A reservoir flood inflow set probability prediction method based on water regime self-adaptation

Abstract

The application provides a reservoir flood inflow set probability prediction method based on water regime self-adaptation, comprising: obtaining upstream basin multi-rainfall station precipitation and inflow data, dividing sub-basins and calculating surface average rainfall, constructing structurally different machine learning member models for multi-step prediction; constructing a water regime index from the larger one of the flow amplitude and the cumulative rainfall in the early stage, so that it rises in advance before the flood rises, and the length of the sliding window is determined according to the index and the two-dimensional foresight period; in the window, the Bayesian model with time decay is used to estimate the average weight and variance, and the redundant members with error correlation are corrected by weight reduction; the point prediction and prediction interval are generated by adaptive sharpening. The window length, time decay and weight sharpening are driven and linked by the same water regime index, and are switched to short window, fast decay and strong sharpening at the same time in the flood precursor period. The application can improve the accuracy, timeliness and reliability of the prediction in the flood steep rising stage and near the flood peak.

Description

Technical Field

[0001] This invention relates to the field of hydrological forecasting technology, and in particular to a method for ensemble probability forecasting of reservoir inflow floods based on hydrological adaptive forecasting. Background Technology

[0002] Reservoir inflow flood forecasting is a core technical aspect of reservoir flood control, water conservancy, and watershed water resources management. Accurate, reliable inflow forecasts with clearly defined uncertainties are crucial for reservoirs to make informed decisions regarding the timing and volume of flood discharges during floods, ensuring dam safety and the safety of downstream residents and their property, and balancing power generation and water supply benefits.

[0003] Traditional reservoir inflow flood forecasting often employs conceptual hydrological models or single machine learning models to provide deterministic point forecasts. With the development of machine learning and deep learning technologies, various data-driven models, such as Long Short-Term Memory (LSTM) networks, gated recurrent units (GRUs), temporal convolutional networks (TRCs), Transformers, extreme gradient boosting trees (ESBRs), and random forests, have been widely applied to reservoir inflow forecasting, achieving higher forecast accuracy than traditional methods within certain lead times. However, single models are limited by their model structure and training samples, resulting in inconsistent forecast performance under different hydrological conditions. One model may perform well during the normal water period but exhibit severe forecast lag or underestimate of the flood peak during the rapid rise phase; another model may respond promptly near the flood peak but produce persistent biases during the receding phase. Therefore, integrating the forecasting advantages of multiple structurally diverse member models has become a crucial approach to improving the accuracy and reliability of reservoir inflow flood forecasts.

[0004] Bayesian model averaging (BMA) is a widely used multi-model ensemble probabilistic forecasting method. This method assigns posterior weights to each member model, probabilistically weighted and fused the forecasts from multiple models, providing both deterministic point forecasts and probabilistic forecast intervals reflecting forecast uncertainty. However, existing Bayesian model averaging methods and their improved versions for reservoir inflow flood forecasting still have the following shortcomings: (i) Static weights cannot adapt to drastic changes in water conditions. Existing BMA methods estimate weights based on fixed and long historical training periods, resulting in weights that remain unchanged or update slowly throughout the forecast period. Such static weights are ill-suited to the drastic changes in water conditions during floods. During the rapid rise of floodwaters, the relative forecasting performance of each member model differs significantly from that during the normal flood period. Static weights, due to their over-reliance on training samples from the normal flood period, fail to promptly highlight the models that perform better during the rapid rise, leading to delayed and distorted flood peak forecasts.

[0005] (ii) Fixed window length cannot balance robustness and agility. Even with sliding windows for dynamic weight updates, the window length of existing methods is usually a fixed value based on experience. If the window is too long, the response to sudden changes in water conditions will be sluggish, and the weights cannot be adjusted in time before the flood peak arrives; if the window is too short, the weight estimation will fluctuate wildly and be unstable due to insufficient training samples during the stable period. A single fixed window cannot simultaneously balance the estimation robustness during the stable period and the response agility during the steep flood period.

[0006] (III) Hydrological situation identification relies on flow changes, resulting in response lag due to confluence lag. Existing methods often rely solely on changes in inflow to identify hydrological changes. Due to confluence lag in the watershed, when heavy rainfall has occurred upstream and flooding is imminent, the inflow remains low before the inflection point of the flood surge. Flow changes alone cannot detect changes in hydrological conditions before the actual arrival of the flood, causing adjustments to key parameters such as window length and weighting to lag behind the flood process, further exacerbating the delay in flood peak forecasting.

[0007] (iv) Ignoring the error correlation among member models. Multiple member models often have highly correlated forecast errors due to shared input data or structural similarity. Existing Bayesian model averaging methods do not fully consider this error redundancy when estimating weights, resulting in several highly correlated models being weighted repeatedly in the ensemble. This weakens the contribution of models that truly have independent forecasting capabilities and reduces the efficiency of utilizing effective information from ensemble forecasts.

[0008] (v) Uniform parameter configuration is used for different lead times. The correlation between forecast errors and weights of each member model differs significantly between short and long lead times. Existing methods use the same parameter configuration for different lead times, which cannot achieve optimal forecast performance for the different characteristics of each lead time.

[0009] In summary, existing technologies lack a method for ensemble probability forecasting of reservoir inflow floods that can be driven by real-time changes in watershed hydrology, detect changes in hydrology before the flood rises, and make unified and adaptive adjustments to key parameters such as window length, time decay, and weight sharpening for ensemble weight estimation, while taking into account the redundancy of member model errors and the differences in multiple forecast periods. Summary of the Invention

[0010] To address the shortcomings of existing technologies, such as static weights being unable to adapt to drastic changes in hydrological conditions, fixed window lengths failing to balance robustness and agility, hydrological identification relying on flow changes leading to response lags, neglecting the error correlation between member models, and using uniform parameter configurations for different forecast periods, this invention provides a hydrological adaptive ensemble probability forecasting method for reservoir inflow floods. By constructing a hydrological index that can rise in advance before the flood surge, this method uniformly drives the coordinated adjustment of three key parameters in ensemble weight estimation: sliding window length, time-effect decay factor, and weight sharpening intensity. Combined with weight reduction correction for member model error redundancy and differentiated configurations for multiple forecast periods, this method achieves high-precision and high-reliability ensemble probability forecasting of reservoir inflow floods.

[0011] To achieve the above objectives, this invention provides a method for ensemble probability forecasting of reservoir inflow floods based on hydrological adaptive forecasting, the method specifically comprising: Step S1: Obtain time-by-time precipitation data and inflow observation data from multiple rain gauge stations in the upstream basin of the reservoir; divide the upstream basin into several sub-basins according to topography and water system, and calculate the time-by-time average rainfall of each sub-basin; align the average rainfall of each sub-basin with the inflow by time to form a complete time-series dataset indexed by time, and divide it into training set, validation set and test set in chronological order; Step S2: Build Several structurally distinct machine learning-based flood forecasting member models. Each member model takes the average rainfall sequence and inflow sequence of each sub-basin within a preset historical window as input, and adopts a direct multi-step prediction strategy to output the future first to second... Forecast value of inflow for the next period, The foreseeable period number is denoted as , ; Step S3: At the predicted time The flow rate amplitude component is constructed based on the relative changes in inflow rate between adjacent time periods. Precursor indicators for rainfall-runoff generation are constructed based on the weighted cumulative amount of average rainfall in each sub-basin during the preceding accumulation period. This is used to characterize the initial rainfall that has fallen into the watershed but has not yet been converted into inflow due to the confluence lag time; the number of periods in the initial accumulation period is determined based on the watershed confluence lag time, so that when the inflow has not yet started to rise and the flow amplitude component is still at a low value, the hydrological index is dominated by the rainfall-runoff precursor index, thus increasing in advance before the inflow inflow starts to rise; the flow amplitude component is taken as... Precursor indicators of rainfall-induced runoff The larger one is used as the hydrological indicator. ; Step S4: For each forecast period Based on the aforementioned hydrological indicators With the aforementioned forecast period The length of the sliding window is determined by both dimensions. ,make Follow Increases and monotonically decreases, and follows It increases while monotonically decreasing; Step S5: In a length of Within the sliding window, establish a time-decrease factor. The average log-likelihood function of the local Bayesian model is obtained by solving the problem using the expectation-maximization algorithm, thus yielding the... Weights of each member model With variance , The time-decrease factor Follow Increase and decrease; then calculate the correlation strength between each pairwise prediction error sequence of each member model within the window, and perform weight reduction correction on redundant member models whose error correlation strength exceeds a preset threshold to obtain the time-varying weights after redundancy removal. ; Step S6: Use random The increased weight sharpening intensity affects the time-varying weights after redundancy removal. Sharpening is performed to obtain the sharpening weight. The predicted values ​​of each member model are weighted and summed according to the sharpening weights to obtain the deterministic point prediction; based on the sharpening weights and the variance... The forecast interval is constructed by considering the degree of dispersion between the forecast values ​​of each member model, and the ensemble probability forecast result of the inflow flood is output. Wherein, the sliding window length The aforementioned time-decrease factor The weighted sharpening intensity and the other two are derived from the same hydrological index. A unified driving force and coordinated action enable the aforementioned rainfall-induced runoff precursor indicators to... During the period leading up to a sharp rise in floodwaters, all three factors simultaneously shift towards a shorter window, faster decay, and stronger sharpening; during the stable period, they simultaneously revert to a longer window, slower decay, and weaker sharpening.

[0012] Furthermore, the flow rate amplitude component mentioned in step S3 Precursor indicators of rainfall-induced runoff The calculation formula is: , , In the formula: for Inbound traffic at all times for Inbound traffic at all times The preset reference flow rate; For the number of sub-basins, For sub-basin serial numbers, This refers to the time period number within the previous accumulated time period. For the first Each sub-basin Average rainfall over a period of time. For the first The weight of each sub-basin For the preset reference rainfall, This represents the number of time periods corresponding to the average confluence delay time in the upstream basin. Indicates will Limited to the interval The truncation function within.

[0013] Furthermore, sub-basin weights According to the The confluence delay time from the outlet of each sub-basin to the reservoir section is determined, and sub-basins with shorter confluence delay times are assigned greater weights. The weights of all sub-basins are then normalized. Precursor indicators of rainfall-induced runoff Prioritize responses to rainfall in sub-basins that contribute more quickly to the rise in inflow.

[0014] Furthermore, the sliding window length mentioned in step S4 Determine by the following formula: In the formula, and Forecast period The corresponding upper and lower limits of window length, For the floor function, Between the upper and lower limits, depending on the hydrological indicators Linear interpolation and rounding are used to shorten the historical data window used for weight estimation when the current flood is more severe or the forecast period is longer; for any condition satisfying... The two prediction period numbers are: and .

[0015] Furthermore, the upper limit of the window length and lower limit The validation set is used for each forecast period The optimal selection criteria are as follows: the selection criteria are to make the deterministic accuracy of the ensemble probability forecast on the validation set optimal for the given forecast period; and for short forecast periods where the weights of the member models are relatively stable over time, a larger upper and lower window limit is assigned to suppress the weight estimation jitter caused by insufficient samples; and for long forecast periods where the correlation between the forecast error of the member models and the corresponding weights changes rapidly over time, a smaller upper and lower window limit is assigned to ensure rapid tracking of the current optimal member model.

[0016] Furthermore, in step S4, an asymmetric window adjustment strategy is adopted for the fluctuation phase of the inbound flow: when the inbound flow is in the rising phase, the length of the sliding window is adjusted. With water condition indicators Increase the rate of increase and shorten the sliding window; when the inflow is in a declining phase, the sliding window length... The price recovers gradually over time in defined steps, with the recovery rate being less than the shortening rate of the upward phase.

[0017] Furthermore, the average log-likelihood function of the local Bayesian model with time-decrease factor described in step S5 is: , In the formula: For the sub-prediction model weight vector; The variance vector is formed by the variances corresponding to each sub-prediction model; The time period number within the window; for Real-time inflow observation values; For the k-th member model pair Timeframe, Forecast Period Forecast value of inflow; and The two numbers to be solved are the first and second numbers. Weights and variances of each member model; Indicated by For the mean, For variance, in The normal probability density function that takes values ​​at a given location; The time-degradation factor ,in, As the attenuation reference value, The attenuation adjustment coefficient and the two satisfy the following conditions: Thus ensuring .

[0018] Furthermore, the redundancy reduction correction mentioned in step S5 specifically includes: remember For the first in the window For each member model's prediction error sequence, calculate the correlation coefficient between each pairwise error sequence, and define the reciprocal of the error correlation strength: In the formula, For the first The inverse of the error correlation strength of each member model, For the first The and the first The correlation coefficients between the error sequences of each member model; For the Weights of each member model After correction and normalization, the expression is: In the formula, For the first The inverse of the error correlation strength of each member model, For the first The weights of each member model are used to obtain the time-varying weights after redundancy removal. .

[0019] Furthermore, step S6 employs water condition indicators. Increased sharpness index The weighted sharpening intensity is characterized by the following expression: ,in, To sharpen the baseline value and , To sharpen the adjustment coefficient and , to sharpen index With water condition indicators As the weight increases, the weight distribution also concentrates towards the member models with larger weights. Sharpening weight The calculation formula is: In the formula, Indicates the first Time-varying weights after redundancy removal from the member model of Power of; Indicates the first Time-varying weights after redundancy removal from the member model of Power; Deterministic point forecasts are as follows: In the formula, For the first Member model pair Timeframe, Forecast Period Forecast value of inflow; The total variance of the forecast is: Predicting the deterministic points Centered on, with The forecast interval is constructed based on the scale.

[0020] Furthermore, the K structurally distinct machine learning flood forecasting member models include at least three of the following: Long Short-Term Memory Network (LSTM) model, Gated Recurrent Unit (GRU) model, Temporal Convolutional Network (TRC) model, Transformer model, Artificial Neural Network (ANN) model, Extreme Gradient Boosting Tree (EPB) model, and Random Forest model.

[0021] Compared with the prior art, the present invention has the following beneficial effects: (1) Achieve early detection of the sudden rise in floodwaters and overcome the lag in parameter adjustment. The hydrological index constructed in this invention integrates the flow amplitude component and the rainfall-runoff precursor index, taking the maximum value of the two. Since the rainfall-runoff precursor index accumulates the rainfall that has already fallen into the watershed but has not yet been converted into inflow due to confluence lag, it can rise in advance before the inflection point of inflow. Therefore, this invention can detect changes in hydrological conditions before the actual arrival of floods, allowing the parameter adjustment of the ensemble weighted estimation to occur before the flood process. This overcomes the shortcomings of existing technologies that rely solely on flow changes, resulting in parameter adjustments always lagging behind the flood, significantly improving the timeliness of flood peak forecasting and reducing flood peak lag and underestimation.

[0022] (2) Unified driving force and coordinated linkage, taking into account both agility during the period of rapid growth and stability during the period of stability. This invention uses a single hydrological index to drive the coordinated adjustment of three key parameters: sliding window length, time-dependent decay factor, and weight sharpening intensity. During the pre-flood surge period, these three parameters simultaneously switch to shorter windows, faster decay, and stronger sharpening, allowing the aggregate weights to quickly focus on the member model performing best under the current hydrological conditions. During stable periods, they simultaneously revert to longer windows, slower decay, and weaker sharpening, ensuring the robustness of the weight estimation. This unified, coordinated mechanism balances agility during surges with robustness during stable periods, overcoming the shortcomings of existing fixed-parameter or single-parameter adjustments that cannot simultaneously address both.

[0023] (3) Introduce redundancy reduction correction to improve the effectiveness of ensemble forecasts and the efficiency of information utilization. This invention introduces a redundancy reduction correction based on the inverse of the correlation strength of member model errors in weight estimation. This reduces the weight of redundant member models with highly correlated forecast errors, thereby suppressing the phenomenon of similar models being repeatedly weighted, highlighting the contributions of truly independent and complementary member models, and improving the effectiveness and information utilization efficiency of ensemble forecasts.

[0024] (4) Differentiated configuration of multiple forecast periods and asymmetric window adjustment to improve adaptability under different forecast scenarios This invention configures upper and lower limits for window lengths for different forecast periods and optimizes them based on the rank correlation coefficient between error and weight using a validation set. Furthermore, it employs an asymmetric window adjustment strategy for fluctuations in inflow. This allows the invention to achieve superior forecast performance for different forecast periods and different fluctuation stages, overcoming the shortcomings of existing technologies that use uniform parameter configurations for all forecast periods.

[0025] (5) Output complete ensemble probability forecast results to provide reliable uncertainty information for flood control decision-making. The present invention outputs a complete set of probabilistic forecast results, including deterministic point forecasts and probabilistic forecast intervals. The forecast intervals take into account both the variance of the member models themselves and the degree of dispersion among the member models, which can provide reliable uncertainty information for reservoir flood control scheduling decisions.

[0026] In summary, this invention can effectively improve the accuracy, timeliness, and reliability of flood forecasting for reservoirs, especially during the rapid rise of floodwaters and near the flood peak, and has good engineering application value. Attached Figure Description

[0027] Figure 1 This is a flowchart of the overall process for a reservoir inflow flood ensemble probability forecasting method based on hydrological adaptive characteristics.

[0028] Figure 2 This is a schematic diagram illustrating the effect of deterministic point forecasts and forecast intervals for inflow floods; where (a), (b), and (c) represent deterministic point forecasts and forecast intervals for lead times of 1 hour, 3 hours, and 7 hours, respectively. Detailed Implementation

[0029] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0030] like Figure 1 The diagram shown is the overall flowchart of the reservoir inflow flood ensemble probability forecasting method based on hydrological adaptive method of the present invention. The specific steps are as follows: Step S1: Data Acquisition and Preprocessing Acquire time-period precipitation data and inflow observation data from multiple rain gauge stations in the upstream basin of the reservoir; divide the upstream basin into several sub-basins according to topography and water system, calculate the time-period average rainfall of each sub-basin; align the average rainfall of each sub-basin with the inflow by time to form a complete time-series dataset indexed by time, and divide it into training set, validation set and test set in chronological order; Step S2: Multi-member model construction and multi-step forecasting Construct K structurally distinct machine learning-based flood forecast member models. Each member model takes the average rainfall sequence and inflow sequence of each sub-basin within a preset historical window as input, and adopts a direct multi-step prediction strategy to output the future first to second... Forecast value of inflow for the next period, The foreseeable period number is denoted as , ; Step S3: Construction of hydrological status indicators At the predicted time The flow rate amplitude component is constructed based on the relative changes in inflow rate between adjacent time periods. Precursor indicators for rainfall-runoff generation are constructed based on the weighted cumulative amount of average rainfall in each sub-basin during the preceding accumulation period. This is used to characterize the initial rainfall that has fallen into the watershed but has not yet been converted into inflow due to the confluence lag time; the number of periods in the initial accumulation period is determined based on the watershed confluence lag time, so that when the inflow has not yet started to rise and the flow amplitude component is still at a low value, the hydrological index is dominated by the rainfall-runoff precursor index, thus increasing in advance before the inflow inflow starts to rise; the flow amplitude component is taken as... Precursor indicators of rainfall-induced runoff The larger one is used as the hydrological indicator. ; Step S4: Adaptively determine the length of the sliding window For each forecast period Based on the aforementioned hydrological indicators With the aforementioned forecast period The length of the sliding window is determined by both dimensions. ,make Follow Increases and monotonically decreases, and follows It increases while monotonically decreasing; Step S5: Time-varying weight estimation and redundancy reduction correction In length Within the sliding window, establish a time-decrease factor. The average log-likelihood function of the local Bayesian model is obtained by solving the problem using the expectation-maximization algorithm, thus yielding the... Weights of each member model With variance , The time-decrease factor Follow Increase and decrease; then calculate the correlation strength between each pairwise prediction error sequence of each member model within the window, and perform weight reduction correction on redundant member models whose error correlation strength exceeds a preset threshold to obtain the time-varying weights after redundancy removal. ; Step S6: Weight Sharpening and Probability Prediction Output Adopting random The increased weight sharpening intensity affects the time-varying weights after redundancy removal. Sharpening is performed to obtain the sharpening weight. The predicted values ​​of each member model are weighted and summed according to the sharpening weights to obtain the deterministic point prediction; based on the sharpening weights and the variance... The forecast interval is constructed by considering the degree of dispersion between the forecast values ​​of each member model, and the ensemble probability forecast result of the inflow flood is output. Wherein, the sliding window length The aforementioned time-decrease factor The weighted sharpening intensity and the other two are derived from the same hydrological index. A unified driving force and coordinated action enable the aforementioned rainfall-induced runoff precursor indicators to... During the period leading up to a sharp rise in floodwaters, all three factors simultaneously shift towards a shorter window, faster decay, and stronger sharpening; during the stable period, they simultaneously revert to a longer window, slower decay, and weaker sharpening.

[0031] In one specific embodiment of the present invention, the flow rate amplitude component in step S3 The calculation formula is In the formula, for Inbound traffic at all times for Inbound traffic at all times Preset reference flow rate; precursor indicators of rainfall-induced runoff The calculation formula is: In the formula: For the number of sub-basins, For sub-basin serial numbers, This refers to the time period number within the previous accumulated time period. For the first Each sub-basin Average rainfall over a period of time. Let i be the weight of the i-th sub-basin. For the preset reference rainfall, This represents the number of time periods corresponding to the average confluence delay time in the upstream basin. Indicates will Limited to the interval The truncation function within.

[0032] In one specific embodiment of the present invention, the weight of the i-th sub-basin According to the The confluence delay time from the outlet of each sub-basin to the reservoir section is determined, and sub-basins with shorter confluence delay times are assigned greater weights. The weights of all sub-basins are then normalized. Precursor indicators of rainfall-induced runoff Prioritize responses to rainfall in sub-basins that contribute more quickly to the rise in inflow.

[0033] In one specific embodiment of the present invention, the sliding window length mentioned in step S4 The expression is: In the formula, and Forecast period The corresponding upper and lower limits of window length, For the floor function, Between the upper and lower limits, depending on the hydrological indicators Linear interpolation and rounding are used to shorten the historical data window used for weight estimation when the current flood is more severe or the forecast period is longer; for any condition satisfying... The two prediction period numbers are: and .

[0034] In one specific embodiment of the present invention, the upper limit of the window length is... and lower limit The validation set is used for each forecast period The optimal selection criteria are as follows: the selection criteria are to make the deterministic accuracy of the ensemble probability forecast on the validation set optimal for the given forecast period; and for short forecast periods where the weights of the member models are relatively stable over time, a larger upper and lower window limit is assigned to suppress the weight estimation jitter caused by insufficient samples; and for long forecast periods where the correlation between the forecast error of the member models and the corresponding weights changes rapidly over time, a smaller upper and lower window limit is assigned to ensure rapid tracking of the current optimal member model.

[0035] In one specific embodiment of the present invention, step S4 employs an asymmetric window adjustment strategy for the fluctuation phase of the inbound flow: when the inbound flow is in the rising phase, the sliding window length... With water condition indicators Increase the rate of increase and shorten the sliding window; when the inflow is in a declining phase, the sliding window length... The price recovers gradually over time in defined steps, with the recovery rate being less than the shortening rate of the upward phase.

[0036] In one specific embodiment of the present invention, the average log-likelihood function of the local Bayesian model with time-decrease factor in step S5 is: In the formula, For the sub-prediction model weight vector; The variance vector is formed by the variances corresponding to each sub-prediction model; The time period number within the window; for Real-time inflow observation values; For the k-th member model pair Timeframe, Forecast Period Forecast value of inflow; and The two numbers to be solved are the first and second numbers. Weights and variances of each member model; Indicated by For the mean, For variance, in Normal probability density function for values ​​taken at each location; time decay factor ,in, As the attenuation reference value, The attenuation adjustment coefficient and the two satisfy the following conditions: Thus ensuring .

[0037] In one specific embodiment of the present invention, the redundancy reduction correction in step S5 specifically includes: [The text abruptly ends here, likely due to an incomplete source.] For the first in the window For each member model's prediction error sequence, calculate the correlation coefficient between each pairwise error sequence, and define the reciprocal of the error correlation strength: In the formula, For the first The inverse of the error correlation strength of each member model, For the first The and the first The correlation coefficients between the error sequences of the nth member model; for the nth Weights of each member model After correction and normalization, the time-varying weights after redundancy removal are obtained. The expression is: In the formula, For the first The inverse of the error correlation strength of each member model, For the first The weights of each member model.

[0038] In one specific embodiment of the present invention, step S6 employs water condition indicators. Increased sharpness index The weighted sharpening intensity is characterized by the following expression: ,in, To sharpen the baseline value and , To sharpen the adjustment coefficient and , to sharpen index With water condition indicators As the weight increases, the weight distribution also concentrates towards the member models with larger weights. Sharpening weight The calculation formula is: In the formula, Indicates the first Time-varying weights after redundancy removal from the member model of Power; Indicates the first Time-varying weights after redundancy removal from the member model of Power; Deterministic point forecasts are as follows: In the formula, For the first Member model pair Timeframe, Forecast Period Forecast value of inflow; The total variance of the forecast is: Predicting the deterministic points Centered on, with The forecast interval is constructed based on the scale.

[0039] In one specific embodiment of the present invention, the K structurally distinct machine learning flood forecasting member models include at least three of the following: Long Short-Term Memory Network model, Gated Recurrent Unit model, Temporal Convolutional Network model, Transformer model, Artificial Neural Network model, Extreme Gradient Boosting Tree model, and Random Forest model.

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] Example 1 (1) Study area and data foundation This embodiment uses a reservoir in the Changjiang River basin of Jiangxi Province as the research object to forecast the inflow flood of the reservoir. A total of 29 rain gauge stations were set up in the basin, and inflow flow observations were conducted at the reservoir cross-section, collecting data on 25 flood events. The first 16 flood events were used as the training set, the 17th to 20th flood events as the validation set, and the 21st to 25th flood events as the test set.

[0042] Based on the underlying surface conditions, drainage system structure, and digital elevation model, the upstream basin was divided into three sub-basins. For each sub-basin, the Thiessen polygon method was used to calculate the time-series isotropic rainfall from station precipitation. The isotropic rainfall and inflow of each sub-basin were aligned by time to form a complete time-series dataset indexed by time.

[0043] (2) Member model construction and multi-step forecasting This embodiment uses seven models—Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Temporal Convolutional Network (TCN), Transformer, Artificial Neural Network (ANN), Extreme Gradient Boosting Tree (XGBoost), and Random Forest (RF)—to predict inflow floods for the next 1 to 7 hours. Each model takes historical rainfall and flow sequences from the previous 18 hours as input and employs a direct multi-step prediction strategy to output the inflow forecast values ​​for the next 1 to 7 hours in a single step.

[0044] The prediction accuracy metrics (Nash efficiency coefficient (NSE), root mean square error (RMSE), and mean absolute error (MAE)) of each member model on the test set are shown in Table 1.

[0045] Table 1. Prediction accuracy metrics for each model's test set during the 1-7 hour lead time.

[0046] As shown in Table 1, the forecast accuracy of each member model exhibits significant differences and complementarity across different lead times. In the 1-hour ultra-short-term lead time, the RMSE of RF and XGBoost is 61.60. and 61.83 The MAE values ​​were 38.96. and 36.48 Both are superior to LSTM (RMSE is 79.08). MAE is 53.53 This indicates that the tree model has good fitting ability in ultra-short-term forecasts. As the lead time extends to 4 hours or more, the advantages of time-series neural network models such as LSTM and TCN gradually become apparent; for example, the RMSE of LSTM is 131.85 for a 4-hour lead time. It is superior to RF's 134.74. And XGBoost's 138.13 The RMSE of TCN during the 7-hour forecast period was 170.98. This is better than XGBoost's 184.53. And LSTM's 183.47 This indicates that neural network models, which excel at capturing temporal dependencies, are more robust over longer foreseeability periods. Furthermore, ANN and Transformer generally outperform other models in both RMSE and MAE across all foreseeability periods, with Transformer achieving an RMSE of 236.93, particularly in the 7-hour foreseeability period. This indicates that its generalization ability in the flood forecasting task of this embodiment is relatively limited.

[0047] The results above indicate that each model has its own strengths and weaknesses under different forecast periods and hydrological conditions, and a single model cannot maintain optimal forecast performance across all forecast periods. Therefore, ensemble forecasting, which integrates the advantages of multiple structurally diverse member models, can compensate for the shortcomings of a single model in specific scenarios and improve the overall accuracy and reliability of forecasts across all forecast periods.

[0048] (3) Construction of hydrological indicators In this embodiment, let For the predicted time, first construct the flow rate amplitude component. It reflects the relative change in inflow rate between adjacent time periods: (1); In the formula, and They are respectively Time and Inbound traffic at any given time For the preset reference flow, Indicates will Limited to the interval The truncation function within. In this embodiment, the reference flow rate... Take the flow rate variation of adjacent time periods in the entire training set. The 90th quantile takes the value of This ensures that the flow rate fluctuation component during periods of sharp inflow is close to 1, while it is close to 0 during periods of stability, thus providing good differentiation.

[0049] Secondly, construct indicators of rainfall-induced runoff. This reflects the rainfall that has already fallen into the basin upstream, but has not yet been converted into inflow due to the confluence lag: (2); In the formula, For the first Each sub-basin Average rainfall over a period of time. For the first The weight of each sub-basin For the preset reference rainfall, This is the number of time periods accumulated in the previous period, and is taken as the number of time periods corresponding to the average confluence delay time of the upstream basin.

[0050] In this embodiment, the upstream watershed is divided into: Three sub-basins were identified. By calculating the cross-correlation function between the average rainfall sequence and the inflow sequence in each sub-basin, the optimal lag times between rainfall and inflow in the three sub-basins were obtained as approximately [values ​​missing]. , and The corresponding peak values ​​of the cross-correlation coefficients are approximately , and Based on this, the number of time periods corresponding to the average confluence delay is determined. (i.e., accumulated in the early stage) ); Sub-basin weight Based on the confluence delay time, the weights are normalized by the reciprocal of the delay time of each sub-basin. Sub-basins with shorter confluence delay times are assigned greater weights. In this embodiment, the weights of each sub-basin are set as follows: , , Reference rainfall Take the training set before each flood rise The median of the weighted cumulative areal rainfall over a given period is taken as... .

[0051] The final hydrological index is the maximum of the two values: (3); Precursor indicators of rainfall runoff generation after heavy rainfall in the upper reaches of the basin The inflow rate begins to rise synchronously with the rainfall; however, due to the rainfall-runoff response lag (the average runoff lag in this example is approximately 14-15 hours), the inflow rate does not show a significant inflection point until more than ten hours after the heavy rainfall. Therefore, several hours to more than ten hours before the inflection point of the inflow rate arrives, the hydrological indicators... That is, it has already been The preemptive rise allows for adaptive adjustments to parameters such as window length, time decay, and weight sharpening to occur before the flood surge, thus overcoming the deficiency that parameter adjustments always lag behind the flood process when relying solely on flow changes.

[0052] (4) Adaptive determination of sliding window length In this embodiment, for each forecast period Based on hydrological indicators With Forecast Period Two-dimensional adaptive determination of sliding window length: (4); In the formula, and Forecast period The corresponding upper and lower limits of window length, Let be the floor function, and for any satisfy and .

[0053] The upper and lower limits of the window length are determined by optimization on the validation set for each forecast period. The optimization criterion is to achieve the optimal deterministic accuracy of the ensemble probability forecast on the validation set for that forecast period, while also considering the robustness and tracking ability of the weight estimation: for short forecast periods where the weights of the member models are relatively stable over time, larger upper and lower limits of the window are assigned to suppress weight fluctuations; for long forecast periods where the error-weight correlation changes rapidly over time, smaller upper and lower limits of the window are assigned to ensure rapid tracking of the current optimal member model. In this embodiment, the upper and lower limits of the window length for each forecast period are optimized using the validation set, as shown in Table 2.

[0054] Table 2. Prediction accuracy metrics for each model's test set during the 1-7 hour lead time.

[0055] As shown in Table 2, the weights of the member model are relatively stable within a 1-hour lead time. Appropriately increasing the window size helps to suppress weight fluctuations. The upper and lower limits of the window are set as follows: , For forecast periods of 2 hours and above, the error-weight relationship changes rapidly over time, and excessively long windows will introduce outdated information. Therefore, smaller upper and lower limits of the window are uniformly adopted. , This ensures that the dynamic weight estimation can quickly track the current optimal member model. The above values ​​satisfy... and The constraint of monotonic non-increase with the forecast period.

[0056] Furthermore, this embodiment employs an asymmetric window adjustment strategy for the inflow fluctuation phases: when the inflow is rising, the window length shortens at the rising rate as the hydrological indicators increase; when the inflow is falling, the window length recovers gradually in limited steps, with the recovery rate less than the shortening rate during the rising phase. In this embodiment, the limited step size for the window recovery during the falling phase is set to 1.

[0057] (5) Time-varying weight estimation and redundancy reduction correction In length Within the sliding window, the average log-likelihood function of the local Bayesian model with a time-decrease factor is established: (5); In the formula, The time period number within the window. for Real-time inflow observation values For the first Member model pair Timeframe, Forecast Period The inflow forecast value, and The two numbers to be solved are the first and second numbers. Weights and variances of each member model. For For the mean, For variance, in The normal probability density function that takes values ​​at a given location.

[0058] The aging decay factor is: (6); in For attenuation reference value, The attenuation adjustment coefficient and the two satisfy the following conditions: To ensure This embodiment takes , During the stable period ( ) The decline is slow, especially during the precursor period of a sharp rise ( ) Recent samples receive higher weight.

[0059] The Expectation-Maximization (EM) algorithm is used to iteratively solve the log-likelihood function: in the expectation step, the implicit belonging probability of each member model at each time period is calculated based on the current weights and variance; in the maximization step, the weights of each member model are updated based on the implicit belonging probability and the time decay weights. With variance .

[0060] Then, redundancy reduction and weighting correction are performed. For the first in the window The prediction error sequence of each member model, Given the member model index, calculate the correlation coefficient between each pair of member error sequences. And define the reciprocal of the error correlation strength: (7); The weights are corrected and normalized using the following formula to obtain the time-varying weights after redundancy removal: (8); In the formula, For the first The inverse of the error correlation strength of each member model, For the first The weights of each member model.

[0061] (6) Weight sharpening and probability forecast output In this embodiment, a sharpening index that increases with the increase of hydrological indicators is used. Characterizes the weighted sharpening intensity: (9); In the formula To sharpen the baseline value and , To sharpen the adjustment coefficient and This embodiment takes , .

[0062] The time-varying weights after redundancy removal are then sharpened to obtain the sharpened weights: (10); Based on this, the deterministic point forecast is calculated: (11); In the formula, For the first Member model pair Timeframe, Forecast Period The inflow forecast value.

[0063] The total forecast variance consists of two parts: the variance of the member models themselves and the dispersion among the member models. (12); In deterministic point forecast Centered on, with Using a given confidence level as the scale, forecast intervals are constructed, and the output is a probabilistic forecast result for the inflow flood ensemble, containing both deterministic point forecasts and probabilistic forecast intervals. In this embodiment, the confidence level for the probabilistic forecast interval is set to 90%.

[0064] It should be noted that the above sliding window length , aging decay factor With sharpening index All three are based on the same hydrological index. Unified driver: When because During the period leading up to a sharp rise in floodwaters, the window length shortens, the time-dependent decay accelerates, and the sharpening intensifies. All three simultaneously switch towards a "short window, rapid decay, and strong sharpening" configuration, allowing the ensemble weights to quickly focus on the member model that performs best under the current flood conditions. During the stable period... The three factors converge and revert to a long window, slow decay, and weak sharpening to ensure the robustness of the weight estimation.

[0065] (7) Verification results To verify the beneficial effects of the present invention, this embodiment is systematically verified on the test set. The comparison of NSE, RMSE, and MAE of the traditional BMA and the method of the present invention at various prediction periods is shown in Table 3.

[0066] Table 3 Comparison of Predictive Accuracy of Traditional BMA and the Invention Method at Various Forecast Periods

[0067] As shown in Table 3, the method of this invention outperforms the traditional BMA in all three indicators (NSE, RMSE, and MAE) for each forecast period, and the improvement increases with the extension of the forecast period. In the 1-hour ultra-short-term forecast, RMSE decreased from 62.54 to 52.76; in terms of NSE, both reached 0.99 in the 1-hour forecast period, with no significant difference, because the accuracy of each member model in ultra-short-term forecasts is close to saturation. As the forecast period is extended to 7 hours, the forecast performance of the traditional BMA decreases significantly, while the advantages of the method of this invention continue to expand: RMSE decreased from 179.55 to 143.22, a decrease of about 20.2%; MAE decreased from 116.27 to 95.93, a decrease of about 17.5%; and NSE increased from 0.92 to 0.95, a relative improvement of about 3.3%. The above results indicate that the present invention, through a dynamic weight adjustment mechanism driven by hydrological adaptive factors, effectively suppresses the cumulative amplification effect of errors in long forecast periods, and significantly improves the accuracy and stability of ensemble forecasts in long forecast periods.

[0068] Table 4 further presents the improvement percentage (%) of the traditional BMA method and the method of this invention compared to the best single member model for each forecast period. Both columns are calculated based on the best-performing single member model under the same forecast period. For example, the improvement percentage of NSE is calculated by subtracting the NSE of the best single model from the NSE of this method, and then dividing the result by the NSE of the best single model. The improvement percentage of RMSE is calculated by subtracting the RMSE of this method from the RMSE of the best single model, and then dividing the result by the RMSE of the best single model. The improvement percentage of MAE is calculated by subtracting the MAE of this method from the MAE of the best single model, and then dividing the result by the MAE of the best single model. A positive improvement percentage indicates that it is better than the best single model.

[0069] Table 4. Improvement (%) compared to the best single model

[0070] As shown in Table 4, the improvement of traditional BMA compared to the optimal single model is not stable. In multiple forecast periods of 1h, 5h, 6h, and 7h, there are even negative improvements (e.g., the improvements in NSE, RMSE, and MAE in 7h are -0.77, -5.01, and -3.36, respectively), indicating that fixed weights are difficult to effectively combine member models with increased performance fluctuations in long forecast periods. In contrast, the method of this invention shows positive improvements in RMSE and MAE in all forecast periods. The improvement in RMSE is maintained at a relatively high level of 12.56% to 16.24%, and the improvement in MAE is maintained at 10.70% to 14.95%. In terms of NSE, in the 1h forecast period, the accuracy of each single model is close to saturation (NSE≈0.99), so it is basically the same as the optimal single model. In the other forecast periods, the improvement in NSE increases significantly with the extension of the forecast period (from about 1.02% in 2h to about 2.15% in 7h). This fully demonstrates that the dynamic weight adjustment mechanism of the present invention can quickly capture the local evolution of member performance, promptly highlight the better model at the current stage, and weaken the interference of the error divergence model.

[0071] Table 5 shows a comparison of the forecast interval coverage (CR) and average width (AW) for each forecast period between the traditional BMA and the method of this invention.

[0072] Table 5 Comparison of Forecast Interval Coverage (%) and Average Width (m³ / s)

[0073] As shown in Table 5, the interval coverage of both methods is close to the nominal confidence level of 90%, indicating that both probabilistic forecasts have good reliability. However, in terms of average width, the forecast interval of the method in this invention is generally significantly smaller than that of the traditional BMA for each forecast period. For example, the 1-hour forecast interval decreases from 200.13 to 163.99, and the 7-hour forecast interval decreases from 552.00 to 428.42. This indicates that the method in this invention significantly narrows the forecast interval without sacrificing coverage, thereby improving the sharpness and information content of the probabilistic forecast. The reason for this is that the linkage of the three parameters enables the weights to quickly focus during the steep rise period, and the variance estimation is more in line with the current water situation, thus avoiding the problem of excessive widening of the interval in the long forecast period due to the static weights of the traditional BMA.

[0074] Figure 2 This is a comparison chart of the probabilistic forecasting performance of inflow flood ensemble in this embodiment of the invention. It is used to demonstrate the performance of the deterministic point forecast and probabilistic forecast interval of the method of the present invention under different lead times, and to compare it with the traditional Bayesian model averaging (BMA) method. Figure 2 This visually demonstrates the improvements of the present invention's method compared to traditional BMA in three aspects: peak flood tracking capability, long-term forecast accuracy and stability, and forecast interval sharpness. Figure 2Based on the observed patterns, as the forecast period extends from 1 hour to 7 hours, the point forecast curves of the method of this invention closely follow the measured process line throughout the entire forecast period, especially near each flood peak, where the degree of fit is significantly better than that of the traditional BMA. The forecast interval adaptively widens during periods of increased divergence among members, such as flood peaks, and adaptively narrows during periods of stability. The overall width is generally narrower than that of the traditional BMA interval for the same forecast period. Moreover, while narrowing the interval, it can still effectively enclose the measured process line, demonstrating higher probability forecast sharpness while maintaining coverage reliability.

[0075] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for ensemble probability forecasting of reservoir inflow floods based on hydrological adaptive forecasting, characterized in that, include: Step S1: Obtain time-by-time precipitation data and inflow observation data from multiple rain gauge stations in the upstream basin of the reservoir; The upstream basin is divided into several sub-basins, and the time-by-time average rainfall of each sub-basin is calculated. The average rainfall of each sub-basin is aligned with the inflow of water into the reservoir by time to form a complete time-series dataset indexed by time, and then divided into training set, validation set and test set in chronological order. Step S2: Construct K structurally distinct machine learning-based flood forecast member models. Each member model takes the average rainfall sequence and inflow sequence of each sub-basin within a preset historical window as input, and adopts a direct multi-step prediction strategy to output the future first to second... Forecast value of inflow for the next period, The foreseeable period number is denoted as , ; Step S3: At the predicted time The flow rate amplitude component is constructed based on the relative changes in inflow rate between adjacent time periods. ; Precursor indicators for rainfall-runoff generation are constructed based on the weighted cumulative amount of average rainfall in each sub-basin during the preceding cumulative period. The number of time periods in the early accumulation period is determined based on the basin confluence lag time; the flow amplitude component is taken. Precursor indicators of rainfall-induced runoff The larger one is used as the hydrological indicator. ; Step S4: For each forecast period Based on the aforementioned hydrological indicators With the aforementioned forecast period The length of the sliding window is determined by both dimensions. ,make Follow Increases and monotonically decreases, and follows It increases while monotonically decreasing; Step S5: In a length of Within the sliding window, establish a time-decrease factor. The average log-likelihood function of the local Bayesian model is obtained by solving the problem using the expectation-maximization algorithm, thus yielding the... Weights of each member model With variance , The time-decrease factor Follow Increase and decrease; then calculate the correlation strength between each pairwise prediction error sequence of each member model within the window, and perform weight reduction correction on redundant member models whose error correlation strength exceeds a preset threshold to obtain the time-varying weights after redundancy removal. ; Step S6: Use random The increased weight sharpening intensity affects the time-varying weights after redundancy removal. Sharpening is performed to obtain the sharpening weight. The predicted values ​​of each member model are weighted and summed according to the sharpening weights to obtain the deterministic point prediction; based on the sharpening weights and the variance... The forecast interval is constructed by considering the degree of dispersion between the forecast values ​​of each member model, and the ensemble probability forecast result of the inflow flood is output. Wherein, the sliding window length The aforementioned time-decrease factor The weighted sharpening intensity and the other two are derived from the same hydrological index. A unified driving force and coordinated action enable the aforementioned rainfall-induced runoff precursor indicators to... During the pre-flood surge, which is dominated by the rise of floodwaters, all three factors simultaneously shift towards a shorter window, faster attenuation, and stronger sharpening.

2. The method according to claim 1, characterized in that, The flow rate amplitude component in step S3 Precursor indicators of rainfall-induced runoff The calculation formula is as follows: ， ， In the formula: for Inbound traffic at all times for Inbound traffic at all times The preset reference flow rate; For the number of sub-basins, For sub-basin serial numbers, This refers to the time period number within the previous accumulated time period. For the first Each sub-basin Average rainfall over a period of time. Let i be the weight of the i-th sub-basin. For the preset reference rainfall, This represents the number of time periods corresponding to the average confluence delay time in the upstream basin. Indicates will Limited to the interval The truncation function within.

3. The method according to claim 2, characterized in that, Sub-basin weight According to the The confluence delay time from the outlet of each sub-basin to the reservoir section is determined, and sub-basins with shorter confluence delay times are assigned greater weights. The weights of all sub-basins are then normalized. .

4. The method according to claim 1, characterized in that, The sliding window length mentioned in step S4 Determine using the following formula: ， In the formula, and Forecast period The corresponding upper and lower limits of window length, Let be the floor function, and for any condition satisfying , The two prediction period numbers are: and .

5. The method according to claim 4, characterized in that, The upper limit of window length and lower limit The validation set is used for each forecast period The selection criteria are optimized to ensure that the deterministic accuracy of the ensemble probability forecast is optimal on the validation set for the given forecast period. For short forecast periods where the weights of the member models are relatively stable over time, a larger upper and lower window limit is assigned. For long forecast periods where the correlation between the forecast error of the member models and the corresponding weights changes rapidly over time, a smaller upper and lower window limit is assigned.

6. The method according to claim 1, characterized in that, In step S4, an asymmetric window adjustment strategy is adopted for the fluctuation phase of the inbound flow: when the inbound flow is in the rising phase, the sliding window length is adjusted. With water condition indicators Increase the sliding window length according to the rate of increase; when the inflow is in a declining phase, the sliding window length is... The price recovers gradually over time in defined steps, with the recovery rate being less than the shortening rate of the upward phase.

7. The method according to claim 1, characterized in that, The time-degradation factor mentioned in step S5 The mean log-likelihood function of the local Bayesian model is: ， In the formula: The time period number within the window; for Real-time inflow observation values; For the k-th member model pair Timeframe, Forecast Period Forecast value of inflow; and The two numbers to be solved are the first and second numbers. Weights and variances of each member model; Indicated by For the mean, For variance, in The normal probability density function that takes values ​​at a given location; The time-degradation factor ,in, As the attenuation reference value, The attenuation adjustment coefficient and the two satisfy the following conditions: .

8. The method according to claim 1, characterized in that, The redundancy reduction correction mentioned in step S5 specifically refers to: remember For the first in the window For each member model's prediction error sequence, calculate the correlation coefficient between each pairwise member error sequence, and define the reciprocal of the error correlation strength: In the formula, For the first The inverse of the error correlation strength of each member model, For the first The and the first The correlation coefficients between the error sequences of each member model; For the Weights of each member model After correction and normalization, the time-varying weights after redundancy removal are obtained. The expression is: In the formula, For the first The inverse of the error correlation strength of each member model, For the first The weights of each member model.

9. The method according to claim 1, characterized in that, Step S6 uses water condition indicators Increased sharpness index The weighted sharpening intensity is characterized by the following expression: ,in, To sharpen the baseline value and , To sharpen the adjustment coefficient and ; Sharpening weight The calculation formula is: In the formula, Indicates the first Time-varying weights after redundancy removal from the member model of Power of; Indicates the first Time-varying weights after redundancy removal from the member model of Power of; Deterministic point forecasts are as follows: In the formula, For the first Member model pair Timing, Forecast Period Forecast value of inflow; The total variance of the forecast is: Predicting the deterministic points Centered on, with The forecast interval is constructed based on the scale.

10. The method according to claim 1, characterized in that, The K structurally distinct machine learning flood forecasting member models include at least three of the following: Long Short-Term Memory Network (LSTM) model, Gated Recurrent Unit (GRU) model, Temporal Convolutional Network (TRC) model, Transformer model, Artificial Neural Network (ANN) model, Extreme Gradient Boosting Tree (EPB) model, and Random Forest model.

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