Runoff prediction method and system based on interpretable Bayesian gating circulation unit

Abstract

The invention discloses a runoff prediction method and system based on an interpretable Bayesian gated circulation unit (GRU), and the method comprises the steps: firstly introducing Bayesian reasoning into the GRU, constructing a new model for runoff prediction, carrying out the effective prediction of runoff, and quantifying the uncertainty of runoff prediction, and then, a prediction result of the newly built model is explained by using a SHAPs (SHapley Address Explanation) method, and the importance of the hydrometeorological indexes on runoff prediction is analyzed. The method has high practicability and generalizability, the precision is improved, meanwhile, the theoretical framework of runoff prediction is widened, the uncertainty in runoff prediction is quantified, the interpretability of the model is improved, and technical support can be provided for optimized resource allocation and reservoir operation for water resource management of a drainage basin.

Description

Technical Field

[0001] The invention belongs to the field of hydrological time series prediction, and in particular relates to a runoff prediction method and system based on interpretable Bayesian gated cyclic units. Background Art

[0002] Existing deep learning models generally lack interpretability and uncertainty quantification capabilities in hydrological runoff prediction, making it difficult to obtain reliable prediction results in practical applications, especially when faced with complex and changeable hydrological systems. Although traditional hydrological models based on physical processes have strict physical interpretations, they rely on high-quality physical data and have many limitations when dealing with nonlinear and highly complex hydrological processes. Data-driven methods, such as support vector machines (SVMs) and multi-layer perceptrons (MLPs), have achieved certain results in hydrological prediction, but still have the problem of insufficient characterization of complex nonlinear relationships.

[0003] In order to improve the accuracy of hydrological runoff prediction and the interpretability of the model, a deep learning model combining Bayesian inference and interpretable artificial intelligence methods was proposed to deal with the uncertainty problem in hydrological data and provide a reasonable explanation for the prediction results. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a runoff prediction method and system based on interpretable Bayesian gated cyclic units, aiming to improve the prediction accuracy, quantify the uncertainty in the prediction, and provide a clear explanation for the impact of hydrological and meteorological factors on the prediction, thereby enhancing the interpretability and practicality of the model.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A runoff prediction method based on interpretable Bayesian gated recurrent units, comprising the following steps:

[0007] Obtain the historical daily runoff data and hydrometeorological data of the hydrological station, preprocess and normalize the historical daily flow data and hydrometeorological data, and obtain the runoff sequence Y(t) and hydrometeorological sequence X1(t), X2(t),..., X N (t);

[0008] Determine the model time step q and lag period p, construct the model input data matrix; divide the input matrix into training set and test set;

[0009] The Bayesian inference algorithm is used to optimize the GRU model and build the EB-GRU runoff prediction model; the training set is used to train the established EB-GRU runoff prediction model;

[0010] Use the trained EB-GRU runoff prediction model to perform multi-step prediction on the test set to obtain the runoff data of the hydrological station;

[0011] The SHAP method is used to interpret the EB-GRU runoff prediction model and analyze the contribution of hydrometeorological indices to the model's runoff prediction results.

[0012] Preferably, the GRU model is optimized using a Bayesian inference algorithm, and the construction of an EB-GRU runoff prediction model includes:

[0013] The unit module of GRU consists of two "gate" structures and a candidate state update module, which jointly control the update process of the hidden state:

[0014] The reset gate is used to control the degree of resetting the hidden state, so that the model can effectively capture new information:

[0015] r t =σ(W r x t +U r h t-1 +b r )

[0016] In the formula, x t is the input at time t; W r and U r is the weight matrix of the reset gate; b r is the bias of the reset gate; σ is the Sigmoid activation function; h t-1 is the hidden layer information of the previous calculation period;

[0017] The update gate is used to control the extent to which the current hidden state retains information from the previous hidden state:

[0018] z t =σ(W z x t +U z h t-1 +b z )

[0019] Where W z and U z is the weight matrix of the update gate, b z To reset the gate bias;

[0020] Correct the previous hidden state by resetting the gate, and use the tanh hyperbolic tangent activation function to generate the candidate hidden state for the current time step And through the update gate, the hidden state and candidate state of the previous moment are combined to obtain the new hidden state c t , balance the updating of new information and the retention of historical information:

[0021]

[0022] In the formula, and is the same as the current input x t and the hidden state h at the previous time step t-1 The associated weight matrix, is the bias term of the candidate state, is the Hadamard product;

[0023] Bayesian reasoning is introduced based on the gated recurrent unit GRU, and the uncertainty in the prediction is quantified through the Monte Carlo MCDropout method.

[0024] Preferably, the prediction interval coverage probability PICP and the average prediction interval width MPIW are used to evaluate the quality of the prediction interval, and the calculation formula is:

[0025]

[0026] In the formula, [L i ,U i ] is the prediction interval, Ui is the upper bound of the prediction interval, Li is the lower bound of the prediction interval, d i In the prediction interval [L i ,U i ] is the number of observations in , and K is the number of observations.

[0027] Preferably, the SHAP method is used to interpret the EB-GRU runoff prediction model, and the contribution of the hydro-meteorological index to the model runoff prediction results is analyzed, including:

[0028]

[0029] Where (f, v) is the model output under state v, M is the set of all features, s′ is the feature subset, |s′| is the number of non-zero items in s′, and f v (s′) is the output of the model on the feature subset s′, f v (s′\i) is the prediction made by the model when using the feature subset.

[0030] The present invention also provides a runoff prediction system based on an interpretable Bayesian gated recurrent unit, comprising: an acquisition module, a data partitioning module, a model training module, a prediction module and a contribution evaluation module;

[0031] The acquisition module is used to acquire the historical daily runoff data and hydrometeorological data of the hydrological station, preprocess and normalize the historical daily flow data and hydrometeorological data, and obtain the runoff sequence Y(t) and the hydrometeorological sequence X1(t), X2(t),..., XN (t);

[0032] The data partitioning module is used to determine the model time step q and the lag period p, construct the model input data matrix; and divide the input matrix into a training set and a test set;

[0033] The model training module is used to optimize the GRU model using a Bayesian inference algorithm to construct an EB-GRU runoff prediction model; and to train the established EB-GRU runoff prediction model using a training set;

[0034] The prediction module is used to use the trained EB-GRU runoff prediction model to perform multi-step prediction on the test set to obtain the runoff data of the hydrological station site;

[0035] The contribution evaluation module is used to interpret the EB-GRU runoff prediction model using the SHAP method and analyze the contribution of the hydro-meteorological index to the model runoff prediction results.

[0036] Preferably, the GRU model is optimized using a Bayesian inference algorithm, and the construction of an EB-GRU runoff prediction model includes:

[0037] The unit module of GRU consists of two "gate" structures and a candidate state update module, which jointly control the update process of the hidden state:

[0038] The reset gate is used to control the degree of resetting the hidden state, so that the model can effectively capture new information:

[0039] r t =σ(W r x t +U r h t-1 +b r )

[0040] In the formula, x t is the input at time t; W r and U r is the weight matrix of the reset gate; b r is the bias of the reset gate; σ is the Sigmoid activation function; h t-1 is the hidden layer information of the previous calculation period;

[0041] The update gate is used to control the extent to which the current hidden state retains information from the previous hidden state:

[0042] z t =σ(W z x t +U z h t-1 +b z )

[0043] Where W z and U z is the weight matrix of the update gate, b z To reset the gate bias;

[0044] Correct the previous hidden state by resetting the gate, and use the tanh hyperbolic tangent activation function to generate the candidate hidden state for the current time step And through the update gate, the hidden state and candidate state of the previous moment are combined to obtain the new hidden state c t , balance the updating of new information and the retention of historical information:

[0045]

[0046] In the formula, and is the same as the current input x t and the hidden state h at the previous time step t-1 The associated weight matrix, is the bias term of the candidate state, is the Hadamard product;

[0047] Bayesian reasoning is introduced based on the gated recurrent unit GRU, and the uncertainty in the prediction is quantified through the Monte Carlo MCDropout method.

[0048] Preferably, the prediction interval coverage probability PICP and the average prediction interval width MPIW are used to evaluate the quality of the prediction interval, and the calculation formula is:

[0049]

[0050] In the formula, [L i ,U i ] is the prediction interval, Ui is the upper bound of the prediction interval, Li is the lower bound of the prediction interval, d i In the prediction interval [L i ,U i ] is the number of observations in , and K is the number of observations.

[0051] Preferably, the SHAP method is used to interpret the EB-GRU runoff prediction model, and the contribution of the hydro-meteorological index to the model runoff prediction results is analyzed, including:

[0052]

[0053] Where (f, v) is the model output under state v, M is the set of all features, s′ is the feature subset, |s′| is the number of non-zero items in s′, and f v (s′) is the output of the model on the feature subset s′, fv (s′\i) is the prediction made by the model when using the feature subset.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] The interpretable Bayesian gated unit (EB-GRU) model of the present invention can effectively quantify the uncertainty in the prediction process while improving the accuracy of runoff prediction, and provide an explanatory analysis of the contribution of hydrological and meteorological factors. Compared with traditional models, the EB-GRU runoff prediction model has higher prediction reliability, especially in the short-term runoff dynamic prediction. In addition, the model combines Bayesian inference and SHAP methods, making the prediction results not only more accurate, but also clearly interpretable, providing important decision-making support for water resources management and flood prevention and disaster reduction. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0057] Figure 1 A schematic diagram of an EB-GRU runoff prediction model according to an embodiment of the present invention;

[0058] Figure 2 Schematic diagram of the GRU unit structure of an embodiment of the present invention;

[0059] Figure 3 A schematic diagram of the importance of precipitation, temperature and water level data at the Qilianshan Station according to an embodiment of the present invention;

[0060] Figure 4 A schematic diagram of PICP values ​​predicted by EB-GRU intervals at different lag periods according to an embodiment of the present invention;

[0061] Figure 5 Schematic diagram of MPIW value of EB-GRU interval prediction under different lag periods according to an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] Embodiment 1

[0065] The present invention provides a runoff prediction method based on an interpretable Bayesian gated unit (EB-GRU) model, such as Figure 1 As shown, the specific steps include:

[0066] Step 1: Data collection: obtain the historical daily runoff data and water level data of the hydrological stations in the middle and lower reaches of the Yangtze River, collect precipitation and temperature data from the meteorological stations, preprocess and normalize the data, and obtain the runoff series Y(t) and the index series X1(t), X2(t),...,X N (t);

[0067] Step 2: Determine the time step q and lag time p, construct the model input data matrix, and divide the input matrix into a training set and a test set. In this study, the time step is set to 4 days.

[0068] Step 3: Model training: Use the training dataset to train the EB-GRU runoff prediction model that combines Bayesian inference and GRU to quantify uncertainty;

[0069] The EB-GRU runoff prediction model is specifically:

[0070] The unit module of GRU consists of two "gate" structures and a candidate state update module, such as Figure 2 As shown, these modules jointly control the update process of the hidden state:

[0071] a. The reset gate is used to control the degree of resetting the hidden state, so that the model can effectively capture new information:

[0072] r t =σ(W r x t +U r h t-1 +b r )

[0073] In the formula, x t is the input at time t; W r and U r is the weight matrix of the reset gate; b r is the bias of the reset gate; σ is the Sigmoid activation function; h t-1 is the hidden layer information of the previous calculation period;

[0074] b. The update gate is used to control the extent to which the current hidden state retains the information of the previous hidden state:

[0075] z t =σ(W z x t +U z h t-1 +b z )

[0076] In the formula, W z and U z is the weight matrix of the update gate, b z To reset the gate bias;

[0077] c. Correct the previous hidden state by resetting the gate, and use the tanh hyperbolic tangent activation function to generate the candidate hidden state for the current time step And through the update gate, the hidden state and candidate state of the previous moment are combined to obtain the new hidden state c t , in order to balance the updating of new information and the retention of historical information

[0078]

[0079] In the formula, and is the same as the current input x t and the hidden state h at the previous time step t-1 The associated weight matrix, is the bias term of the candidate state, is the Hadamard product.

[0080] Bayesian inference is introduced based on the GRU network, and the uncertainty in the prediction is quantified through the Monte Carlo (MC) Dropout method.

[0081] Step 4: Model prediction. Use the trained EB-GRU model to make multi-step predictions for runoff under a lag period of 1-7 days. Use the Nash-Sutcliffe efficiency coefficient (NSE) and relative root mean square error (RRMSE) to verify the accuracy of the model prediction. The calculation formulas for NSE and RRMSE are:

[0082]

[0083] Where K is the number of observations during the test period, y for,i is the predicted value, y obs,i is the observed value, is the mean of the observed sample.

[0084] Step 5, uncertainty and performance assessment, uses the prediction interval coverage probability (PICP) and mean prediction interval width (MPIW) to assess the quality of the prediction interval for runoff ( Figure 4 and Figure 5 ), the formulas are as follows:

[0085]

[0086]

[0087] In the formula, [y Li ,y Ui ] is the prediction interval, Ui is the upper bound, Li is the lower bound, d i is in the prediction interval [y Li ,y Ui ] is the number of observations within ].

[0088] Step 6: Interpretability analysis, using the SHapley Additive exPlanations (SHAP) method to calculate the Shapley value of each predictor, interpret the prediction results of the EB-GRU runoff prediction model, and evaluate the contribution of precipitation, water level, and temperature indicators at the Qilianshan station to the flow prediction, such as Figure 3 As shown, the calculation formula is as follows:

[0089]

[0090] Where i is the indicator to be evaluated, (f, v) is the model output under state v, M is the set of all features, including precipitation, water level and temperature, s′ is the feature subset consisting of i removed from M, |s′| is the number of non-zero items in s′, and f v (s′) is the output of the model on the feature subset s′, f v (s′\i) is the prediction made by the model when using a subset of features (all features except for the same instance v).

[0091] The daily runoff data of Qilianshan Station were analyzed using two control groups and the present prediction model. The two control groups were multilayer perceptron (MLP) and support vector machine (SVM), as shown in Table 1. The prediction accuracy of different prediction times was evaluated using NSE and RRMSE.

[0092] Table 1

[0093]

[0094]

[0095] It can be seen from Table 1 that the RRMSE value of the prediction model of the present invention is smaller than that of the control group model, and the NSE value is larger than that of the control group model, which shows that the prediction effect of the present model is better than other models at different lead times, and the EB-GRU prediction model can improve the prediction accuracy.

[0096] Embodiment 2

[0097] The present invention also provides a runoff prediction system based on an interpretable Bayesian gated recurrent unit, comprising: an acquisition module, a data partitioning module, a model training module, a prediction module and a contribution evaluation module;

[0098] The acquisition module is used to obtain the hydrological data of the hydrological station and the meteorological data of the meteorological station, preprocess and normalize the historical daily flow data and meteorological data, and obtain the runoff sequence Y(t) and the hydrological and meteorological sequence X1(t), X2(t),..., X N (t);

[0099] The data partitioning module is used to determine the model time step q and lag period p, construct the model input data matrix; divide the input matrix into training set and test set;

[0100] The model training module is used to optimize the GRU model using the Bayesian inference algorithm and construct the EB-GRU runoff prediction model; the training set is used to train the established EB-GRU runoff prediction model;

[0101] The prediction module is used to use the trained EB-GRU runoff prediction model to perform multi-step predictions on the test set to obtain the runoff data of the hydrological station;

[0102] The contribution evaluation module is used to interpret the EB-GRU runoff prediction model using the SHAP method and analyze the contribution of the hydro-meteorological index to the model runoff prediction results.

[0103] In this embodiment, the Bayesian inference algorithm is used to optimize the GRU model, and the construction of the EB-GRU prediction model includes:

[0104] The unit module of GRU consists of two "gate" structures and a candidate state update module, which jointly control the update process of the hidden state:

[0105] The reset gate is used to control the degree of resetting the hidden state, so that the model can effectively capture new information:

[0106] r t =σ(W r x t +U r h t-1 +b r )

[0107] In the formula, x t is the input at time t; W r and U r is the weight matrix of the reset gate; b r is the bias of the reset gate; σ is the Sigmoid activation function; ht-1 is the hidden layer information of the previous calculation period;

[0108] The update gate is used to control the extent to which the current hidden state retains information from the previous hidden state:

[0109] z t =σ(W z x t +U z h t-1 +b z )

[0110] Where W z and U z is the weight matrix of the update gate, b z To reset the gate bias;

[0111] Correct the previous hidden state by resetting the gate, and use the tanh hyperbolic tangent activation function to generate the candidate hidden state for the current time step And through the update gate, the hidden state and candidate state of the previous moment are combined to obtain the new hidden state c t , balance the updating of new information and the retention of historical information:

[0112]

[0113] In the formula, and is the same as the current input x t and the hidden state h at the previous time step t-1 The associated weight matrix, is the bias term of the candidate state, is the Hadamard product;

[0114] Bayesian reasoning is introduced based on the gated recurrent unit GRU, and the uncertainty in the prediction is quantified through the Monte Carlo MCDropout method.

[0115] In this embodiment, the prediction interval coverage probability PICP and the average prediction interval width MPIW are used to evaluate the quality of the prediction interval, and the calculation formula is:

[0116]

[0117] In the formula, [y Li ,y Ui ] is the prediction interval, d i is in the prediction interval [y Li ,y Ui ], Ui is the upper bound, Li is the lower bound, and K is the number of observations.

[0118] In this example, the SHAP method is used to interpret the EB-GRU runoff prediction model, and the contribution of the hydro-meteorological index to the model runoff prediction results is analyzed, including:

[0119]

[0120] Where (f, v) is the model output under state v, M is the set of all features, s′ is the feature subset, |s′| is the number of non-zero items in s′, and f v (s′) is the output of the model on the feature subset s′, f v (s′\i) is the prediction made by the model when using the feature subset.

[0121] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A runoff prediction method based on interpretable Bayesian gated recurrent units, characterized in that: The following steps are involved: Obtain the historical daily runoff data and hydrometeorological data of the hydrological station, preprocess and normalize the historical daily flow data and hydrometeorological data, and obtain the runoff series Y(t) and hydrometeorological series X1(t), X2(t),..., X N (t); Determine the model time step q and lag period p, construct the model input data matrix; divide the input matrix into training set and test set; The Bayesian inference algorithm is used to optimize the GRU model and build the EB-GRU runoff prediction model; the training set is used to train the established EB-GRU runoff prediction model; Use the trained EB-GRU runoff prediction model to perform multi-step prediction on the test set to obtain the runoff data of the hydrological station; The SHAP method is used to interpret the EB-GRU runoff prediction model and analyze the contribution of hydrometeorological indices to the model's runoff prediction results.

2. The runoff prediction method based on interpretable Bayesian gated recurrent units according to claim 1, characterized in that: The Bayesian inference algorithm is used to optimize the GRU model, and the EB-GRU runoff prediction model is constructed, including: The unit module of GRU consists of two "gate" structures and a candidate state update module, which jointly control the update process of the hidden state: The reset gate is used to control the degree of resetting the hidden state, so that the model can effectively capture new information: r t =σ(W r x t +U r h t-1 +b r ) In the formula, x t is the input at time t; W r and U r is the weight matrix of the reset gate; b r is the bias of the reset gate; σ is the Sigmoid activation function; h t-1 is the hidden layer information of the previous calculation period; The update gate is used to control the extent to which the current hidden state retains information from the previous hidden state: z t =σ(W z x t +U z h t-1 +b z ) Where W z and U z is the weight matrix of the update gate, b z To reset the gate bias; Correct the previous hidden state by resetting the gate, and use the tanh hyperbolic tangent activation function to generate the candidate hidden state for the current time step And through the update gate, the hidden state and candidate state of the previous moment are combined to obtain the new hidden state c t , balance the updating of new information and the retention of historical information: In the formula, and is the same as the current input x t and the hidden state h at the previous time step t-1 The associated weight matrix, is the bias term of the candidate state, is the Hadamard product; Bayesian reasoning is introduced based on the gated recurrent unit GRU, and the uncertainty in the prediction is quantified through the Monte Carlo MCDropout method.

3. The runoff prediction method based on interpretable Bayesian gated recurrent units according to claim 1, characterized in that: The quality of the prediction interval is evaluated using the prediction interval coverage probability PICP and the average prediction interval width MPIW, calculated as follows: In the formula, [L i ,U i ] is the prediction interval, Ui is the upper bound of the prediction interval, Li is the lower bound of the prediction interval, d i In the prediction interval [L i ,U i ] is the number of observations in , and K is the number of observations.

4. The runoff prediction method based on interpretable Bayesian gated recurrent units according to claim 1, characterized in that: The SHAP method is used to interpret the EB-GRU runoff prediction model, and the contribution of hydro-meteorological indices to the model runoff prediction results is analyzed, including: Where (f, v) is the model output under state v, M is the set of all features, s′ is the feature subset, |s′| is the number of non-zero items in s′, and f v (s′) is the output of the model on the feature subset s′, f v (s′\i) is the prediction made by the model when using the feature subset.

5. A runoff prediction system based on interpretable Bayesian gated recurrent units, characterized in that: include: Acquisition module, data partitioning module, model training module, prediction module and contribution evaluation module; The acquisition module is used to acquire the historical daily runoff data and hydrometeorological data of the hydrological station, preprocess and normalize the historical daily flow data and hydrometeorological data, and obtain the runoff sequence Y(t) and the hydrometeorological sequence X1(t), X2(t),..., X N (t); The data partitioning module is used to determine the model time step q and the lag period p, construct the model input data matrix; and divide the input matrix into a training set and a test set; The model training module is used to optimize the GRU model using a Bayesian inference algorithm to construct an EB-GRU runoff prediction model; and to train the established EB-GRU runoff prediction model using a training set; The prediction module is used to use the trained EB-GRU runoff prediction model to perform multi-step prediction on the test set to obtain the runoff data of the hydrological station site; The contribution evaluation module is used to interpret the EB-GRU runoff prediction model using the SHAP method and analyze the contribution of the hydro-meteorological index to the model runoff prediction results.

6. The runoff prediction system based on interpretable Bayesian gated recurrent units according to claim 5, characterized in that: The Bayesian inference algorithm is used to optimize the GRU model, and the EB-GRU prediction model is constructed including: The unit module of GRU consists of two "gate" structures and a candidate state update module, which jointly control the update process of the hidden state: The reset gate is used to control the degree of resetting the hidden state, so that the model can effectively capture new information: r t =σ(W r x t +U r h t-1 +b r ) In the formula, x t is the input at time t; W r and U r is the weight matrix of the reset gate; b r is the bias of the reset gate; σ is the Sigmoid activation function; h t-1 is the hidden layer information of the previous calculation period; The update gate is used to control the extent to which the current hidden state retains information from the previous hidden state: z t =σ(W z x t +U z h t-1 +b z ) Where W z and U z is the weight matrix of the update gate, b z To reset the gate bias; Correct the previous hidden state by resetting the gate, and use the tanh hyperbolic tangent activation function to generate the candidate hidden state for the current time step And through the update gate, the hidden state and candidate state of the previous moment are combined to obtain the new hidden state c t , balance the updating of new information and the retention of historical information: In the formula, and is the same as the current input x t and the hidden state h at the previous time step t-1 The associated weight matrix, is the bias term of the candidate state, is the Hadamard product; Bayesian reasoning is introduced based on the gated recurrent unit GRU, and the uncertainty in the prediction is quantified through the Monte Carlo MCDropout method.

7. The runoff prediction system based on interpretable Bayesian gated recurrent units according to claim 5, characterized in that: The quality of the prediction interval is evaluated using the prediction interval coverage probability PICP and the average prediction interval width MPIW, calculated as follows: In the formula, [L i ,U i ] is the prediction interval, Ui is the upper bound of the prediction interval, Li is the lower bound of the prediction interval, d i In the prediction interval [L i ,U i ] is the number of observations in , and K is the number of observations.

8. The runoff prediction system based on interpretable Bayesian gated recurrent units according to claim 5, characterized in that: The SHAP method is used to interpret the EB-GRU runoff prediction model, and the contribution of hydro-meteorological indices to the model runoff prediction results is analyzed, including: Where (f, v) is the model output under state v, M is the set of all features, s′ is the feature subset, |s′| is the number of non-zero items in s′, and f v (s′) is the output of the model on the feature subset s′, f v (s′\i) is the prediction made by the model when using the feature subset.

Images