increased significantly over time, and is recorded as a significant upward trend signal. When the trend statistic is less than zero and the absolute value of the standardized statistic is greater than the preset critical value, the natural runoff sequence is judged to have decreased significantly over time, and is recorded as a significant downward trend signal. When the absolute value of the standardized statistic is less than or equal to the preset critical value, it is determined that the natural runoff sequence has no significant trend over time, and is recorded as a random fluctuation signal, which is an invalid trend signal. Significant upward trend signals and significant downward trend signals are combined into effective trend signals.

6. The comprehensive analysis method for hydrological element change trends according to claim 5, characterized in that, Step S3 includes the following steps: The zero mean and unit variance of the natural runoff series are calculated to eliminate the original trend term and scale effect of the natural runoff series, thus obtaining the standardized natural runoff series. Morlet wavelet is selected as the mother function for wavelet analysis. A continuous wavelet transform is performed on the standardized natural runoff sequence to obtain wavelet coefficient matrices containing different scales and time positions; where the wavelet transform is expressed as: In the formula, These are continuous wavelet transform coefficients. The scaling factor controls the wavelet period length, and b is the wavelet translation parameter on the signal time axis. For the real number field, For time variables, The input is the function value of the natural runoff sequence. This is the conjugate form of the Morlet wavelet function; Calculate the wavelet variance in the wavelet coefficient matrix and plot the wavelet variance plot; The main periodic components are identified by wavelet variance plots, sorted by wavelet variance size, and the period with the largest variance is taken as the main oscillation period. The three periods with the largest variance are combined to form a multi-level periodic feature. The dominant period and average variation period in the multi-level periodic characteristics are identified, and a periodic oscillation pattern of hydrological elements is constructed.

7. The comprehensive analysis method for hydrological element change trends according to claim 6, characterized in that, The process of determining the dominant period and average variation period in the multi-level periodic characteristics and constructing the periodic oscillation spectrum of hydrological elements is as follows: The period with the largest wavelet variance in the multi-level periodic features is determined as the dominant period; On the dominant period scale, identify the peak and trough positions of the real part curve of the wavelet, calculate the time span of adjacent phase points in the same direction, and take the arithmetic mean of all spans as the average variation period. The sign characteristics of the real part values ​​in the wavelet coefficient matrix are extracted. When the real part value is continuously positive, it is marked as the high water season; when the real part value is continuously negative, it is marked as the low water season. The zero-crossing point of the real part value is marked as the phase transition critical point, thus obtaining the wavelet real part sign label. A time-period phase distribution diagram is plotted based on wavelet real part notation, with the vertical axis representing the scale range of the dominant period and the average variation period, and the horizontal axis representing the time series; Based on the time-period phase distribution map, combined with the oscillation intensity variation of the dominant period and the distribution density of the phase transition critical point, a periodic oscillation spectrum including period length, oscillation amplitude, phase state and transition frequency is constructed.

8. The comprehensive analysis method for hydrological element change trends according to claim 7, characterized in that, Step S5 includes the following steps: Step S51: Align the effective trend signal, the periodic oscillation spectrum, and the trend state description on the time axis, and calculate the consistency score of the three in pointing to the trend direction in each time period. Step S52: Identify the time delay effect between valid trend signals, periodic oscillation patterns, and trend state descriptions, and establish a trend transmission delay compensation mechanism; Step S53: Dynamically adjust the fusion weights of effective trend signals, periodic oscillation patterns and trend state descriptions based on the consistency score, and combine the trend transmission delay compensation mechanism to perform time alignment processing on the input variables, and construct an adaptive weight allocation trend identification model; Step S54: Run the trend identification model to output the hydrological change trend, which includes the trend direction and intensity of change of the target watershed.

9. A comprehensive analysis system for the changing trends of hydrological elements, characterized in that, For performing the comprehensive analysis method of hydrological element change trends as described in claim 1, the comprehensive analysis system of hydrological element change trends includes: The data preprocessing module is used to acquire time series data of hydrological elements in the target watershed and eliminate the influence of upstream reservoir regulation on the time series data of hydrological elements to obtain the natural runoff sequence. The trend detection module is used to perform linear trend analysis on natural runoff sequences at different time scales to obtain regression slope parameters. When a non-zero trend signal is detected in the regression slope parameter, a non-parametric significance test is triggered to generate a valid trend signal. The periodic analysis module is used to decompose the time-frequency wavelet of the natural runoff sequence into multi-level periodic features; identify the main oscillation period of the multi-level periodic features, label it as the dominant period, and calculate the average variation period to construct the periodic oscillation spectrum of hydrological elements. The persistence assessment module uses the Hurst index, calculated through the main oscillation cycle, as the persistence analysis result; it combines the phase state of the average change cycle and the dominant cycle to correct the persistence analysis result, thus obtaining a cycle-corrected trend state description. The comprehensive identification module is used to construct a trend identification model using effective trend signals, periodic oscillation patterns, and trend state descriptions as input variables; and to output the hydrological change trend of the target watershed using the trend identification model.

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