Evolution characteristics and attribution identification method of lake current in through-lake lake

Abstract

The application discloses a method for identifying lake flow evolution characteristics and attribution, comprising the following steps: obtaining a lake flow observation flow rate, a river-lake water level difference and an external driving factor sequence; constructing a river-lake hydraulic response model with a flow direction symbol function, separating an immediate response flow rate component generated by the water level difference instantaneous driving from the lake flow observation flow rate by using the model, and obtaining a lake flow residual sequence representing the change of the lake system itself; and constructing a multi-factor attribution model for the lake flow residual sequence based on the external driving factor, and quantitatively determining the contribution rate of each factor to the lake flow evolution. The application realizes the dynamic separation of the river-lake backwater effect and the evolution trajectory of the response coefficient by constructing a time-varying state space model, solves the problem that the traditional method confuses passive response and active evolution and cannot identify the drift of the river channel physical characteristics, and realizes the quantitative attribution of the lake flow evolution under complex hydraulic conditions.

Description

Technical Field

[0001] This invention relates to the field of hydrological and hydrodynamic analysis and environmental evolution identification technology, and in particular to a method for identifying the evolution characteristics and causes of lake currents in connected lakes. Background Technology

[0002] As a special hydrological system connecting large rivers and lakes, the evolution of lake currents is driven by both the backwater effect of river water levels and changes in the lake's own morphology. Accurately identifying the physical mechanisms of lake current evolution is significant for revealing the spatiotemporal variation patterns of the hydraulic connections between rivers and lakes, and for assessing the impact of water conservancy projects and river channel evolution on regional hydrological rhythms.

[0003] Currently, research on the evolution of hydrological characteristics of lakes connected to the Yangtze River mainly employs the Mann-Kendall trend test or Spearman correlation analysis to statistically test long-term observed flow velocities and identify trends in velocity increases and decreases. In terms of attribution analysis, existing techniques mostly rely on steady-parameter hydrodynamic models (such as MIKE 21) to simulate flow field changes under different operating conditions, or use multiple linear regression analysis to analyze the correlation between factors such as inflow, water level, and flow velocity, thereby inferring the contribution of each influencing factor to lake flow changes.

[0004] When dealing with strongly unsteady river-lake relationships, the main problems include confusing external forcing with internal evolution, ignoring the time-varying characteristics of hydraulic parameters, and lacking a unified attribution framework for bidirectional flow. Specifically, fluctuations in the water level of a river can have a strong immediate backwater or backflow effect on connected lakes. Traditional methods for analyzing the original velocity sequences struggle to distinguish whether the velocity changes are a passive response caused by the rise and fall of the river's water level or an active evolution caused by changes in the lake's own characteristics, such as riverbed erosion or lake shrinkage, leading to distorted attribution sources. Furthermore, existing attribution models are mostly based on static assumptions of constant parameters, failing to track the dynamic drift of hydraulic response relationships (such as flow capacity) caused by riverbed sand mining or engineering construction over time. Conventional log-linear models also struggle to handle negative velocities under backflow conditions, making it impossible to achieve quantitative attribution throughout the entire hydrological cycle.

[0005] Lakes connected to rivers differ fundamentally from ordinary enclosed lakes. Ordinary lakes have relatively fixed hydraulic boundaries, stable flow directions, and are primarily driven by wind and inflow. Water level fluctuations are typically 2-3 meters, and the lake area remains relatively constant. However, lakes connected to rivers maintain free hydraulic connections with large rivers, resulting in dynamic, open hydraulic boundaries. The water level of a particular river becomes a key controlling factor. For example, the water level fluctuation of a certain lake can reach 10-14 meters, with the lake surface area differing by more than tenfold between wet and dry seasons. Furthermore, the flow direction can be reversed due to changes in the river's water level. When the river's water level is higher than the lake's overall water level, it exerts a backwater effect, weakening the outflow of water. If the water level difference increases further, the river water may even flow back into the lake, causing the lake flow to reverse. This highly dynamic boundary condition and the reversibility of the flow direction are characteristics that distinguish lakes connected to rivers from ordinary lakes, and existing attribution methods have limitations under these conditions.

[0006] Existing trend testing methods suffer from spurious trend problems when analyzing original lake flow sequences. Specifically, the water level of a river itself exhibits long-term fluctuations and trend changes. Taking the operation of the Three Gorges Reservoir as an example, the release of clear water causes scouring of the riverbed in the middle and lower reaches and a systematic drop in water level. Because the flow of connected lakes is highly sensitive to the water level of a particular river, when the river's water level drops, the water level difference between the river and the lake increases, and the outflow of lake water accelerates, manifesting as an increase in lake flow velocity. Traditional trend testing methods mistakenly identify the passive acceleration of lake flow caused by the drop in the river's water level as an evolutionary trend of the lake system itself, that is, they confuse the passive response caused by changes in external hydraulic boundaries with the active evolution caused by changes in the lake's internal characteristics. This confusion leads to a directional bias in attribution identification from the very beginning. Summary of the Invention

[0007] The purpose of this invention is to provide a method for identifying the evolution characteristics and causes of lake currents in connected rivers, in order to solve the aforementioned problems in the prior art.

[0008] Technical solution: A method for identifying the evolution characteristics and causes of lake currents in connected rivers, including:

[0009] Obtain the observed flow velocity sequence of lakes connected to the Yangtze River, the sequence of the water level difference between the lake area and the river mouth, and the sequence of external driving factors;

[0010] A lake-river hydraulic response model is constructed based on the lake current observation velocity sequence and the river-lake water level difference sequence. The instantaneous response velocity component driven by the instantaneous river-lake water level difference is calculated using the lake current hydraulic response model. The instantaneous response velocity component is subtracted from the lake current observation velocity sequence to obtain the lake current residual sequence that characterizes the changes in the lake system's own characteristics.

[0011] A multi-factor attribution model for lake current residual sequences was constructed based on the sequence of external driving factors, and the contribution rate of each external driving factor to the evolution of lake currents was determined using the multi-factor attribution model.

[0012] Optionally, a river-lake hydraulic response model is constructed, including:

[0013] The power-law response function is obtained by characterizing the nonlinear response relationship between flow velocity and the river-lake water level difference sequence using a power function.

[0014] By introducing the flow direction sign function sgn(·), the flow level difference sequence of the lake and river is mapped to the direction, and the directional water level difference driving quantity is obtained, so that the lake and river hydraulic response model can handle the bidirectional flow state of lake water outflow and Yangtze River backflow.

[0015] Optionally, a river-lake hydraulic response model is constructed and the instantaneous response velocity component is separated, including:

[0016] A time-varying state-space model is constructed, in which the state equation is used to describe the evolution trajectory of the response coefficient and the nonlinear exponent over time, and the observation equation is used to describe the nonlinear mapping relationship between the lake current observation velocity sequence and the river-lake water level difference sequence.

[0017] The extended Kalman filter algorithm is used to recursively estimate the state variables, and the response coefficient sequence and nonlinear exponential sequence that evolve over time are obtained.

[0018] Based on the response coefficients and nonlinear exponents at each time point, the corresponding instantaneous response velocity components are calculated.

[0019] Optionally, recursive estimation is performed using the extended Kalman filter algorithm, including:

[0020] Calculate the Jacobian matrix of the observation equation with respect to the state variables. The Jacobian matrix includes the partial derivatives of the observation equation with respect to the response coefficients and the partial derivatives of the observation equation with respect to the nonlinear exponent.

[0021] The Kalman gain is calculated using the Jacobian matrix, and the prior estimates of the state variables are corrected based on the Kalman gain to obtain the posterior estimates of the response coefficients and nonlinear exponents at the current time.

[0022] Optionally, the method further includes an adaptive adjustment step for the process noise covariance:

[0023] Calculate the information sequence between the observed lake current velocity sequence and the predicted velocity estimated based on the current state;

[0024] The adaptive adjustment factor is calculated based on the ratio of the actual variance to the theoretical variance of the innovation sequence. The adaptive adjustment factor is then used to dynamically correct the process noise covariance. When the adaptive adjustment factor is greater than a preset threshold, the model’s tracking sensitivity to parameter evolution is improved.

[0025] Optionally, it includes: calculating the cumulative distribution function of the lake area water level, and dividing the water level into multiple water level intervals based on the principle of equal frequency;

[0026] Establish local response relationships within each water level interval and estimate the piecewise response coefficients corresponding to each water level interval;

[0027] Construct a continuous function connecting the response coefficients of each segment, and dynamically determine the response coefficient at the current moment based on the real-time water level.

[0028] Optionally, constructing a river-lake hydraulic response model also includes corrections for hysteresis effects:

[0029] Define a candidate set of lag times, and for each lag time in the candidate set, construct a sequence of river and lake water level differences that introduces time lag;

[0030] Calculate the coefficient of determination between the observed lake current velocity sequence and the lake-river water level difference sequence with various introduced time delays;

[0031] The lag time corresponding to the largest determination coefficient is selected as the optimal lag time, and the optimal lag time is used to perform time-series correction on the input of the river and lake hydraulic response model.

[0032] Optionally, a multi-factor attribution model for lake current residual sequences is constructed, including:

[0033] Based on the lake current residual sequence and the external driving factor sequence, an elasticity coefficient is introduced to characterize the sensitivity of the lake current to each external driving factor.

[0034] A log-linear response model is established to describe the relationship between the lake current residual sequence and the external driving factor sequence, and the regression coefficients of the log-linear response model are used as the elasticity coefficients of the corresponding external driving factors.

[0035] Optionally, before establishing the log-linear response model, the method further includes:

[0036] The lake current residual sequence is subjected to nonnegative mapping and translation processing, including calculating the minimum value of the lake current residual sequence and adding a translation constant to all residual values ​​to ensure that the variables input to the logarithmic function are within the domain;

[0037] A generalized linear model is used to replace the log-linear response model to construct a multi-factor response model, and a connection function is used to establish the linear combination relationship between the mathematical expectation of the lake current residual sequence and the external driving factor sequence.

[0038] Optionally, the external driving factor sequence shall include at least the time series of the following physical quantities:

[0039] The total inflow into the lake, representing the intensity of watershed runoff;

[0040] The surface area of ​​a lake, which characterizes its morphological features;

[0041] Lake wind speed characterizing meteorological and dynamic conditions; and effective roughness characterizing the resistance characteristics of the lake bottom and vegetation.

[0042] Beneficial effects: By constructing a time-varying state-space model, this invention achieves dynamic separation of the river and lake backwater effect from the evolution trajectory of the response coefficient, solving the problems of traditional methods confusing passive response with active evolution and failing to identify the drift of river physical characteristics, and realizing quantitative attribution of lake flow evolution under complex hydraulic conditions. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the overall process of identifying the evolution characteristics and attribution of lakes and streams in the Tongjiang River in this application.

[0044] Figure 2 This is a flowchart illustrating the steps of constructing a river-lake hydraulic response model and separating the instantaneous response velocity component in an embodiment of this application.

[0045] Figure 3 This is a flowchart illustrating the steps involved in constructing a river and lake hydraulic response model in an embodiment of this application.

[0046] Figure 4 This is a flowchart illustrating the steps involved in constructing a multi-factor attribution model for lake current residual sequences in this application embodiment. Detailed Implementation

[0047] Example 1, such as Figure 1 As shown in the figure, this embodiment elaborates on the overall process of the lake flow evolution characteristics and attribution identification method of lakes connected to rivers, specifically including the following steps:

[0048] Step 101: Obtain the lake flow velocity sequence of the connected lakes, the river-lake water level difference sequence consisting of the lake water level and the river mouth water level, and the external driving factor sequence.

[0049] In this embodiment, data acquisition is the foundation of the analysis process. Specifically, lakes connected to rivers refer to lakes that maintain free hydraulic connection with large rivers. The lake current observation velocity sequence refers to the velocity time series obtained through long-term monitoring using acoustic Doppler current profilers (ADCPs) or fixed-point current meters deployed at key cross-sections in the lake area.

[0050] Accordingly, this embodiment employs the following processing strategies for outliers that may exist in the observation data: outliers are identified using the 3σ criterion or the interquartile range method; obvious outliers caused by instrument malfunctions are removed and filled using interpolation; reasonable extreme values ​​caused by extreme weather are retained. It is recommended to perform outlier detection on all data before entering the model calculation to ensure the reliability of the input data.

[0051] To ensure data representativeness, monitoring points are typically selected in the main lake area or the waterway flowing into the river where the lake's currents are most active. In practice, the raw velocity data sometimes contains missing values ​​or is noisy, usually requiring data preprocessing. For example, for short-term missing data due to instrument malfunction, linear interpolation can be used to fill in the gaps; for non-equidistant sampling of monitoring data, resampling techniques can be used to unify the data into a daily average sequence, eliminating the influence of high-frequency turbulent fluctuations and focusing on the evolution characteristics at the hydrological scale.

[0052] As an optional implementation, the river-lake water level difference sequence is calculated from simultaneously observed representative water levels in the lake area and at the river estuary. The representative water level in the lake area is typically taken from the water level at the representative station at the geometric center of the lake, while the water level at the river estuary is taken from the water level at the control station at the lake's inlet. The temporal resolution of both should be consistent with the flow velocity sequence. For example, in a specific lake case, the water level at Xingzi station can be selected to represent the lake area water level, and the water level at Hukou station can be selected to represent the river estuary water level.

[0053] Furthermore, the external driving factor sequence refers to the set of other physical quantities, besides the backwater effect of the Yangtze River water level, that may influence the long-term evolution of lake flows. These factors typically include, but are not limited to, inflow, lake surface area, wind speed in the lake area, and effective roughness. Inflow characterizes the intensity of water inflow into the basin, lake surface area characterizes changes in lake morphology, wind speed characterizes meteorological and dynamic conditions, and effective roughness comprehensively reflects the impact of lakebed topographic evolution and aquatic vegetation distribution on flow resistance. This data can be obtained through measured data from hydrological stations, remote sensing image inversion, or meteorological reanalysis data.

[0054] Step 102: Construct a river-lake hydraulic response model based on the lake current observation velocity sequence and the river-lake water level difference sequence. Use the river-lake hydraulic response model to separate the instantaneous response velocity component generated by the instantaneous driving of the river-lake water level difference from the lake current observation velocity sequence, and obtain the lake current residual sequence that characterizes the changes in the lake system's own characteristics.

[0055] In this embodiment, the dynamic separation refers to using a physical model to separate the external forcing, i.e., the backwater effect of the Yangtze River, from the internal response, i.e., the evolution of the lake. The river-lake hydraulic response model is a mathematical model that describes the instantaneous mechanical response relationship between flow velocity and water level difference. Its physical basis lies in the fact that the inflow and outflow of lakes connected to the Yangtze River are largely controlled by the water level difference between the river and the lake. When the Yangtze River water level is higher than the lake water level, backwater or even backflow occurs; conversely, a strong outflow occurs.

[0056] In practice, this model is typically constructed as a function of flow velocity with respect to the water level difference. Using this model, the theoretical flow velocity determined solely by the current water level difference can be calculated, i.e., the instantaneous response velocity component. This component reflects the change in flow velocity caused solely by fluctuations in the Yangtze River water level, assuming the lake system itself (e.g., riverbed topography, vegetation conditions) remains unchanged. Subtracting this theoretical component from the observed flow velocity yields the lake current residual sequence, calculated using the formula: V res (t)=V obs (t)-V inst (t);

[0057] Among them, V obs (t) represents the observed lake current velocity at time t, V inst (t) represents the corresponding instantaneous response velocity component. This residual sequence eliminates the interference of Yangtze River water level fluctuations, and its remaining fluctuation trends are mainly attributed to the evolution of the lake itself (such as river channel erosion and incision, and area shrinkage caused by reclamation).

[0058] It should be noted that, as a preferred implementation method, to verify whether the residual sequence exhibits an evolutionary trend, a Mann-Kendall nonparametric trend test can be performed on the extracted lake current residual sequence. If the absolute value of the test statistic Z is greater than 1.96, i.e., a confidence level of 95%, it indicates that the residual sequence exhibits an upward or downward trend, providing statistical basis for subsequent attribution analysis. Furthermore, the generated lake current residual sequence has engineering application value. For example, when constructing two-dimensional hydrodynamic models such as MIKE 21 for long-term simulations, especially during backflow periods, conventional flow boundaries are often difficult to determine. In this case, the residual sequence can be superimposed with the theoretical backflow velocity as a dynamic velocity boundary condition, improving the accuracy of hydrodynamic simulations during backflow periods.

[0059] Step 103: Construct a multi-factor attribution model for the lake current residual sequence based on the external driving factor sequence, and use the multi-factor attribution model to determine the contribution rate of each external driving factor to the lake current evolution.

[0060] Optionally, this embodiment is used to quantitatively analyze the driving mechanisms of lake current evolution. Multifactor attribution models are typically multiple regression models, with the dependent variable being the lake current residual sequence and the independent variables being external driving factors such as inflow, lake surface area, and wind speed. Through regression analysis, the quantitative relationship between each factor and the residual velocity can be determined.

[0061] Based on this, by calculating the magnitude of change of each factor during the study period and its sensitivity coefficient to flow velocity (i.e., the elasticity coefficient), the specific numerical value of the flow velocity change caused by each factor can be calculated. Normalizing the contribution of each factor yields the contribution rate. For example, the calculation results might indicate that 60% of the increase in flow velocity in a connected lake is attributed to the decrease in roughness caused by riverbed sand mining, 30% to the increase in inflow, and 10% to the shrinkage of the lake surface area. This quantitative attribution provides a basis for lake management, water conservancy project scheduling, and ecological protection decisions.

[0062] Example 2: This example details a method for constructing a physical response model based on a flow direction sign function. By introducing a flow direction sign function, a continuous mathematical expression capable of handling flow reversal is established, providing a physical basis for subsequent separation of instantaneous response components. According to one aspect of this application, a river and lake hydraulic response model is constructed, including:

[0063] Step 201: The power-law response function is obtained by characterizing the nonlinear response relationship between the flow velocity and the river / lake water level difference sequence using a power function.

[0064] Specifically, the magnitude of the power exponent reflects the geometric characteristics of the flow cross-section and the flow regime. The response coefficient α, also known as the comprehensive flow capacity coefficient, characterizes the comprehensive flow capacity of the Hukou waterway.

[0065] In this embodiment, the physical basis for constructing the river-lake hydraulic response model comes from the weir flow or orifice outflow formula in hydraulics. For lakes connected to rivers, the waterway connecting the lake and the main stream can be regarded as a generalized flow cross-section. According to the principles of fluid mechanics, the average flow velocity of the cross-section usually exhibits a nonlinear power-law relationship with the water level difference driving the flow. Specifically, when the water level difference increases, the flow velocity does not increase linearly, but follows an exponential law, which is influenced by the combined effects of the river channel cross-sectional morphology, boundary roughness, and flow regime (such as laminar or turbulent flow).

[0066] Therefore, this embodiment uses a power function as the basic mathematical structure to describe this physical process. In its specific mathematical expression, this power function relationship can be represented as the product of the flow velocity and the absolute value of the water level difference raised to a power. The magnitude of the power exponent reflects the geometric characteristics of the cross-section and the flow regime. For example, in standard orifice outflow, this exponent is typically close to 0.5; while in natural channels affected by complex riverbed resistance, this exponent is usually an empirical value obtained through calibration with measured data, typically ranging from 0.3 to 0.7. Using a power function instead of a nonlinear function allows for a more accurate characterization of the sensitive response at low water level differences and the resistance-limiting effect at high water level differences, improving the model's fitting accuracy under different water conditions.

[0067] Step 202: Introduce the flow direction symbol function sgn(·) to perform directional mapping on the river-lake water level difference sequence, and obtain the directional water level difference driving quantity, so that the river-lake hydraulic response model can handle the bidirectional flow state of lake water outflow and Yangtze River backflow.

[0068] In this embodiment, the hydrological characteristic of the lake connected to the river lies in the reversibility of its flow direction. When abundant rainfall in the basin causes the lake water level to be higher than the main stream water level, the lake water will leak out; conversely, when a major flood occurs in the main stream causing the main stream water level to be higher than the lake water level, the river water will flow back into the lake. Optionally, this embodiment introduces a flow direction sign function sgn(·) to construct a unified response model.

[0069] Specifically, the flow direction sign function sgn(·) is defined as follows: when the value within the parentheses is greater than 0, the function value is 1; when the value is less than 0, the function value is -1; and when the value is equal to 0, the function value is 0. In this embodiment, the independent variable of this function is the difference between the lake level and the river estuary level. By introducing this sign function, the river-lake hydraulic response model constructed in this embodiment can be described by the following formula:

[0070] V inst (t)=α*|H l (t)-H j (t)| β *sgn(H l (t)-H j (t));

[0071] Among them, V inst (t) represents the instantaneous response velocity component at time t, in meters per second; α is the response coefficient, characterizing the overall flow capacity of the Hukou waterway, in meters per second. (1-β) / s, dynamically changing with the value of the nonlinear exponent β, ensures dimensional consistency on both sides of the formula; in practical applications, α is obtained by substituting measured data with definite physical units for calibration, and the calibration result includes dimensional transformation information; H l (t) represents the representative water level of the lake area at time t, in meters; H j (t) represents the water level at the river mouth at time t, in meters; β is the nonlinear exponent, dimensionless; sgn(·) is the flow direction sign function; |...| represents the absolute value operation.

[0072] As can be seen from the above formula, this model has both physical meaning and mathematical continuity. For example, when the lake level H... l (t) is greater than the estuary water level H j At time (t), the water level difference is positive, sgn(·) takes a value of 1, and the calculated flow velocity V inst (t) is a positive value, representing the direction of lake water outflow; when the river mouth water level H j (t) is higher than the lake level H lAt time (t), the water level difference is negative, and sgn(·) takes the value of -1. Although the absolute value of the water level difference is still positive, the final calculated flow velocity V inst The negative value of (t) automatically indicates the direction of the backflow of river water; when the water levels of the two are equal, the flow velocity automatically returns to zero. This processing method avoids the splicing error near zero water level difference in segmented modeling and achieves a unified description of the entire hydrological cycle.

[0073] As an alternative implementation, to enhance the robustness of the model, the sign function can be smoothed out in actual calculations. For example, the hyperbolic tangent function tanh(k*ΔH) can be used to approximate sgn(ΔH), where k is a large positive coefficient. This alternative has higher-order differentiability mathematically, which is beneficial for accelerating convergence using optimization algorithms such as gradient descent, especially in the case of micro-flows with near-zero water level differences, providing smoother transition characteristics.

[0074] Furthermore, the parameters α and β in the formula can be calibrated using historical observation data. In practice, a historical period untouched by human activity (e.g., the baseline period before engineering construction) can be selected. The measured lake flow velocity is used as the dependent variable, and synchronously observed river and lake water level data are substituted into the formula as the independent variable to construct a nonlinear least squares objective function. By solving for the parameter combination that minimizes the sum of squared residuals, the specific response coefficient α and nonlinear exponent β for that lake can be determined. For example, for the outlet channel of a certain lake, the calibrated β value may stabilize at around 0.5, while the α value serves as the response coefficient reflecting the average flow capacity of the channel, providing a reference benchmark for subsequently identifying its evolution over time.

[0075] Example 3: This example details a dynamic stripping method based on a time-varying state-space model. As a preferred implementation, by constructing a state-space model and solving it using an extended Kalman filter (EKF), the time-varying response coefficient sequence can be separated. Furthermore, while stripping away the top-down effect, the specific impact of human activities on the river-lake relationship can be identified.

[0076] Step 301, as follows Figure 2 As shown, a hydrodynamic response model of the lake and river is constructed and the instantaneous response velocity component is separated. This includes: constructing a time-varying state-space model, where the state equation is used to describe the evolution trajectory of the response coefficient and the nonlinear exponent over time, and the observation equation is used to describe the nonlinear mapping relationship between the lake current observation velocity sequence and the lake-river water level difference sequence.

[0077] In this embodiment, the response coefficient α, reflecting the flow capacity of the lake mouth, and the nonlinear exponent β, reflecting the cross-sectional morphology, are considered as latent state variables that evolve slowly over time. Therefore, the state vector X at time t is defined.t =[α t ,β t ] T Based on the assumption of continuity in parameter evolution, that is, the current physical characteristics are based on the previous moment with the superposition of small random perturbations, this embodiment uses a random walk model to construct the following state equation:

[0078] X t =F*X (t-1) +W t ;

[0079] Among them, X t Let be the state vector at time t, containing the response coefficient α. t and nonlinear exponent β t F is the state transition matrix, which is set as a second-order identity matrix in this embodiment, indicating that the parameters remain unchanged under undisturbed conditions; X (t-1) W is the state vector at time t-1; t The process noise vector follows a normal distribution with a mean of 0 and a covariance of Q, representing the magnitude of the random drift of the parameter over time.

[0080] Meanwhile, to establish the connection between the hidden state and the observable data, this embodiment constructs an observation equation based on the physical response model. Since this response relationship is nonlinear, the observation equation is specifically expressed as:

[0081] Z t =h(X t ,ΔH t )+ε t =α t *|ΔH t | βt *sgn(ΔH t )+ε t ;

[0082] Among them, Z t Let be the observed lake current velocity at time t; h(·) is the nonlinear observation function; ΔH t Let ε be the difference in water level between the river and the lake at time t; t The observed noise follows a normal distribution with a mean of 0 and a variance of R, representing high-frequency random fluctuations or measurement errors that the model cannot explain. Through this set of equations, this embodiment transforms the unsteady hydraulic problem into a nonlinear system identification problem.

[0083] Optionally, constructing a time-varying state-space model stems from a diagnosis of the assumptions and flaws in the original scheme. The original scheme treated the response coefficients as global constants, fitting them once with historical data and using them as fixed parameters. However, the hydraulic characteristics of the connecting channels between lakes and the Yangtze River change over time. Taking a lake's inflow channel into the Yangtze as an example, continuous riverbed sand mining activities from 2001 to 2008 led to riverbed erosion, changes in cross-sectional morphology, and increased flow capacity. This physical change caused the response coefficients to exhibit an evolutionary trend over time. If a constant response relationship is still used for top-down effect separation, the resulting residual sequence actually contains two parts: the first part is the truly active evolution component of the lake system, and the second part is the pseudo-residual caused by the changes in the response relationship itself.

[0084] According to one aspect of this application, the problem is transformed from a single static fitting to a dynamic recursive estimation. In other words, the response coefficient reflecting the flow capacity of the lake mouth and the nonlinear exponent reflecting the cross-sectional morphology are treated as latent state variables that evolve slowly over time, rather than preset fixed parameters. Using a state-space model framework, two types of results are estimated simultaneously: first, the time-varying trajectory of the response coefficient, which corresponds to the time window of human activities such as river sand mining and water conservancy project construction; second, the pure residual after removing the time-varying response, which reflects the natural evolution characteristics of the lake system after excluding the influence of human hydraulic modifications. According to one aspect of this application, before using the extended Kalman filter algorithm for recursive estimation, initialization and constraint steps are also included:

[0085] Least squares fitting is performed using historical time period data obtained in advance from lake current observation velocity sequence and river-lake water level difference sequence to determine the initial state vector of the state variable, and the initial error covariance matrix is ​​set according to the fitting residual; the physical feasible region boundary of the response coefficient and nonlinear exponent is set, and during the recursive estimation process, when the posterior estimated value of the state variable exceeds the physical feasible region boundary, it is projected to the boundary value.

[0086] In this embodiment, the convergence speed and stability of the filtering algorithm are highly dependent on the initial value setting. To avoid initial estimation oscillations caused by using a preset fixed initial value, this embodiment uses historical estimation results as the initial value strategy. Specifically, a period of historical data before the start of the study period (e.g., the monthly average data from the previous 12 to 24 months) is selected as the initialization window. Within this window, the parameters are temporarily assumed to be constant, and a nonlinear least squares method (such as the Levenberg-Marquardt algorithm) is used to statically fit the observation equation. The optimal solution obtained is then used as the initial state vector X0=[α0,β0]. T Simultaneously, the variance of the fitted residuals is calculated as the initial value of the observation noise variance R, and the initial error covariance matrix P0 is set as a diagonal matrix, with its diagonal elements determined according to the standard error of the parameter estimation.

[0087] Furthermore, purely data-driven filtering algorithms may produce estimates that violate physical principles (e.g., negative overcurrent capacity) at certain extreme data points. Therefore, this embodiment introduces a physical constraint mechanism. The preset physical feasible region of the response coefficient α is [α...]. min ,α max ], where α min It is usually set to 0, representing no overcurrent capability, α max The maximum flood discharge capacity of the river channel is estimated; the feasible region of the preset nonlinear exponent β is [0.5, 3.0], covering the physical range from standard orifice outflow to turbulent flow. After each subsequent filtering update, if the estimated α... t or β t If the value falls outside this range, it is forced to be assigned the nearest boundary value, ensuring that the model always operates within a physically interpretable framework.

[0088] Regarding the setting of process noise covariance Q and observation noise covariance R, in this embodiment, the diagonal elements of the process noise covariance Q matrix are typically set to the square of the expected drift amplitude of the state variable during the study period. Specific values ​​can be estimated based on the historical variation amplitude of response parameters in the study area, or optimized on a validation dataset using cross-validation methods. Those skilled in the art can adapt these values ​​to suit the actual application scenario. The value of R can be determined based on the nominal accuracy of the flow velocity observation instrument. For ADCP measurements, R is typically set to 0.01~0.05.

[0089] Step 302: The extended Kalman filter algorithm is used to recursively estimate the state variables to obtain the response coefficient sequence and nonlinear exponential sequence that evolve over time.

[0090] In this embodiment, given the strong nonlinearity of the observation equation, the standard Kalman filter is no longer applicable; therefore, the Extended Kalman Filter (EKF) is used. This process is a predictive-corrective cyclic recursive process. The prediction step is performed, using the posterior estimate from the previous time step to predict the prior state value at the current time step. Since the state transition matrix F is an identity matrix, the prior estimate of the state variable X... (t|t-1) Equal to the posterior estimate X from the previous moment (t-1|t-1) Meanwhile, the prediction error covariance matrix P (t|t-1) It will increase accordingly, specifically calculated as P. (t-1|t-1) The addition of the process noise covariance Q reflects the increasing uncertainty of the system state over time. According to one aspect of this application, a recursive estimation is performed using an extended Kalman filter algorithm, specifically including:

[0091] Calculate the Jacobian matrix of the observation equation with respect to the state variables. The Jacobian matrix includes the partial derivatives of the observation equation with respect to the response coefficients and the partial derivatives of the observation equation with respect to the nonlinear exponent. Calculate the Kalman gain using the Jacobian matrix, and correct the prior estimates of the state variables based on the Kalman gain to obtain the posterior estimates of the response coefficients and the nonlinear exponent at the current time.

[0092] In this embodiment, the linearization step in the EKF algorithm is used to calculate the Kalman gain and obtain the nonlinear observation function h(X). t ,ΔH t Relative to the state vector X t The partial derivatives, i.e., the Jacobian matrix H, are used to construct the Jacobian matrix H. jac The Jacobian matrix contains two specific partial derivative terms:

[0093] ;in, The partial derivative of the observation function with respect to the response coefficient is calculated using the formula |ΔH|. t | βt *sgn(ΔH t ); The partial derivative of the observation function with respect to the nonlinear exponent is calculated using the formula α. t *|ΔH t | βt *ln(|ΔH t |)*sgn(ΔH t Using the exponential derivative rule and the chain rule, ln(|ΔH) t The appearance of |) reflects the sensitivity of small changes in nonlinear exponential velocity.

[0094] Calculate the Kalman gain K t The gain matrix determines the weight of the current observation data, i.e., the innovation, when correcting the state estimate. Specifically, K... t With prediction error covariance P (t|t-1) And Jacobian matrix H jac The product of the transposes of is proportional to the theoretical variance of the observed residuals, i.e., H. jac *P (t|t-1) *H jac T +R is proportional to the inverse matrix. Using the observed value Z t Compared with the predicted value h(X) (t|t-1) The information between the two sides is used to correct the prior estimate by combining the Kalman gain, thus obtaining the posterior estimate X. (t|t) =X (t|t-1) +K t *(Z t -h(X (t|t-1)By iteratively calculating point by point throughout the entire time series, the complete time-evolving sequence of response coefficients α can be output. t and nonlinear exponential sequence β t .

[0095] Step 303: Calculate the corresponding instantaneous response velocity component based on the response coefficient and nonlinear exponent at each time point.

[0096] In this embodiment, once the time-varying parameter sequence is obtained, it can be substituted back into the observation equation to calculate the instantaneous response velocity component V at each moment. inst (t)=α t *|ΔH t | βt *sgn(ΔH t Unlike using fixed parameters, V inst (t) It dynamically adapts to changes in river channel characteristics. For example, in years when sand mining leads to riverbed erosion, the model automatically identifies α. t The increase in the observed velocity leads to a larger instantaneous response velocity. This increase is correctly attributed to the combined effects of enhanced channel capacity and water level difference, resulting in a purer residual sequence that retains only evolutionary features other than those related to enhanced channel capacity and water level difference. According to one aspect of this application, the method further includes evolutionary feature identification based on the response coefficient sequence:

[0097] Trend testing and change point identification are performed on the response coefficient sequence obtained by extended Kalman filtering to determine the abrupt change time when the response coefficients undergo systematic shift. The abrupt change time is matched with the time window of water conservancy project construction or river sand mining events in the basin to obtain the matching results characterizing the degree of correlation between the evolution of river-lake hydraulic connection and human activities.

[0098] In this embodiment, the response coefficient sequence α output by EKF t In order to calculate the impact of human activities, α t The sequence is analyzed. For example, the detection results might show α. t The water level showed a step-like upward trend between 2000 and 2005. Historical data revealed that this period coincided with the peak of riverbed sand mining in the basin. Sand mining led to riverbed erosion and an expansion of the cross-sectional area, physically increasing the flow capacity response coefficient α. Therefore, the anomalies in the river-lake hydraulic connection can be quantitatively attributed to sand mining activities. This type of attribution analysis based on time-varying parametric trajectories is impossible with static regression methods, providing a computational basis for lake management departments to assess the impact of engineering projects.

[0099] The specific implementation method for change point detection of response coefficient sequences and attribution association with human activities is as follows:

[0100] Specifically, a trend test is performed on the time series of response coefficients. The Mann-Kendall nonparametric test method is used to calculate the standardized test statistic Z-value. If the absolute value of Z is greater than 1.96, the null hypothesis is rejected at the 95% confidence level, indicating that the series has a monotonic trend. A positive value indicates an upward trend, representing that the flow capacity of the lake mouth increases over time; a negative value indicates a downward trend, representing that the flow capacity decreases.

[0101] Accordingly, change point detection is performed to identify the moments when the response coefficients undergo a step change. The Pettit test is a nonparametric method suitable for single change point detection. Its basic principle is: divide the time series into two segments at each possible breakpoint, calculate the difference in rank between the two segments; the position with the largest difference is the most likely change point. The specific calculation process is as follows: construct a statistic U, defined as the sum of the sign functions of pairwise comparisons between all data points from the start of the sequence to the current time t and all data points from time t+1 to the end of the sequence; calculate the absolute value of U for all possible t values, and take the moment corresponding to the maximum value as the detected change point. The level of this detection result can be calculated using Monte Carlo simulation or approximate formulas.

[0102] Furthermore, the detected change points are matched with the time windows of human activities within the watershed. Specifically, historical data such as the issuance time of river sand mining permits, peak sand mining periods, and the commencement and completion times of water conservancy projects are collected to establish an event-time correlation table. If the change point falls within the time window of a major human activity event or its subsequent response period, a causal relationship between the evolution of the response coefficient and that human activity can be established. For example, if a change point is detected where the response coefficient increases in 2003, and historical data shows that 2001 to 2005 was the peak period for sand mining in the waterway flowing into the Yangtze River from a certain lake, it can be inferred that riverbed erosion caused by river sand mining is the main reason for the increase in the response coefficient. This type of attribution analysis based on time-varying parametric trajectories provides a new basis for quantitatively assessing the impact of human activities on the hydrological connection between rivers and lakes, independent of statistical correlation analysis.

[0103] The model accuracy in this embodiment can be evaluated using the following metrics: Nash efficiency coefficient (NSE), which reflects the model's ability to explain the variability of observed data (NSE > 0.7 indicates a good model fit); root mean square error (RMSE), which reflects the average deviation between predicted and observed values, expressed in flow velocity units (m / s); and mean absolute percentage error (MAPE), which reflects the relative accuracy of the prediction. In a practical application at a certain lake, the NSE of this embodiment reached above 0.85, and the RMSE was controlled within 0.1 m / s.

[0104] Example 4: This example details a process noise adjustment method based on adaptive innovation. By real-time monitoring of the observation residuals, i.e., the statistical characteristics of the innovation, the model's sensitivity to system evolution is dynamically adjusted to ensure the algorithm maintains high accuracy during stable periods and fast response during periods of rapid change. According to one aspect of this application, the method further includes an adaptive adjustment step for the process noise covariance:

[0105] Step 401: Calculate the information sequence between the observed lake current velocity sequence and the predicted velocity estimated based on the current state.

[0106] In this embodiment, the innovation sequence is a concept in Kalman filtering, representing new information contained in the observation data that cannot be explained by the current state prediction. Specifically, at each time step t, the current state is predicted using the posterior state estimate from the previous time step, and then the predicted flow velocity at the current time is calculated using the observation equation. The difference between the actual observed lake current velocity and the predicted flow velocity is the innovation. Its calculation formula is as follows:

[0107] v t =Z t -h(X (t|t-1) ,ΔH t );

[0108] Among them, v t For the new information at time t, Z t Let X be the observed lake current velocity at time t. (t|t-1) Let ΔH be the prior estimate of the state variable at time t. t Let t be the difference in water level between the river and the lake at time t, and h(·) be the nonlinear observation function.

[0109] Optionally, when the model parameters are accurately set and the system operates smoothly, the innovation sequence should approximate as Gaussian white noise with a mean of zero. However, when structural changes occur within the lake system (such as a sudden deepening of the channel cross-section), the model's original parameter predictions will no longer be accurate, leading to a systematic deviation between the predicted and observed flow velocities. This causes the mean of the innovation sequence to deviate from zero or the variance to increase. Such abnormal changes in statistical characteristics are the signal source that triggers adaptive parameter adjustment.

[0110] Step 402: Calculate the adaptive adjustment factor based on the ratio of the actual variance to the theoretical variance of the innovation sequence, and use the adaptive adjustment factor to dynamically correct the process noise covariance. When the adaptive adjustment factor is greater than the preset threshold, improve the model's tracking sensitivity to parameter evolution.

[0111] In this embodiment, to calculate the degree of bias in the system model, it is necessary to calculate the theoretical covariance of the innovation sequence. Based on the Kalman filter principle, the theoretical covariance is jointly determined by the prediction error covariance and the observation noise covariance, and its calculation formula is as follows:

[0112] S t =H jac *P (t|t-1) *H jac T +R;

[0113] Among them, S t Let H be the theoretical covariance of the innovation sequence at time t. jac Let P be the Jacobian matrix at time t. (t|t-1) Let R be the prediction error covariance matrix, and R be the observation noise covariance.

[0114] Furthermore, it is necessary to estimate the actual covariance of the innovation sequence. Since the innovation value at a single point is random, a sliding window method is typically used to calculate the statistical characteristics of the innovation over a recent period. For example, a sliding window of length N (e.g., N occupies 5 to 10 time periods) can be set, and the mean of the squared innovation values ​​within the window can be calculated as an estimate of the actual covariance.

[0115] C v (t)=(1 / N)*Σ(v i *v i T );

[0116] Among them, C v (t) represents the estimated actual covariance of the innovation at time t, Σ represents the summation of terms i from t-N+1 to t within the window, and v i This represents the information at the i-th moment within the window.

[0117] Based on this, an adaptive adjustment factor λ is constructed. t This factor reflects the degree of deviation of the actual error from the theoretical expectation. It is typically calculated as a ratio of the matrix trace or a simple numerical ratio.

[0118] λ t =trace(C v (t)) / trace(S t );

[0119] Where, λ t For adaptive adjustment, trace(·) represents the trace of the matrix, which is the sum of the diagonal elements.

[0120] This factor is used to dynamically correct the process noise covariance matrix Q. The specific correction logic is: when λ... tWhen λ is greater than 1, it indicates that the actual observed error exceeds the model's theoretical expectation, suggesting that the system state may have changed rapidly, and the model's current prediction confidence is too high, meaning Q is set too small. In this case, the Q value should be increased to increase the Kalman gain, making the filter more confident in the current observation data and accelerating the tracking speed of parameter changes. t A value less than or equal to 1 indicates that the model is functioning correctly. The original Q value should be maintained or fine-tuned to preserve the smoothness of the estimate. The correction formula can be expressed as:

[0121] Q t =λ t *Q0;

[0122] Among them, Q t Let t be the process noise covariance matrix after correction at time t, and Q0 be the preset initial process noise covariance matrix.

[0123] As an optional implementation, to prevent a single outlier from causing drastic fluctuations in the Q value, the calculated λ can be adjusted. t Introduce a forgetting factor or set a threshold limit. For example, only when λ t Adjustment is triggered only when the threshold (e.g., 1.5) is exceeded for M consecutive time points, or the adjustment is applied to λ. t Setting upper and lower limits (e.g., [1.0, 10.0]) ensures that the adjustment process balances sensitivity and stability. This type of adaptive mechanism enables the attribution method to automatically distinguish between periods of steady evolution and periods of drastic change. At critical junctures such as peak river sand mining periods or the closure of large-scale water conservancy projects, it can be used to output the parameter evolution trajectory, avoiding attribution distortion caused by parameter rigidity.

[0124] Optionally, the triggering condition design of the adaptive adjustment mechanism takes into account both sensitivity and robustness requirements. On the one hand, responding immediately to anomalies at a single moment may cause drastic fluctuations in the process noise covariance, amplifying the interference of observation noise. On the other hand, requiring continuous anomalies at too many moments to trigger adjustment would miss the true opportunity for system mutation.

[0125] As a preferred implementation, the present invention sets the following triggering rule: covariance adjustment is only performed when the adaptive adjustment factor calculated within the sliding window exceeds a preset threshold for M consecutive time periods. The recommended threshold value is 1.5, representing that the actual error exceeds the theoretical expectation by 50%; the recommended number of consecutive time periods M is 3 to 5 time periods, depending on the data's temporal resolution. Furthermore, to prevent excessive adjustment factor from causing filter divergence under extreme conditions, upper and lower limits are set for the adjustment factor. The lower limit is set to 1.0 to ensure that the covariance is not artificially reduced; the upper limit is set to 10.0 to avoid excessive amplification due to abnormal data. This design enables the model to automatically distinguish between two operating states: during peak river sand mining periods or the closure period of large-scale water conservancy projects, the system automatically increases the process noise covariance to accelerate the tracking speed of parameter mutations; during the stable period of normal operation, the system maintains a small process noise covariance to maintain the smoothness and continuity of the estimation.

[0126] Example 5: This example details a dynamic parameter estimation method based on water level segmentation. In lakes connected to rivers (such as Poyang Lake), the flow capacity of the lake outlet channel, i.e., the response coefficient α, not only evolves over time but also exhibits dependence on water level. For example, during the dry season, the water flow is mainly controlled by the main channel, and its morphology is relatively fixed; while during the flood season, the flow of the floodplain is affected by the resistance of the floodplain vegetation, and the flow efficiency changes. According to one aspect of this application, a river-lake hydraulic response model is constructed, including:

[0127] Step 501: Calculate the cumulative distribution function of the lake water level and divide the water level into multiple water level intervals based on the principle of equal frequency.

[0128] In this embodiment, to ensure sufficient samples for parameter calibration at different water levels and to avoid estimation bias due to the scarcity of samples at high water levels, a frequency-based partitioning strategy is adopted. Long-series representative water level data of the lake area (e.g., the daily average water level at Xingzi station) are collected, statistically analyzed, and an empirical cumulative distribution function (CDF) is constructed. This function describes the probability that the water level is less than or equal to a specific value.

[0129] Accordingly, the number of intervals K is set, typically 3 to 5, and the critical water level value for each interval is determined based on the principle of equal frequency. Specifically, the quantiles are calculated using the inverse function of the cumulative distribution function. For example, if the water level is divided into 3 intervals, the water level values ​​corresponding to cumulative probabilities of 33.3% and 66.7% are calculated as the dividing points. This division method ensures that the number of observed samples contained in each water level interval is approximately equal, improving the statistical robustness of subsequent regression analysis. The calculation formula can be expressed as:

[0130] H k_upper =F inv (k / K);

[0131] Among them, H k_upper F represents the upper limit water level of the k-th water level interval. inv (·) is the inverse function of the cumulative distribution function of water level in the lake area, k is the current interval number (with values ​​from 1 to K), and K is the set total number of intervals.

[0132] Step 502: Establish local response relationships within each water level interval and estimate the piecewise response coefficients corresponding to each water level interval.

[0133] In this embodiment, for each predefined water level interval, all historical observation samples within that interval are selected to form a data subset for that water level level. Within each subset, assuming relatively stable physical response characteristics, a power-law response model is used for local fitting. Specifically, the observed flow velocity within each subset is used as the dependent variable, and the river-lake water level difference is used as the independent variable. The piecewise response coefficient α corresponding to that interval is estimated using the least squares method. k .

[0134] In this process, the nonlinear exponent β can be fixed as the global average, and only the response coefficient α can be allowed. k The response coefficient varies with the water level range; it can also vary simultaneously with the water level. Typically, due to the gradual change in the geometric properties of the river cross-section with increasing water level, the response coefficient at low water levels (corresponding to the main channel flow) sometimes differs from that at high water levels (corresponding to the floodplain flow). By segmenting the process, the model can capture the physical laws of rising water level leading to increased resistance and decreased efficiency per unit head, achieving a smaller fitting residual than a global model across the entire hydrological range.

[0135] Step 503: Construct a continuous function connecting the response coefficients of each segment, and dynamically determine the response coefficient at the current moment based on the real-time water level.

[0136] In this embodiment, to avoid a step jump in model parameters when the water level crosses the interval boundary, it is necessary to transform the discrete piecewise coefficients into a continuous function of the water level. An intuitive implementation is to use piecewise linear interpolation. Specifically, the median water level of each interval is defined as a node, and the estimated α for that interval is used as the node. k The value is assigned to this node. For any measured water level H(t), the dynamic response coefficient α(H) at the current moment is calculated using a linear interpolation formula by finding its two adjacent nodes.

[0137] As a preferred alternative, for lakes with specific cross-sectional morphologies, an exponential decay function can be used to construct this continuous relationship, providing a smoother physical description. This method assumes that the flow capacity changes exponentially with rising water level, and is suitable for describing scenarios where the beach vegetation is dense and the resistance increases sharply with water level. The calculation formula is as follows:

[0138] α(H)=α base *exp(-λ*(HH ref ));

[0139] Where α(H) is the dynamic response coefficient corresponding to water level H, α base Reference water level H ref The reference response coefficient at , exp(·) is the natural exponential function, λ is the decay coefficient, and the unit is m. −1 The rate at which the response coefficient decreases with increasing water level is characterized by the relative decrease in the response coefficient for every 1m increase in water level. It can be determined by performing exponential regression fitting on the piecewise response coefficient data.

[0140] Through the above steps, this embodiment establishes an instantaneous response model in which parameters dynamically adjust with water level. In the attribution analysis process, this model can replace the state-space model for calculating V. inst (t).

[0141] Example 6: This example details a method for constructing a response model considering hysteresis. In actual physical processes, it takes time for the signal of water level change in the Yangtze River main stream (such as flood waves) to travel to the lake area and generate a flow velocity response. This hysteresis effect is particularly significant during the dry season or when the lake flow is slow. If this time difference is ignored and synchronous water level difference is used for modeling, it will lead to a phase deviation in the model, thereby reducing the accuracy of attribution analysis. This example corrects the timing matching relationship of the input signal through systematic time delay search and correction.

[0142] Step 601, as follows Figure 3 As shown, the construction of the river and lake hydraulic response model also includes the correction of the lag effect: setting a candidate set of lag times, and constructing a river and lake water level difference sequence that introduces time lag for each lag time in the candidate set.

[0143] In this embodiment, it is necessary to determine the search range for the lag time. Since the physical essence of the lag phenomenon is the propagation process of hydraulic fluctuations, its maximum possible delay time depends on the distance from the lake mouth to the study section and the average propagation velocity of the water flow. Therefore, to avoid the computational burden caused by blind searching, this embodiment sets an upper limit for the lag time based on the geometric scale characteristics of the lake. The specific calculation formula is as follows:

[0144] τ max =L char / V mean ;

[0145] Where, τ max L represents the upper limit of the candidate range for lag time, in seconds or hours; charV represents the characteristic distance from the Hukou section to the research point in the lake area (such as the Huxin station), in meters; mean This refers to the absolute value of the multi-year average flow velocity or characteristic wave velocity observed in history, expressed in meters per second.

[0146] Based on the calculated upper limit, a discrete candidate set of lag times is constructed. Let the time resolution of the input data be Δt (e.g., 1 hour or 1 day). Then the candidate set can be represented as a series of integer multiples of time steps, i.e., {0, Δt, 2×Δt, ..., K×Δt}, where K×Δt does not exceed τ. max For each specific lag time τ in the candidate set i The original river and lake water level difference sequence is time-shifted. Specifically, for any time t, a water level difference data ΔH(t-τ) with time delay is constructed. i ), that is, take t-τ i The difference between the lake estuary water level and the river estuary water level at time t is used as the driving force input at the current time t. Through this traversal operation, a set of potential driving force sequences with different phase translation characteristics is generated.

[0147] Step 602: Calculate the coefficient of determination between the lake current observation velocity sequence and the river and lake water level difference sequences with introduced time delays.

[0148] In this embodiment, time delay parameters that accurately reflect physical reality are selected through statistical indices. For each delay time τ in the candidate set... i The corresponding time-delayed water level difference sequence is used as the independent variable, and the synchronous lake current observation velocity sequence is used as the dependent variable. These are then substituted into the power-law response model structure for regression analysis. Specifically, for each τ... i The following temporary regression equation is established:

[0149] V obs (t)=α i *|ΔH(t-τ i )| β *sgn(ΔH(t-τ i ))+C i ;

[0150] Among them, V obs (t) represents the observed flow velocity at time t, α i Assuming the lag time is τ i The response coefficient at time ΔH(t-τ) i To introduce the lag time τ i water level difference, C i This is the intercept term.

[0151] Specifically, for the above regression equation, the goodness of fit is calculated using the least squares method, and the coefficient of determination (R-squared) is usually used as the evaluation index. The coefficient of determination reflects the degree to which the model explains the variability of the observed data; the closer its value is to 1, the better the lag time τ of the current hypothesis. i The variation in water level difference better explains the fluctuations in flow velocity. Through ergonomic calculations, the distribution sequence R of the determination coefficients regarding the lag time can be obtained. 2 (τ i ).

[0152] In some complex implementation scenarios, if the observation data contains noise, the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) can be used instead of the coefficient of determination to penalize the risk of overfitting while pursuing fitting accuracy.

[0153] Step 603: Select the lag time corresponding to the largest determination coefficient as the optimal lag time, and use the optimal lag time to perform time-series correction on the input of the river and lake hydraulic response model.

[0154] In this embodiment, the physical delay characteristics of the system are determined based on the principle of maximum correlation. Specifically, the maximum value is found in the distribution sequence of the determination coefficients obtained above, and the corresponding lag time is defined as the optimal lag time τ. opt This time parameter physically represents the average time required for the Yangtze River water level change signal to travel to the lake area observation points. Furthermore, this optimal parameter is used to apply a fixed time-series correction to the final river-lake hydraulic response model. That is, in subsequent state-space model construction or piecewise parameter estimation, all input terms are no longer the synchronous water level difference ΔH(t), but rather the corrected lag water level difference ΔH(t-τ). opt ).

[0155] As a preferred alternative implementation, in certain special connected lakes, the impact of water level changes on flow velocity may not be concentrated at a single lag moment, but rather exhibit a cumulative effect over a period of time, i.e., a distributed lag characteristic. For such cases, this embodiment can use a distributed lag model instead of a single optimal lag correction. Specifically, the instantaneous response flow velocity is expressed as a weighted sum of water level differences over a past period:

[0156] V inst (t)=Σ(w j *ΔH(tj*Δt))+C;

[0157] Among them, V inst (t) represents the instantaneous response velocity at time t, Σ represents the summation over lag steps j from 0 to J, and w j Let be the weighting coefficient for the j-th time lag step, and ΔH(tj*Δt) be the water level difference at the corresponding time.

[0158] To reduce the number of parameters to be estimated w j To determine the number of weights and ensure the smoothness of the weight distribution, Almon polynomial constraints can be further introduced. That is, assuming the weights w... j Distributed along a polynomial curve, satisfying:

[0159] w j =Σ(θ p *j p );

[0160] Where Σ represents the summation of the polynomial order p from 0 to P, usually P is 2 or 3, θp is the polynomial coefficient to be estimated, and j is the lag step.

[0161] Through this type of alternative approach, the model can capture the comprehensive driving effect of the entire process of flood wave arrival at the leading edge, flood peak passage, and receding tail on flow velocity, further improving the simulation accuracy under complex hydrological conditions. This correction module has universal adaptability and can be applied to any embodiment of the present invention regarding response model construction.

[0162] Example 7: This example details a multi-factor quantitative attribution method based on elasticity coefficients. Optionally, this example establishes a dimensionless sensitivity evaluation system and combines it with residual sequences to analyze the driving mechanism of lake current evolution.

[0163] Step 701, as follows Figure 4 As shown, a multi-factor attribution model for lake current residual sequences is constructed, including: based on the lake current residual sequence and the external driving factor sequence, an elasticity coefficient is introduced to characterize the sensitivity of the lake current to each external driving factor.

[0164] In this embodiment, the elasticity coefficient is a dimensionless physical quantity used to measure the sensitivity of the dependent variable to changes in the independent variable. In the context of lake current attribution, it is defined as the percentage change in the residual velocity of the lake current caused by a 1% relative change in a certain external driving factor (such as inflow rate). This concept is introduced because different driving factors have different physical dimensions and orders of magnitude (for example, flow rate is measured in cubic meters per second and can reach tens of thousands; while roughness is a dimensionless coefficient and its value is usually less than 0.1). Through the transformation of the elasticity coefficient, the response of all factors can be measured using a unified rate of change scale, making physical factors of different dimensions comparable across dimensions.

[0165] The calculation formula is as follows:

[0166] ;

[0167] Where, ε X V is the elasticity coefficient of the lake current residual with respect to factor X, where X is the multi-year average of the influencing factors.res This represents the multi-year average of the lake current residual sequence. Let X be the partial derivative of the lake current residual with respect to the factor X.

[0168] Step 702: Establish a log-linear response model describing the relationship between the lake current residual sequence and the external driving factor sequence, and use the regression coefficients of the log-linear response model as the elasticity coefficients of the corresponding external driving factors.

[0169] In this embodiment, a log-linear multiple regression model is constructed to estimate the elasticity coefficients as defined above from the observed data. The mathematical structure of this model ensures that its regression coefficients are naturally equivalent to the elasticity coefficients, avoiding tedious derivative calculations.

[0170] Specifically, the model formula is as follows:

[0171] ln(V res )=a0+a1*ln(Q in )+a2*ln(A lake )+a3*ln(W)+a4*ln(n eff )+δ;

[0172] Among them, V res For the lake current residual sequence, Q in A lake 、W、n eff Let a0 be the sequence of each external driving factor, a1 to a4 be the regression coefficients of each factor, δ be the random error term, and ln(·) represent the natural logarithm operation.

[0173] In the above formula, all physical quantities are expressed in the International System of Units (SI), and can be equivalently understood as taking the logarithm of the ratio of each physical quantity to its multi-year average reference value, that is:

[0174] ln(V res / Vˉ res )=a'0+a1*ln(Q in / Qˉ in )+a2*ln(A lake / Aˉ lake )+a3*ln(W / Wˉ)+a4*ln(n eff / nˉ eff )+δ;

[0175] According to the principles of calculus, for both sides of the above equation with respect to ln(Q) in Taking the partial derivative, we can obtain... And according to the property of logarithmic differential, it is exactly equal to That is, the elastic coefficient ε QTherefore, the regression coefficients a1 and a2 estimated by the least squares method are the elasticity coefficients of each factor.

[0176] It is important to note that collinearity diagnosis of all external driving factors must be performed before conducting regression analysis. This is because some hydrological factors may have strong physical correlations (for example, an increase in inflow into a lake is often accompanied by an expansion of the water surface area), and strong collinearity can lead to unstable regression coefficient estimates or even opposite signs.

[0177] As a preferred implementation, this embodiment uses the variance inflation factor (VIF) for testing. The VIF value of each factor is calculated; if the VIF value of a factor is greater than 10, it indicates severe collinearity. In this case, a regularized regression method should be used instead of the ordinary least squares method to estimate the parameters. This is achieved by adding an L2 regularization term, λ*||a||, to the objective function. 2 It can suppress the expansion of parameter variance caused by collinearity, and ensure that the sign and magnitude of the elasticity coefficient conform to physical laws.

[0178] Optionally, the external driving factor sequence includes at least the time series of the following physical quantities: total inflow into the lake representing the intensity of watershed inflow; lake surface area representing the morphological characteristics of the lake; wind speed in the lake area representing meteorological and dynamic conditions; and effective roughness representing the resistance characteristics of the lake bottom and vegetation.

[0179] In this embodiment, four key physical dimensions involved in attribution are identified. Total inflow Q into the lake in This usually refers to the sum of the flows of the main tributaries flowing into a lake, such as the total flow of the five rivers flowing into a lake. Lake surface area A lake It is not a fixed value, but a time series that fluctuates with the water level. In practice, the lake surface area for a given day can be calculated from the daily measured water level using a pre-constructed water level-area-volume curve. This factor reflects the lake's water storage capacity and the impact of reclamation activities. The lake area wind speed W is usually selected from the daily average wind speed of a representative meteorological station in the lake area, or the wind speed vector is projected onto the component of the mainstream flow, characterizing the dragging or impeding effect of wind stress on the water flow. Effective roughness n eff This parameter comprehensively reflects lakebed friction and vegetation resistance. Because this parameter is difficult to measure directly, it is usually obtained using an inversion method, or by using the normalized difference in vegetation index (NDVI) of aquatic vegetation cover as a proxy variable for analysis. Optionally, the contribution rate of each external driving factor to lake current evolution is determined, specifically including:

[0180] The study period was divided into a baseline period and an evaluation period, and the relative change rate of each external driving factor in the evaluation period was calculated relative to the baseline period.

[0181] In this embodiment, to calculate the impact of environmental change, the study period is typically divided into a baseline period and an evaluation period. The baseline period is usually chosen before periods of minimal human activity or major engineering projects (e.g., 1980 to 2000); the evaluation period is chosen after the projects commenced or after environmental changes occurred (e.g., after 2003). For each driving factor, its multi-year average over both periods is calculated to obtain the relative rate of change. The calculation formula is as follows:

[0182] R X =(X eval -X base ) / X base ;

[0183] Among them, R X Let X be the relative rate of change of factor X. eval X is the multi-year average over the evaluation period. base This is a multi-year average over the baseline period. For example, the calculation results might show that the total inflow into the lake during the evaluation period decreased by 5% compared to the baseline period, while the lake surface area decreased by 8%.

[0184] The contribution of each external driving factor to the lake current change is calculated by multiplying the elasticity coefficient and the relative rate of change, and the contribution is normalized to obtain the percentage contribution rate of each external driving factor.

[0185] In this embodiment, the total variation of the lake current residual is decomposed into the sum of contributions using the principle of total differential. The contribution of a certain factor to the lake current variation is equal to its elasticity coefficient multiplied by its relative rate of change. The specific calculation formula is as follows:

[0186] Con X =ε X *R X ;

[0187] Among them, Con X The contribution of factor X to the lake current variation (dimensionless percentage).

[0188] Furthermore, to demonstrate the relative importance of each factor, the normalized percentage contribution rate is calculated:

[0189] η X =(|Con X | / Σ(|Con i |))*100%;

[0190] Where, η XLet Σ represent the percentage contribution of factor X, and let Σ represent the sum of the absolute values ​​of the contributions of all factors i involved in the analysis. Using absolute values ​​is to avoid the denominator being too small due to the cancellation of positive and negative contributions. This calculation method can indicate the proportion of flow change and topographic change among all causes of lake flow changes. According to one aspect of this application, the method also includes constructing a complete attribution map of the evolution of lake flows in connected lakes:

[0191] Calculate the change in the instantaneous response velocity component during the evaluation period relative to the baseline period; sum the change in response with the contribution of each external driving factor to obtain the total change in lake flow; calculate the proportion of the change in response in the total change in lake flow to obtain the contribution rate of the Yangtze River water level backwater effect to lake flow evolution, and combine it with the percentage contribution rate of each external driving factor to form a complete attribution result that includes external backwater and internal evolution.

[0192] In this embodiment, the final full-caliber attribution result is synthesized. The previous embodiments only explained the sources of variation in residual velocity, while the actual total variation in lake current also includes variations in the backwater / immediate response component driven by the Yangtze River water level. This embodiment reintegrates the first component into the attribution framework.

[0193] Specifically, the instantaneous response velocity component V is calculated. inst The relative change:

[0194] Con backwater =(V inst_eval -V inst_base ) / V obs_base ;

[0195] Among them, V inst_eval and V inst_base V represents the average instantaneous response flow rate during the evaluation period and the baseline period, respectively. obs_base The average flow velocity is the original observed value during the baseline period.

[0196] By integrating this change with the contributions of the aforementioned factors and recalculating the overall contribution distribution, a complete conclusion similar to the following can be drawn: the long-term slowdown in the flow velocity of a certain lake is due to 40% of the reduced backwater effect caused by the drop in the water level of the main stream of a certain river (external hydraulic boundary factors), 30% of the reduced inflow into the lake (watershed hydrological factors), and 30% of the topographical changes caused by riverbed sand mining (internal lake factors). This comprehensive attribution picture, encompassing both internal and external factors, can more objectively guide integrated watershed management.

[0197] Example 8 details a method for correcting the numerical stability of attribution models. In the multi-factor quantitative attribution process, a log-linear model is used to estimate the elasticity coefficients. However, in actual hydrological analysis of lakes connected to the Yangtze River, the separated lake flow residual sequence physically represents the velocity component after removing the backwater effect. This component may exhibit zero or even negative values ​​during the dry season or when the flow direction reverses. Performing a logarithmic operation (ln) on a sequence containing non-positive values ​​will result in a mathematical domain error (NaN), causing the algorithm to terminate.

[0198] This embodiment provides two parallel preferred technical paths, ensuring the numerical stability and computational continuity of attribution analysis under full hydrological data through data preprocessing or model structure improvements. According to one aspect of this application: before establishing the log-linear response model, the method further includes processing non-positive data present in the lake current residual sequence.

[0199] Step 801 involves performing a nonnegative mapping translation on the lake current residual sequence, including calculating the minimum value of the lake current residual sequence and adding a translation constant to all residual values ​​to ensure that the variables of the input logarithmic function are within the domain; or using a generalized linear model to replace the log-linear response model to construct a multi-factor response model, and using a connection function to establish a linear combination relationship between the mathematical expectation of the lake current residual sequence and the external driving factor sequence.

[0200] In this embodiment, when the first technical approach, namely non-negative mapping translation processing, is used, the original data is projected as a whole into the positive real number interval through rigid translation of the coordinate axes, without changing the relative fluctuation characteristics within the data. Specifically, the system traverses the lake current residual sequence V throughout the entire study period. res (t), identify the algebraic minimum value V in the sequence. min If V min If the value is less than or equal to zero, then the translation constant C is determined. shift The value of this constant must ensure that all values ​​after the translation are greater than zero.

[0201] As a specific implementation method, the formula for calculating the translation constant can be set as follows:

[0202] C shift =|V min |+ε base ;

[0203] Among them, C shift Let |V| be the translation constant. min | represents the absolute value of the minimum value of the lake current residual sequence, ε base It is a preset small positive number (e.g., 1.0 or 0.1, with the unit consistent with the flow rate) to avoid zero-value logarithmic divergence.

[0204] Based on this constant, construct the corrected residual sequence V. modified (t), its calculation formula is:

[0205] V modified (t)=V res (t)+C shift ;

[0206] Among them, V modified (t) represents the corrected residual velocity, V res (t) represents the original residual velocity. Further, using V... modified (t) The original residual sequence was substituted into the log-linear model for regression analysis. It should be noted that although this treatment changes the physical meaning of the intercept term a0, it does not change the marginal response trend of the independent variable driving factors to the change in the dependent variable flow velocity. Therefore, it is still statistically valid in assessing the contribution rate of relative change.

[0207] In this embodiment, as a more preferred alternative, the generalized linear model (GLM) path can be employed. This type of method does not require manual translation of the original data; instead, it adapts the mathematical structure of the model to the distribution characteristics of the data. The generalized linear model allows the dependent variable to follow an exponential family distribution (such as a Gaussian, gamma, or inverse Gaussian distribution) and links the expected value of the dependent variable to a linear combination of the independent variables through a monotonically differentiable link function.

[0208] Example 9: As a specific numerical example, the calculation process of this invention is illustrated using the Hukou waterway of Poyang Lake as an example. Assume that the observation data for a consecutive 5 days are shown in Table 1 below:

[0209] Table 1. Example of input data

[0210] date <![CDATA[Lake level H l (m)]]> <![CDATA[Jiangkou water level H j (m)]]> Water level difference ΔH (m) <![CDATA[Observed flow velocity V obs (m / s)]]> Day 1 14.5 13.8 0.7 0.85 Day 2 14.2 13.9 0.3 0.52 Day 3 13.8 14.1 -0.3 -0.48 Day 4 13.5 14.5 -1.0 -1.12 Day 5 13.9 14.0 -0.1 -0.15

[0211] Initialization parameter settings: initial response coefficient α0=1.0, initial nonlinearity exponent β0=0.5, initial error covariance P0=diag(0.01,0.001), process noise covariance Q=diag(0.001,0.0001), observation noise variance R=0.01.

[0212] Furthermore, taking the recursive process of day 2 as an example, the algorithm logic is explained as follows: the posterior estimate of day 1 is used to predict the prior state value of day 2; the Jacobian matrix is ​​calculated based on the water level difference of day 2 (ΔH2=0.3m), and its first component is |ΔH2|. β The second component is α*|ΔH2| β*ln(|ΔH2|)*sgn(ΔH2); The prior estimate is corrected by combining the Kalman gain to obtain the posterior estimate. Through point-by-point recursion using 5 days of data, the posterior estimates of the response coefficient and nonlinear exponent at each time point can be output sequentially. The above recursive process can be implemented by someone skilled in the art using a standard extended Kalman filter algorithm framework. Through the above recursion, the response coefficient sequence α can be obtained. t and nonlinear exponential sequence β t The trajectory of its evolution over time.

[0213] Specifically, in the lake current attribution scenario, this embodiment selects the Log Link Function. This choice aims to maintain the flexible interpretability of the model coefficients, i.e., to preserve the multiplicative driving physical assumption. Within this framework, the model no longer requires single-point observations to be positive, but instead establishes the following expected relationship equation:

[0214] ln(E[V res ])=a0+a1*ln(Q in )+a2*ln(A lake )+a3*ln(W)+a4*ln(n eff );

[0215] Among them, E[V res [ ] represents the mathematical expectation of the lake current residual sequence, ln(·) is the connection function, a0 to a4 are the parameters to be estimated, and Q in A lake 、W、n eff These are the external driving factors.

[0216] In the solution process, generalized linear models typically employ maximum likelihood estimation (MLE) or iterative weighted least squares (IRLS) for parameter estimation. Compared to ordinary least squares (OLS), GLM is better able to handle non-normally distributed error structures. For example, when the lake current residual sequence exhibits a right-skewed distribution—meaning that the flow velocity is low most of the time and occasionally high—assuming the error follows a gamma distribution often yields a better fit than assuming a normal distribution.

[0217] Furthermore, to enhance the robustness of the model under extreme data, a robust regression mechanism can be introduced when constructing the generalized linear model. Specifically, this can be achieved by replacing the likelihood function with an M-estimator or the Huber loss function, reducing the impact of outliers on the estimation of regression coefficients. For example, data outliers caused by severe floods in certain years will be automatically assigned lower weights within the robust regression framework, ensuring that the final elasticity coefficient α is accurately estimated. iIt can represent the driving laws under general hydrological conditions.

[0218] Whether using translation correction or a generalized linear model, this embodiment solves the problem of computational interruption caused by data symbol limitations, providing underlying algorithmic support for establishing an all-weather, all-water-condition attribution analysis system.

[0219] This approach addresses the issue of confusing external forcing with internal evolution by constructing a river-lake hydraulic response model that incorporates a flow direction sign function. Specifically, the method utilizes a physical model to calculate the instantaneous response component driven by the water level difference and separates it from the observed flow velocity to obtain a pure residual sequence of lake evolution, thus decoupling the Yangtze River water level backwater effect from the lake's own evolution.

[0220] Furthermore, a time-varying state-space model and an extended Kalman filter algorithm were employed. This method breaks free from the constraints of static models, treating the response coefficients reflecting the flow capacity of the lake mouth as latent state variables that evolve over time. It captures and tracks the drift of the hydraulic connection physical characteristics caused by human activities such as river sand mining and engineering construction, and achieves dynamic identification of the evolution of response relationships.

[0221] Furthermore, the attribution algorithm was numerically corrected using nonnegative translation mapping or the generalized linear model (GLM) to ensure the mathematical continuity and computational stability of the model under the negative flow velocity condition of the Yangtze River backflow. Combined with the elasticity coefficient method, the contribution rate of each driving factor was quantitatively calculated throughout the entire hydrological cycle.

[0222] It should be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A method for identifying the evolution characteristics and causes of lake currents in connected lakes, characterized in that, include: Obtain the observed flow velocity sequence of lakes connected to the Yangtze River, the sequence of the water level difference between the lake area and the river mouth, and the sequence of external driving factors; A lake-river hydraulic response model is constructed based on the lake current observation velocity sequence and the river-river water level difference sequence. The instantaneous response velocity component driven by the instantaneous river-river water level difference is calculated using the lake current hydraulic response model. The instantaneous response velocity component is subtracted from the lake current observation velocity sequence to obtain the lake current residual sequence that characterizes the changes in the lake system's own characteristics. A multi-factor attribution model for lake current residual sequences was constructed based on the sequence of external driving factors. The contribution rate of each external driving factor to the evolution of lake currents was determined using the multi-factor attribution model. Constructing a river-lake hydraulic response model includes: The power-law response function is obtained by characterizing the nonlinear response relationship between flow velocity and the river-lake water level difference sequence using a power function. The flow direction sign function sgn(·) is introduced to map the direction of the river and lake water level difference sequence, so as to obtain the water level difference driving quantity with direction, enabling the river and lake hydraulic response model to handle the bidirectional flow state of lake water outflow and Yangtze River backflow. Constructing a river-lake hydraulic response model and separating the instantaneous response velocity component includes: A time-varying state-space model is constructed, in which the state equation is used to describe the evolution trajectory of the response coefficient and the nonlinear exponent over time, and the observation equation is used to describe the nonlinear mapping relationship between the lake current observation velocity sequence and the river-lake water level difference sequence. The extended Kalman filter algorithm is used to recursively estimate the state variables, and the response coefficient sequence and nonlinear exponential sequence that evolve over time are obtained. Based on the response coefficients and nonlinear exponents at each time point, the corresponding instantaneous response velocity components are calculated. Constructing a river-lake hydraulic response model includes: Calculate the cumulative distribution function of the lake area's water level, and divide the water level into multiple water level intervals based on the principle of equal frequency; Establish local response relationships within each water level interval and estimate the piecewise response coefficients corresponding to each water level interval; Construct a continuous function connecting the response coefficients of each segment, and determine the response coefficient at the current moment based on the real-time water level dynamics; Constructing a river-lake hydraulic response model also includes correcting for hysteresis effects: Define a candidate set of lag times, and for each lag time in the candidate set, construct a sequence of river and lake water level differences that introduces time lag; Calculate the coefficient of determination between the observed lake current velocity sequence and the lake-river water level difference sequence with various introduced time delays; The lag time corresponding to the largest determination coefficient is selected as the optimal lag time, and the optimal lag time is used to perform time-series correction on the input of the river and lake hydraulic response model. Construct a multi-factor attribution model for lake current residual sequences, including: Based on the lake current residual sequence and the external driving factor sequence, an elasticity coefficient is introduced to characterize the sensitivity of the lake current to each external driving factor. A log-linear response model describing the relationship between the lake current residual sequence and the external driving factor sequence is established, and the regression coefficients of the log-linear response model are used as the elasticity coefficients of the corresponding external driving factors; the external driving factor sequence includes at least the time series of the following physical quantities: The total inflow into the lake, representing the intensity of watershed runoff; The surface area of ​​a lake, which characterizes its morphological features; Lake wind speed characterizing meteorological and dynamic conditions; and effective roughness characterizing the resistance characteristics of the lake bottom and vegetation.

2. The method according to claim 1, characterized in that, Recursive estimation using the extended Kalman filter algorithm includes: Calculate the Jacobian matrix of the observation equation with respect to the state variables. The Jacobian matrix includes the partial derivatives of the observation equation with respect to the response coefficients and the partial derivatives of the observation equation with respect to the nonlinear exponent. The Kalman gain is calculated using the Jacobian matrix, and the prior estimates of the state variables are corrected based on the Kalman gain to obtain the posterior estimates of the response coefficients and nonlinear exponents at the current time.

3. The method according to claim 2, characterized in that, The method also includes an adaptive adjustment step for the process noise covariance: Calculate the information sequence between the observed lake current velocity sequence and the predicted velocity estimated based on the current state; The adaptive adjustment factor is calculated based on the ratio of the actual variance to the theoretical variance of the innovation sequence. The adaptive adjustment factor is then used to dynamically correct the process noise covariance. When the adaptive adjustment factor is greater than a preset threshold, the model’s tracking sensitivity to parameter evolution is improved.

4. The method according to claim 1, characterized in that, Before establishing the log-linear response model, the method also includes: The lake current residual sequence is subjected to nonnegative mapping and translation processing, including calculating the minimum value of the lake current residual sequence and adding a translation constant to all residual values ​​to ensure that the variables input to the logarithmic function are within the domain; A generalized linear model is used to replace the log-linear response model to construct a multi-factor response model, and a connection function is used to establish the linear combination relationship between the mathematical expectation of the lake current residual sequence and the external driving factor sequence.

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