A medium- and long-term runoff probability forecasting method based on a hybrid vector autoregression and GARCH-Copula model

Abstract

The present invention discloses a medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model, including: collecting and collating a long series of medium- and long-term runoff data of the basin where the station to be forecast is located, selecting a forecasting model for simulation forecasting and analyzing the statistical characteristic parameters of the forecast error; performing dynamic probability forecasting without considering the spatiotemporal correlation of the residual errors of the multi-station runoff forecast; considering the correlation evolution characteristics of the time history and spatial dimensions of the residual errors of the multi-station runoff forecast, coupling the EGARCH model to eliminate the heteroscedasticity effect of the residual error sequence of the multi-station runoff forecast for dynamic probability forecasting; considering the correlation evolution characteristics of the time history and spatial dimensions of the residual errors of the multi-station runoff forecast, coupling the EGARCH-Copula function to improve the VAR model to describe the spatiotemporal correlation characteristics of the forecast residual errors. The present invention improves the forecast accuracy and reliability, and provides more accurate support information for water resources management decisions.

Description

Technical Field

[0001] The invention relates to a medium- and long-term hydrological forecasting technology in the field of water conservancy projects, and in particular to a medium- and long-term runoff probability forecasting method of a mixed vector autoregression and GARCH-Copula model. Background Art

[0002] Medium- and long-term runoff forecasts are an important basis for dispatching. Limited by the complexity of the medium- and long-term runoff formation process and the chaotic effects of the weather system, the existing single-value forecasting methods based on data-driven or physical process-driven methods still cannot provide accurate and reliable forecast information. At present, the time series method is commonly used to forecast the medium- and long-term runoff process. Such methods often assume that the residual sequence is a stable and independent white noise, which cannot accurately reflect the dynamic changes of the medium- and long-term runoff random terms. And it does not take into account that the forecast error will produce a multi-stage transmission relationship with the iterative recursion of the equation, resulting in the single-value forecast accuracy decreasing with the extension of the forecast period.

[0003] The generalized autoregressive conditionallyheteroskedastic (GARCH) model is a model that can describe the change process of future variance affected by past variance. It can be used to simulate and forecast non-stationary time series with time-varying parameters. It can also describe series with asymmetric fluctuation characteristics. It is an effective extension that considers the non-stationary change characteristics of runoff. However, the explicit expression of the GARCH model is difficult to track the nonlinear information and non-stationary characteristics of the natural runoff process. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to improve the shortcomings of the vector autoregression model in simulating and predicting the medium- and long-term runoff process based on the stationary error sequence, and to provide a medium- and long-term runoff probability forecasting method based on a hybrid vector autoregression and GARCH-Copula model.

[0005] Technical solution: The medium- and long-term runoff probability forecasting method of the hybrid vector autoregression and GARCH-Copula model of the present invention comprises the following steps:

[0006] S1. Convert the medium- and long-term runoff sequence into a stable runoff sample sequence, perform deterministic multi-station runoff single-value forecast on the stable runoff sample sequence based on the vector autoregression VAR model, and further perform deterministic single-value rolling forecast to obtain the runoff forecast value sequence and runoff forecast residual sequence for different forecast periods;

[0007] S2. Without considering the spatiotemporal correlation of multi-station runoff forecast residuals, generate a random scenario set of runoff forecast residuals in different forecast periods, superimpose the forecast residual random scenario set on the runoff forecast value of the vector autoregression model, perform dynamic probability forecasting, and obtain a rolling probability forecast random scenario set;

[0008] S3. Considering the correlated evolution characteristics of multi-station runoff forecast residuals in time and space dimensions, the EGARCH model is coupled to eliminate the heteroscedasticity effect of multi-station runoff forecast residual series for dynamic probability prediction, and a forecast residual scenario set and a runoff probability forecast scenario set that consider time-related uncertainty are generated;

[0009] S4. Considering the correlated evolution characteristics of the time and spatial dimensions of the multi-station runoff forecast residuals, the EGARCH-Copula function is coupled to improve the VAR model to describe the spatiotemporal correlation characteristics of the runoff forecast residuals, and generate a set of runoff probability forecast scenarios that consider the spatiotemporal correlation uncertainties.

[0010] Further, step S1 includes the following steps:

[0011] S11, medium- and long-term runoff series stabilization and transformation processing;

[0012] The ten-day runoff series of year N1 is subtracted from the multi-year mean and divided by the standard deviation of each decade to obtain the runoff observation result after removing the seasonal component; the calculation formula is:

[0013]

[0014] Among them, q i,t is the runoff sample value after de-seasonalization at the ith hydrological station in period t, i = 1, 2, ..., I, I is the total number of hydrological stations, q i,id(t) is the original runoff value of the ith hydrological station, id(t) represents the year and decade of time period t, is the multi-year average runoff value of the ten-day period corresponding to the ith hydrological station id(t), σ i,id(t) is the standard deviation of runoff in the ten-day period corresponding to the ith hydrological station id(t). The runoff sample values ​​after deseasonalization are arranged in chronological order to form a runoff sample sequence {q i,t};

[0015] S12, Single-value forecast of multi-station runoff based on vector autoregression VAR model;

[0016] By setting different lag periods h, an h-order autoregressive equation is established for the runoff series of each station at a regular rate, and the simultaneous form of the multi-station runoff autoregressive equation is constructed:

[0017]

[0018] Among them, Qi,t is the simulated value of runoff forecast at the ith hydrological station in period t; a i,t represents the residual error of runoff forecast at the ith hydrological station in period t; μ i is the constant term of the autoregressive equation of the runoff series of the ith hydrological station; π ij,h is the parameter coefficient of the influence of the i-th hydrological station on the j-th hydrological station in the past h periods, i,j=1,2,…,I; q i,t-1 is the runoff sample value after de-seasonalization at the ith hydrological station in period t-1, q i,t-h is the runoff sample value after removing seasonal components at the ith hydrological station in the th period;

[0019] S13, single value rolling forecast;

[0020] When a longer-term forecast plan is required, a rolling iterative forecast is performed based on the single-value forecast.

[0021] Further, step S2 includes the following steps:

[0022] S21, using Monte Carlo method to sample and generate a random scenario set of runoff forecast residuals;

[0023] According to the established random simulation model, random sampling of scenarios is carried out to establish a random scenario set of runoff forecast residuals in different forecast periods.

[0024]

[0025] in, represents the residual of runoff forecast of the lth scenario of the i-th hydrological station in the forecast period t before the period t-τ, i=1,2,…,I, l=1,2,…,L, τ=1,2,…τ0, I is the total number of hydrological stations, L is the total number of scenarios, τ0 is the total number of forecast periods;

[0026] S22, rolling probability forecast random scenario set generation;

[0027] The forecast residual random scenario set is superimposed on the runoff forecast value of the vector autoregression model to obtain the rolling probability forecast random scenario set that does not consider the temporal and spatial correlation uncertainty of the runoff forecast residual:

[0028]

[0029] in, It represents the runoff forecast value of the lth scenario predicted by the i-th hydrological station in the t-time period before the t-τ time period.

[0030] Further, step S3 includes the following steps:

[0031] S31. Analysis of time evolution characteristics of conditional variance of runoff forecast residuals;

[0032] The EGARCH model is introduced to perform autocorrelation fitting on the conditional variance of the residual sequence extracted from the VAR model, and the autocorrelation relationship of the residual variance and the correlation between the variance and the residual are found as follows:

[0033]

[0034] Among them, g(·) is the conditional variance regression equation of the residual sequence of runoff forecast, a i,t-p′,τ is the residual of runoff forecast at the ith hydrological station with a forecast period of tp′ and a forecast period of τ, p′ is the regression order of the residual of runoff forecast, w is the regression order of the conditional variance of the residual of runoff forecast, is the conditional variance of the residual sequence of runoff forecast at the ith hydrological station with a forecast period of t, is the conditional variance of the residual sequence of runoff forecast at the ith hydrological station with a forecast period of tw and a forecast period of τ.

[0035] S32, Modeling of residual series of runoff forecast based on EGARCH model;

[0036] The EGARCH (p, w) model is established for the residual sequence of runoff forecast at each station at regular intervals:

[0037] a i,t,τ =σ i,t,τ e i,t,τ

[0038]

[0039] Among them, e i,t,τ is the independent and identically distributed random error with zero mean and unit variance corresponding to the residual of runoff forecast for the i-th hydrological station for the forecast period t before the period t-τ, i.e., the forecast period τ; e i,t-u,τ+u is the independent and identically distributed random error with zero mean and unit variance corresponding to the residual of runoff forecast for the i-th hydrological station in the forecast period tu before the forecast period t-(τ+u), that is, the forecast period τ; σ i,t,τ is the conditional standard deviation of the residual series of runoff forecast for the ith hydrological station, forecasting for period t before period t-τ, i.e., with a forecast period of τ; is the conditional variance of the residual sequence of runoff forecast for the i-th hydrological station for the forecast period ts before the period t-(τ+s), i.e., the forecast period is τ, p is the regression order of the random error term,; α i,u and β i,s e i,t-u,τ+u and The coefficient, α i,0 and γ i are all real constants; β i,sIndicates the degree of fluctuation, γ i Indicates the degree of asymmetry;

[0040] S33, according to the runoff forecast value Q' i,t,τ and the corresponding runoff forecast residual a′ i,t,τ , calculate the runoff forecast residual sequence {a′ i,t,τ The correlation coefficient matrix R of a ;

[0041] S34, using Monte Carlo sampling to generate random error scenarios;

[0042] Generate a random error scenario set based on random sampling of the correlation coefficient matrix using Cholesky decomposition The description is as follows:

[0043] R a =AiA T

[0044]

[0045] Among them, A is the triangular matrix decomposed by Cholesky, A T is the transpose of A; The random error of the residual of the runoff forecast corresponding to the lth scenario at the ith hydrological station for the forecast period t before the period t-τ, i.e., the forecast period τ, is generated by random sampling based on Cholesky decomposition; is the random error of the lth scenario corresponding to the residual of the runoff forecast for the i-th hydrological station for the period t-τ before the period t, i.e., the forecast period τ;

[0046] S35, Generation of forecast residual scenario set considering time-dependent uncertainties;

[0047] According to a i,t,1 and Calculate the conditional variance of the residual of the runoff forecast for the i-th hydrological station in the t-th period before the t-1 period And according to Calculate the conditional variance corresponding to the random scenario in the next period Keep moving forward one period at a time, and make rolling forecasts of the conditional variance until the last period t = T set in advance, and calculate the forecast residual scenario set considering time-related uncertainty

[0048] S36, Generation of runoff probability forecast scenario set considering time-dependent uncertainties;

[0049] A set of forecast residual scenarios that will take into account time-dependent uncertainties The runoff forecast value series {Q′ i,t,τ}, calculate the runoff probability forecast scenario set considering time-dependent uncertainty predicted by the EGARCH model

[0050] Furthermore, in step S33, the correlation coefficient matrix R a The expression is;

[0051]

[0052] Where ρ(·) is the correlation coefficient.

[0053] Furthermore, the forecast residual scenario set considering time-dependent uncertainties The expression is:

[0054]

[0055] in, represents the residual of runoff forecast considering time-dependent uncertainty of the lth scenario predicted by the ith hydrological station in period t before period t-τ, It represents the conditional variance of the lth scenario of the i-th hydrological station predicted in the t-time period before the t-τ time period calculated by the EGARCH model, i=1,2,…,I,l=1,2,…,L,τ=1,2,…τ0, I is the total number of hydrological stations, L is the total number of scenarios, and τ0 is the total number of the forecast period.

[0056] Further, step S4 includes the following steps:

[0057] S41. Joint distribution of multivariate random variables of residuals of multi-station runoff forecast based on Copula function;

[0058] According to Sklar's theory, if we make the multivariate random variables (X1, X2, ..., X k ) of the joint distribution F(X1,X2,…,X k ) is expressed as the functions of its marginal distributions F1(X1), F2(X2),…, F k (X k ), name has a Copula function C that satisfies the following formula:

[0059] F(X1,X2,…,X k )=C·[F1(X1),F2(X2),…,F k (X k )]

[0060] If F1(X1),F2(X2),…,F k (X k) is continuous, then the function C is uniquely determined;

[0061] S42, Generation of forecast residual scenario set considering spatiotemporal correlated uncertainties;

[0062] The Copula parameters are used to perform random sampling simulation on the cumulative probability distribution of uncertainty, and the quantile points corresponding to each cumulative probability distribution are obtained through marginal distribution, and a random scenario set of conditional variance based on the forecast uncertainty of the Copula function is generated. And calculate the forecast residual scenario set considering the temporal and spatial correlation uncertainties

[0063] S43, generation of runoff probability forecast scenario set considering spatiotemporal related uncertainties;

[0064] The forecast residual scenario set will take into account the temporal and spatial correlated uncertainties The runoff forecast value series {Q′ i,t,τ}, calculate the runoff probability forecast scenario set based on the Copula function forecast considering the temporal and spatial correlation uncertainty

[0065] The system corresponding to the method includes:

[0066] The data processing unit is used to convert the medium- and long-term runoff sequence into a stable runoff sample sequence, perform deterministic multi-station runoff single-value forecast on the stable runoff sample sequence based on the vector autoregression VAR model, and further perform deterministic single-value rolling forecast to obtain the runoff forecast value sequence and runoff forecast residual sequence for different forecast periods;

[0067] The first probability forecast unit is used to generate a random scenario set of runoff forecast residuals in different forecast periods without considering the spatiotemporal correlation of multi-station runoff forecast residuals, superimpose the forecast residual random scenario set on the runoff forecast value of the vector autoregression model, perform dynamic probability forecasting, and obtain a rolling probability forecast random scenario set;

[0068] The second probability forecasting unit is used to couple the EGARCH model to eliminate the heteroscedasticity effect of the multi-station runoff forecast residual sequence under the condition of considering the correlated evolution characteristics of the time and spatial dimensions of the multi-station runoff forecast residuals, and to perform dynamic probability forecasting, thereby generating a forecast residual scenario set and a runoff probability forecast scenario set that consider time-related uncertainties;

[0069] The third probability forecasting unit is used to couple the EGARCH-Copula function to improve the VAR model to describe the spatiotemporal correlation characteristics of runoff forecast residuals, taking into account the correlated evolution characteristics of the time and spatial dimensions of multi-station runoff forecast residuals, and generate a set of runoff probability forecast scenarios that take into account the temporal and spatial correlation uncertainties.

[0070] An electronic device for storing and executing the method, comprising a memory and a processor, wherein:

[0071] A memory for storing computer programs that can be run on the processor;

[0072] The processor is used to execute the steps of the medium- and long-term runoff probability forecasting method of the mixed vector autoregression and GARCH-Copula model when running the computer program.

[0073] A storage medium for storing the method, wherein a computer program is stored on the storage medium, and when the computer program is executed by at least one processor, the steps of the medium- and long-term runoff probability forecasting method of the mixed vector autoregression and GARCH-Copula model are implemented.

[0074] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: on the basis of considering conditional heteroscedasticity and correlation between multiple variables, the error characteristics of medium- and long-term runoff forecasts can be quantitatively described and evaluated; in view of the shortcomings of simulating and predicting medium- and long-term runoff processes based on stationary error sequences, a medium- and long-term runoff probability forecasting method based on a mixed vector autoregression and GARCH-Copula model is used to simulate and forecast the dynamic change characteristics and multi-order correlation of runoff forecast residuals; a VAR model is used to model and forecast the conditional mean of multi-station runoff time series; and the conditional mean of the residual sequence extracted by the VAR model is used to predict the conditional mean of the residual sequence extracted by the VAR model. The EGARCH model is established based on the conditional variance of the EGARCH model, and the asymmetric influence of positive error and negative error on the variance is distinguished. The Copula function is used to construct the joint probability distribution of the conditional variance predicted by the EGARCH model, which characterizes the temporal and spatial nonlinear correlation of multiple residual time series, improves the fitting goodness of the residual simulation of runoff forecast in complex systems, and provides a reference method for improving accuracy and reducing uncertainty for medium- and long-term runoff probability forecasting. Compared with the traditional forecasting model that ignores the spatial fluctuation correlation characteristics among multiple variables, it narrows the range of probability forecasting and provides more reliable forecasting results for medium- and long-term scheduling decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 is a flow chart of the method of the present invention;

[0076] Figure 2 It is a schematic diagram of the runoff simulation results of the VAR model;

[0077] Figure 3 This is a schematic diagram of the runoff forecast results of the VAR model;

[0078] Figure 4 It is a schematic diagram of the deterministic single value forecast and runoff rolling probability forecast scenarios. DETAILED DESCRIPTION

[0079] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. However, it is obvious to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features known in the art are not described. The order of the relevant steps in the present invention is not restrictive, that is, it can be adjusted by those skilled in the art. The order in the present invention is a case-based writing method, not a restrictive description.

[0080] Copula function can flexibly handle multivariate joint distribution, is suitable for simulating multi-order related forecast uncertainty, and implicitly expresses the nonlinear changes of runoff process. Therefore, the present invention establishes a medium- and long-term runoff probability forecasting method based on Copula function using a hybrid vector autoregression and GARCH-Copula model, such as Figure 1 As shown, the following steps are included:

[0081] S1. Collect and organize the long series of medium- and long-term runoff sequences in the basin where the forecast station is located, select a vector autoregression model of appropriate order to simulate and forecast, and analyze the forecast error characteristics.

[0082] The specific steps include:

[0083] S11, medium- and long-term runoff series stabilization and transformation processing;

[0084] The vector autoregression model is a widely used time series analysis model. It needs to assume that the history and current status of random variables are representative or sustainable. This is a prerequisite for using equation fitting to predict future trend changes. An unsteady time series cannot reasonably explain future trend changes, which requires the data to be stable. Deseasonalization is an effective means to extract runoff components, reduce the complexity of the series, and transform it into a stable series.

[0085] The periodic components of the medium- and long-term runoff series of the station to be predicted are extracted to obtain a stable runoff sample sequence. The long- and medium-term runoff series at the ten-day scale of year N1 is subtracted from the multi-year mean and divided by the standard deviation of each ten-day scale, as shown in formula (1):

[0086]

[0087] Among them, q i,t is the runoff sample value after de-seasonalization at the ith hydrological station in period t, i = 1, 2, ..., I, I is the total number of hydrological stations (i.e., the total number of stations to be forecasted), q i,id(t) is the original runoff value of the ith hydrological station, id(t) represents the year and decade of time period t, is the multi-year average runoff value of the ten-day period corresponding to the ith hydrological station id(t), σ i,id(t) is the standard deviation of runoff in the ten-day period corresponding to the ith hydrological station id(t). The runoff sample values ​​after deseasonalization are arranged in chronological order to form a runoff sample sequence {q i,t}.

[0088] S12, Single-value forecast of multi-station runoff based on vector autoregression (VAR) model;

[0089] A vector autoregression (VAR) model is constructed for the runoff sample sequence of the stations to be predicted in the basin with similar underlying surface conditions to make single-valued runoff forecasts for multiple stations. Different lag periods h are set, and an h-order autoregression equation is established for the runoff sample sequence of each station at regular intervals. The simultaneous form of the multi-station runoff autoregression equation is constructed:

[0090]

[0091] Among them, Q i,t is the simulated value of runoff forecast at the ith hydrological station in period t; a i,t represents the residual error of runoff forecast at the ith hydrological station in period t; μ i is the constant term of the autoregressive equation of the runoff series of the ith hydrological station; π ij,h is the parameter coefficient of the impact of the ith hydrological station on the jth hydrological station in the past h periods, i, j = 1, 2, ..., I. In particular, when i = j, it represents the parameter coefficient of the impact of the runoff of this hydrological station itself in the past period on the runoff in the current period. When i ≠ j, it represents the parameter coefficient of the impact of the runoff of the ith hydrological station in the past period on the runoff of the jth hydrological station in the current period. q i,t-1 is the runoff sample value after de-seasonalization at the ith hydrological station in period t-1, q i,t-h is the runoff sample value after removing seasonal components at the ith hydrological station in the th period.

[0092] Figure 2 It is a schematic diagram of the runoff simulation results of the VAR model for deterministic forecasting. Figure 2 (a) shows the VAR model runoff forecast simulation value and the actual sample runoff value (i.e., the runoff sample sequence {q i,t}), Figure 2 (b) shows the VAR model runoff forecast simulation value and the actual sample runoff value (i.e., the runoff sample sequence {q i,t}), Figure 2 (c) shows the VAR model runoff forecast simulation residuals for the first hydrological station runoff. Figure 2 (d) shows the VAR model runoff forecast simulation residuals for the second hydrological station.

[0093] S13, deterministic single value rolling forecast;

[0094] The vector autoregression model expressed in formula (2) calculates the runoff forecast simulation value Q for the current period t based on the runoff samples from the past period th to the period t-1: i,t , runoff forecast simulation value Q i,t and the runoff sample value q i,t-1 There is only one period between them, that is, in essence, the equation can only provide the runoff forecast simulation value of the next adjacent period each time. The vector autoregression model expressed by equation (2) is applied to the runoff sample sequence during the test period. When a longer-term forecast scheme is required, a rolling iterative forecast is required.

[0095] For example, the i-th hydrological station predicts the runoff value Q′ for period t before period t-1, that is, the runoff forecast value Q′ for the forecast period 1 i,t,1 As shown in formula (3):

[0096] Q′ i,t,1 =f i (q 1,t-1 ,…,q i,t-1 ,…,q I,t-1 ,…,q 1,t-h ,…,q i,t-h ,…,q I,t-h ) (3)

[0097] Among them, the prediction f i (·) is the autoregressive equation of the ith hydrological station in equation (2), i = 1, 2, …, I.

[0098] Q′ i,t,1 Substituting it into the vector autoregression model, the runoff sequence for the next period t+1, that is, the forecast period of 2, can be predicted:

[0099] Q′ i,t+1,2 =f i (Q′ 1,t,1 ,…,Q′ i,t,1 ,…,Q′ I,t,1 ,…,q 1,t-1 ,…,q i,t-1 ,…,q I,t-1 ,…q 1,t-h+1 ,…,q i,t-h+1 ,…,q I,t-h+1 ) (4)

[0100] Among them, Q′ i,t+1,2 is the runoff forecast value of the i-th hydrological station in the t+1 period with a forecast period of 2.

[0101] Step forward one period at a time, substitute the runoff forecast value predicted by the vector autoregression model into the vector autoregression model, and calculate the runoff forecast value Q′ of the ith hydrological station for the period t before the period t-τ, i.e., the forecast period τ. i,t,τ Until the last period t=T set in advance, the forecast period is τ0, and the runoff forecast value is for:

[0102]

[0103] The runoff forecast values ​​of different forecast periods generated by the rolling forecast constitute the runoff forecast value sequence {Q′ i,t,τ}, runoff forecast residual a′ i,t,τ The residual sequence of runoff forecast {a′ i,t,τ}:

[0104] a′ i,t,τ =Q′ i,t,τ -q i,t (6)

[0105] Among them, a′ i,t,τ It represents the residual of runoff forecast when the ith hydrological station forecasts the runoff for period t before period t-τ, i.e., the forecast period is τ.

[0106] Figure 3 This is a schematic diagram of the single-value rolling forecast results of the VAR model. Figure 3 Medium (a) to Figure 3 (d) The forecast period of medium runoff forecast is divided into 1 to 4 time periods (ten days).

[0107] It can be seen that as the forecast period increases, the known quantities gradually decrease and the forecast values ​​gradually increase. Under the cumulative influence of forecast residuals, the forecast accuracy tends to decrease.

[0108] S2. Without considering the spatiotemporal correlation of multi-station runoff forecast residuals, it is assumed that the runoff forecast residuals are stationary white noise and obey Gaussian distribution, and dynamic probability forecasting is performed.

[0109] The specific steps include:

[0110] S21, generation of random scenario set for runoff forecast residual;

[0111] The Monte Carlo method is used for random sampling to establish a random scenario set of runoff forecast residuals for different forecast periods.

[0112]

[0113] in, It represents the residual of runoff forecast of the lth scenario of the i-th hydrological station forecasting the t-th period before the t-τ period, i=1,2,…,I, l=1,2,…,L, L is the total number of scenarios, τ=1,2,…τ0.

[0114] S22, rolling probability forecast random scenario set generation;

[0115] By superimposing the forecast residual random scenario set on the runoff forecast value of the vector autoregression model, the rolling probability forecast random scenario set without considering the spatiotemporal correlation uncertainty of the runoff forecast residual can be obtained:

[0116]

[0117] in, It represents the runoff forecast value of the lth scenario predicted by the i-th hydrological station in the t-time period before the t-τ time period.

[0118] S3, coupled EGARCH model to describe the heteroscedasticity of residual series of runoff forecast in different forecast periods for dynamic probability forecast;

[0119] The specific steps include:

[0120] S31. Analysis of time evolution characteristics of conditional variance of runoff forecast residuals;

[0121] The VAR model simulates and predicts the mean process of the hydrological time series, and its runoff forecast residual sequence has heteroscedasticity. That is, the fluctuation amplitude of the runoff forecast residual sequence is affected by random factors. Continuous large fluctuations are followed by large fluctuations, and continuous small fluctuations are followed by small fluctuations. The variance of the runoff forecast residual sequence will change over time. Moreover, the fluctuation amplitudes of positive and negative residuals are not equal, which is an asymmetric distribution. Therefore, the EGARCH model is introduced to perform autocorrelation fitting on the conditional variance of the runoff forecast residual sequence extracted from the VAR forecast model, find the autocorrelation relationship of the runoff forecast residual variance and the correlation between the variance and the residual (such as formula (9)), and study the law of its conditional variance changing over time.

[0122]

[0123] Among them, g(·) is the conditional variance regression equation of the residual sequence of runoff forecast, a i,t-p′,τ is the residual of runoff forecast at the ith hydrological station with a forecast period of tp′ and a forecast period of τ, p′ is the regression order of the residual of runoff forecast, w is the regression order of the conditional variance of the residual of runoff forecast, is the conditional variance of the residual sequence of runoff forecast at the ith hydrological station with a forecast period of t, is the conditional variance of the residual sequence of runoff forecast at the ith hydrological station with a forecast period of tw and a forecast period of τ.

[0124] S32, Modeling of residual series of runoff forecast based on EGARCH model;

[0125] The EGARCH (p, w) model is established for the residual sequence of runoff forecast at each station at regular intervals, as shown in equations (10) to (11).

[0126] a i,t,τ =σ i,t,τ e i,t,τ (10)

[0127]

[0128] Among them, e i,t,τ is the independent and identically distributed random error with zero mean and unit variance corresponding to the residual of runoff forecast of the ith hydrological station for the forecast period t before the period t-τ, i.e., the forecast period τ, and has a continuous distribution; e i,t-u,τ+u is the independent and identically distributed random error with zero mean and unit variance corresponding to the residual of runoff forecast for the i-th hydrological station in the forecast period tu before the forecast period t-(τ+u), that is, the forecast period τ; σ i,t,τ is the conditional standard deviation of the residual series of runoff forecast for the ith hydrological station, forecasting for period t before period t-τ, i.e., with a forecast period of τ; is the conditional variance of the residual sequence of runoff forecast for the ith hydrological station forecasting t periods before the t-τ period, i.e., with a forecast period of τ; is the conditional variance of the residual sequence of runoff forecast for the ith hydrological station for the forecast period ts before the period t-(τ+s), i.e., the forecast period is τ; α i,u and β i,s e i,t-u,τ+u and The coefficient of , p is the regression order of the random error term, w is the conditional variance regression order of the runoff forecast residual, α i,0 and γ i are real constants. i,s Indicates the degree of fluctuation, γ i Indicates the degree of asymmetry. If γ i =0, it means the forecast residual a i,t-1 The positive and negative values ​​of have a symmetrical effect on the fluctuation range. i ≠0, it means the forecast residual a i,t-1 The impact of positive and negative values ​​on volatility is asymmetric.

[0129] S33, calculating the correlation coefficient matrix of the runoff forecast residual sequence;

[0130] According to equations (3) to (5), the runoff forecast value Q′ is calculated i,t,τ , and the corresponding runoff forecast residual a′ is calculated i,t,τ. Calculate the residual sequence of runoff forecast {a′ i,t,τ The correlation coefficient matrix R of a :

[0131]

[0132] Where ρ(·) is the correlation coefficient.

[0133] S34, random error scenario set generation;

[0134] Given a correlation coefficient matrix, random sampling based on Cholesky decomposition can be used to generate a set of random error scenarios The description is as follows:

[0135] R a =AiA T (13)

[0136]

[0137] Among them, A is the triangular matrix decomposed by Cholesky, A T is the transpose of A; The random error of the residual of the runoff forecast corresponding to the lth scenario at the ith hydrological station for the forecast period t before the period t-τ, i.e., the forecast period τ, is generated by random sampling based on Cholesky decomposition; It is the random error of the lth scenario corresponding to the residual of the runoff forecast for the i-th hydrological station forecasting the t-time period before the t-τ time period, that is, the forecast period is τ. It is obtained by random sampling using the Monte Carlo simulation method and obeys the standard normal distribution.

[0138] S35, Generation of forecast residual scenario set considering time-dependent uncertainties;

[0139] A i,t,1 and Substituting into formula (15), calculate the conditional variance corresponding to the residual of runoff forecast of the ith hydrological station for the forecast period t before the period t-1, that is, the forecast period is 1:

[0140]

[0141] The calculated Substituting into formula (16), we can calculate the conditional variance corresponding to the random scenario in the next period:

[0142]

[0143] in, is the random error of the l-th scenario corresponding to the residual of the runoff forecast with a forecast period of τ when the ith hydrological station forecasts the period t+1-u before the period t-(τ+u-1) based on random sampling of Cholesky decomposition. It is the conditional variance of the residual sequence of runoff forecast for the i-th hydrological station forecasting the period t+1-s before the period t-(τ+s-1), that is, the forecast period is τ.

[0144] Keep moving forward one time period at a time and make rolling forecasts of the conditional variance until the last time period t=T set in advance.

[0145] According to formula (17), the forecast residual scenario set considering time-dependent uncertainty is calculated as

[0146]

[0147] in, represents the residual of runoff forecast considering time-dependent uncertainty of the lth scenario predicted by the ith hydrological station in period t before period t-τ, It represents the conditional variance of the lth scenario of the i-th hydrological station predicted in the t-time period before the t-τ time period calculated by the EGARCH model, i=1,2,…,I,l=1,2,…,L,τ=1,2,…τ0.

[0148] S36, Generation of runoff probability forecast scenario set considering time-dependent uncertainties;

[0149] A set of forecast residual scenarios that will take into account time-dependent uncertainties The runoff forecast value series {Q′ i,t,τ}, the runoff probability forecast scenario set considering time-dependent uncertainty predicted by the EGARCH model is calculated according to formula (18):

[0150]

[0151] in, In order to consider the time-related uncertainty, the i-th hydrological station predicts the runoff forecast value for period t before period t-τ, that is, the forecast period is τ.

[0152] S4. Considering the correlated evolution characteristics of the time and spatial dimensions of the multi-station runoff forecast residuals, the EGARCH-Copula function is coupled to improve the VAR model to describe the temporal and spatial correlation characteristics of the forecast residuals.

[0153] The specific steps include:

[0154] S41. Joint distribution of multivariate random variables of multi-site forecast residuals based on Copula function;

[0155] The variance equation in EGARCH describes the heteroskedasticity of a single variable using a nonlinear quasi-autoregressive function. The Copula function establishes a joint probability distribution for multivariate random variables. It can study the marginal distribution and correlation structure of multidimensional random variables separately, and does not require the marginal distribution of each variable to have the same distribution form. It can flexibly handle the nonlinear and asymmetric correlation between random variables. By coupling the EGARCH model and the Copula function, on the basis of describing the clustering of fluctuations in the residual sequence of runoff forecasts, a joint distribution between multidimensional conditional variances is constructed, identifying and implicitly describing the nonlinear correlation of multi-site runoff processes.

[0156] According to Sklar's theory, if we can make the multivariate random variables (X1, X2, ..., X k ) of the joint distribution F(X1,X2,…,X k ) is expressed as the functions of its marginal distributions F1(X1), F2(X2),…, F k (X k ), name has a Copula function C that satisfies the following formula:

[0157] F(X1,X2,…,X k )=C·[F1(X1),F2(X2),…,F k (X k )] (19)

[0158] If F1(X1),F2(X2),…,F k (X k ) is continuous, then the function C is uniquely determined.

[0159] Different Copula functions are used to connect the marginal distribution and joint distribution of each dimension of multivariate random variables, the parameters of the Copula function are estimated using the AIC criterion, and the KS test method is used for goodness of fit test, so as to describe and calculate the evolution characteristics of residual uncertainty on the basis of considering the spatiotemporal correlation.

[0160] S42, Generation of forecast residual scenario set considering spatiotemporal correlated uncertainties;

[0161] The Copula parameters are used to perform random sampling simulation on the cumulative probability distribution of uncertainty, and the quantile points corresponding to each cumulative probability distribution are obtained through marginal distribution, and a random scenario set of conditional variance based on the forecast uncertainty of the Copula function is generated.

[0162] According to formula (20), the forecast residual scenario set considering the temporal and spatial correlation uncertainty is calculated as

[0163]

[0164] in, represents the residual of runoff forecast considering the temporal and spatial correlation uncertainties of the l-th scenario predicted by the ith hydrological station in the t-th period before the t-τ period, is the conditional variance of the lth scenario predicted in period t by the ith hydrological station before period t-τ, randomly generated based on the Copula function, i=1,2,…,I,l=1,2,…,L,τ=1,2,…τ0.

[0165] S43, generation of runoff probability forecast scenario set considering spatiotemporal related uncertainties;

[0166] The forecast residual scenario set will take into account the temporal and spatial correlated uncertainties The runoff forecast value series {Q′ i,t,τ}, the runoff probability forecast scenario set considering the temporal and spatial correlation uncertainty based on the Copula function forecast is calculated according to formula (21):

[0167]

[0168] in, In order to consider the time and space related uncertainties, the i-th hydrological station predicts the runoff forecast value for period t before period t-τ, that is, the forecast period is τ.

[0169] Figure 4 It is a schematic diagram of the deterministic single value forecast and runoff rolling probability forecast scenarios. Figure 4 Medium (a) to Figure 4 (d) The forecast period of runoff forecast is divided into 1 to 4 time periods (ten days). The red line is the runoff series of the VAR model deterministic single-value rolling forecast, the blue interval is the probability prediction interval assuming that the forecast residual follows a normal distribution, the green interval is the probability prediction interval considering the time-related uncertainty of the forecast residual, and the yellow interval is the probability prediction interval considering the time-related uncertainty of the forecast residual. Figure 4 It is intuitively demonstrated that the average domain width of the probability prediction interval considering the spatiotemporal correlation uncertainty of the forecast residuals is the narrowest.

[0170] The probability forecast results are evaluated and tested from the two aspects of "accuracy" and "reliability".

[0171] Forecast accuracy is usually measured by the root mean square error (RMSE), which reflects the average deviation between the forecast value and the observed value. The mathematical expression of the root mean square error is as follows:

[0172]

[0173] Where T represents the total number of forecast periods, i.e. the length of the forecast period, and y t is the runoff sample value, f(X t ) is the runoff forecast value, e t is the absolute error. The root mean square error (RMSE) is used to evaluate the single-value forecast effect of multi-station runoff based on the vector autoregression (VAR) model. The smaller the root mean square error, the higher the accuracy.

[0174] For a good probabilistic forecast, its forecast results should have low uncertainty and high accuracy and reliability. The narrower the probability forecast interval is, the higher the probability of covering the observed runoff is, the higher its accuracy is and the lower its uncertainty is, so the relative interval width (RIW) is used to characterize it.

[0175] RIW is defined as the average interval width (IW) divided by the coverage ratio CR:

[0176]

[0177] in, and They represent the minimum and maximum forecast values ​​for time period t, respectively. It indicates the number of observed runoffs included in the forecast interval. The value of RIW varies from 0 to +∞. The smaller the value, the lower the forecast uncertainty and the better the forecast effect.

[0178] IW is the average forecast interval width, and the interval width is the difference between the maximum and minimum values ​​predicted at the same time. The smaller the IW value, the closer the forecast interval is to reflecting important uncertainty information. The larger the IW value, that is, the wider the forecast interval, the lower the value of the forecast information. CR is the ratio of the number of observed runoffs included in the forecast interval to the total number of observed runoffs. The larger the CR value, the higher the probability that the number of observed runoffs falls within the forecast interval.

[0179] In summary, the method of the present invention first converts the medium- and long-term runoff sequence into a stable runoff sample sequence, performs deterministic multi-station runoff single-value forecasting on the stable runoff sample sequence based on the vector autoregression model VAR, and further performs deterministic single-value rolling forecasting to obtain the runoff forecast value sequence and runoff forecast residual sequence for different forecast periods; secondly, without considering the spatiotemporal correlation of the multi-station runoff forecast residuals, generates a random scenario set of runoff forecast residuals for different forecast periods, and superimposes the random scenario set of forecast residuals on the runoff forecast value sequence of the vector autoregression model. values, and perform dynamic probability forecasts to obtain a random scenario set for rolling probability forecasts; then, considering the correlated evolution characteristics of the time and spatial dimensions of the multi-station runoff forecast residuals, the EGARCH model is coupled to perform autocorrelation fitting on the conditional variance of the runoff forecast residual sequence extracted from the VAR model, and the runoff forecast residual sequence is modeled based on the EGARCH model. The correlation coefficient matrix of the runoff forecast residual sequence is calculated to generate a random error scenario set, and further generate a forecast residual scenario set considering time-related uncertainty. The forecast residual scenario set of the VAR model is superimposed on the runoff forecast value sequence of different forecast periods of the rolling forecast of the VAR model, and the runoff probability forecast scenario set of the EGARCH model considering the time-related uncertainty is calculated; finally, considering the correlated evolution characteristics of the time and spatial dimensions of the multi-station runoff forecast residuals, the EGARCH model and the Copula function are coupled, and on the basis of describing the clustering of the runoff forecast residual sequence fluctuations, the joint distribution between the multi-dimensional conditional variances is constructed to identify and implicitly describe the nonlinear correlation of the multi-station runoff process; the Copula parameters are used to perform random sampling simulation on the uncertainty cumulative probability distribution, and the quantile points corresponding to each cumulative probability distribution are obtained through the marginal distribution to generate a random scenario set of conditional variance based on the forecast uncertainty of the Copula function, and the forecast residual scenario set considering the time-space related uncertainty is calculated; the forecast residual scenario set considering the time-space related uncertainty is superimposed on the runoff forecast value sequence of different forecast periods of the rolling forecast of the VAR model, and the runoff probability forecast scenario set considering the time-space related uncertainty of the EGARCH model is calculated.

[0180] According to the characteristics of medium- and long-term runoff sequence changes, the present invention uses a vector autoregression model to construct the time series and spatial dependence of the runoff sequence and perform mean process forecasting, considers the fluctuation correlation characteristics of the residual variance, establishes an EGARCH model to describe its heteroscedasticity effect, simulates and forecasts the conditional variance of the residual, and explores the temporal and spatial correlation of the conditional variance of the residual under different scenarios. The dynamic evolution law of the medium- and long-term runoff forecast with multi-site temporal and spatial correlation is studied by using the Copula function to model the residual sequence of the multivariate time series joint PDF. The present invention improves the vector autoregression model, considers the characteristics of conditional heteroscedasticity and temporal and spatial correlation with the forecast residual in the runoff forecast, couples the EGARCH model to describe the heteroscedasticity, introduces the Copula function to describe its temporal and spatial complex correlation, quantitatively describes and evaluates the forecast performance of the proposed model method, improves the forecast accuracy and reliability, and provides more accurate support information for water resources management decisions.

Claims

1. A medium- and long-term runoff probability forecasting method based on a hybrid vector autoregression and GARCH-Copula model, characterized in that: The following steps are involved: S1. Convert the medium- and long-term runoff sequence into a stable runoff sample sequence, perform deterministic multi-station runoff single-value forecast on the stable runoff sample sequence based on the vector autoregression VAR model, and further perform deterministic single-value rolling forecast to obtain the runoff forecast value sequence and runoff forecast residual sequence for different forecast periods; S2. Without considering the spatiotemporal correlation of multi-station runoff forecast residuals, generate a random scenario set of runoff forecast residuals in different forecast periods, superimpose the forecast residual random scenario set on the runoff forecast value of the vector autoregression model, perform dynamic probability forecasting, and obtain a rolling probability forecast random scenario set; S3. Considering the correlated evolution characteristics of multi-station runoff forecast residuals in time and space dimensions, the EGARCH model is coupled to eliminate the heteroscedasticity effect of multi-station runoff forecast residual series for dynamic probability prediction, and a forecast residual scenario set and a runoff probability forecast scenario set that consider time-related uncertainty are generated; S4. Considering the correlated evolution characteristics of the time and spatial dimensions of the multi-station runoff forecast residuals, the EGARCH-Copula function is coupled to improve the VAR model to describe the spatiotemporal correlation characteristics of the runoff forecast residuals, and generate a set of runoff probability forecast scenarios that consider the spatiotemporal correlation uncertainties.

2. The medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model according to claim 1 is characterized in that: Step S1 includes the following steps: S11, medium- and long-term runoff series stabilization and transformation processing; The ten-day runoff series of year N1 is subtracted from the multi-year mean and divided by the standard deviation of each decade to obtain the runoff observation result after removing the seasonal component; the calculation formula is: Among them, q i,t is the runoff sample value after de-seasonalization at the ith hydrological station in period t, i = 1, 2, ..., I, I is the total number of hydrological stations, q i,id(t) is the original runoff value of the ith hydrological station, id(t) represents the year and decade of time period t, is the multi-year average runoff value of the ten-day period corresponding to the ith hydrological station id(t), σ i,id(t) is the standard deviation of runoff in the ten-day period corresponding to the ith hydrological station id(t). The runoff sample values ​​after deseasonalization are arranged in chronological order to form a runoff sample sequence {q i,t }; S12, Single-value forecast of multi-station runoff based on vector autoregression VAR model; By setting different lag periods h, an h-order autoregressive equation is established for the runoff series of each station at a regular rate, and the simultaneous form of the multi-station runoff autoregressive equation is constructed: Among them, Q i,t is the simulated value of runoff forecast at the ith hydrological station in period t; a i,t represents the residual error of runoff forecast at the ith hydrological station in period t; μ i is the constant term of the autoregressive equation of the runoff series of the ith hydrological station; π ij,h is the parameter coefficient of the influence of the i-th hydrological station on the j-th hydrological station in the past h periods, i,j=1,2,…,I; q i,t-1 is the runoff sample value after de-seasonalization at the ith hydrological station in period t-1, q i,t-h is the runoff sample value after removing seasonal components at the ith hydrological station in the th period; S13, single value rolling forecast; When a longer-term forecast plan is required, a rolling iterative forecast is performed based on the single-value forecast.

3. The medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model according to claim 1 is characterized in that: Step S2 includes the following steps: S21, using Monte Carlo method to sample and generate a random scenario set of runoff forecast residuals; According to the established random simulation model, random sampling of scenarios is carried out to establish a random scenario set of runoff forecast residuals in different forecast periods. in, represents the residual of runoff forecast of the lth scenario of the i-th hydrological station in the forecast period t before the period t-τ, i=1,2,…,I, l=1,2,…,L, τ=1,2,…τ0, I is the total number of hydrological stations, L is the total number of scenarios, τ0 is the total number of forecast periods; S22, rolling probability forecast random scenario set generation; The forecast residual random scenario set is superimposed on the runoff forecast value of the vector autoregression model to obtain the rolling probability forecast random scenario set that does not consider the temporal and spatial correlation uncertainty of the runoff forecast residual: in, It represents the runoff forecast value of the lth scenario predicted by the i-th hydrological station in the t-time period before the t-τ time period.

4. The medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model according to claim 1 is characterized in that: Step S3 includes the following steps: S31. Analysis of time evolution characteristics of conditional variance of runoff forecast residuals; The EGARCH model is introduced to perform autocorrelation fitting on the conditional variance of the residual sequence extracted from the VAR model, and the autocorrelation relationship of the residual variance and the correlation between the variance and the residual are found as follows: Among them, g(·) is the conditional variance regression equation of the residual sequence of runoff forecast, a i,t-p′,τ is the residual of runoff forecast at the ith hydrological station with a forecast period of tp′ and a forecast period of τ, p′ is the regression order of the residual of runoff forecast, w is the regression order of the conditional variance of the residual of runoff forecast, is the conditional variance of the residual sequence of runoff forecast at the ith hydrological station with a forecast period of t, is the conditional variance of the residual sequence of runoff forecast at the ith hydrological station with a forecast period of tw and a forecast period of τ; S32, Modeling of residual series of runoff forecast based on EGARCH model; The EGARCH (p, w) model is established for the residual sequence of runoff forecast at each station at regular intervals: a i,t,τ =s i,t,τ e i,t,τ Among them, e i,t,τ is the independent and identically distributed random error with zero mean and unit variance corresponding to the residual of runoff forecast for the i-th hydrological station for the forecast period t before the period t-τ, i.e., the forecast period τ; e i,t-u,τ+u is the independent and identically distributed random error with zero mean and unit variance corresponding to the residual of runoff forecast for the i-th hydrological station in the forecast period tu before the forecast period t-(τ+u), that is, the forecast period τ; σ i,t,τ is the conditional standard deviation of the residual series of runoff forecast for the ith hydrological station, forecasting for period t before period t-τ, i.e., with a forecast period of τ; is the conditional variance of the residual sequence of runoff forecast for the i-th hydrological station for the forecast period ts before the period t-(τ+s), i.e., the forecast period is τ; p is the regression order of the random error term, α i,u and β i,s e i,t-u,τ+u and The coefficient, α i,0 and γ i are all real constants; β i,s Indicates the degree of fluctuation, γ i Indicates the degree of asymmetry; S33, according to the runoff forecast value Q' i,t,τ and the corresponding runoff forecast residual a′ i,t,τ , calculate the runoff forecast residual sequence {a′ i,t,τ The correlation coefficient matrix R of a ; S34, using Monte Carlo sampling to generate random error scenarios; Generate a random error scenario set based on random sampling of the correlation coefficient matrix using Cholesky decomposition The description is as follows: R a =AiA T Among them, A is the triangular matrix decomposed by Cholesky, A T is the transpose of A; The random error of the residual of the runoff forecast corresponding to the lth scenario at the ith hydrological station for the forecast period t before the period t-τ, i.e., the forecast period τ, is generated by random sampling based on Cholesky decomposition; is the random error of the lth scenario corresponding to the residual of the runoff forecast for the i-th hydrological station for the period t-τ before the period t, i.e., the forecast period τ; S35, Generation of forecast residual scenario set considering time-dependent uncertainties; According to a i,t,1 and Calculate the conditional variance of the residual of the runoff forecast for the i-th hydrological station in the t-th period before the t-1 period And according to Calculate the conditional variance corresponding to the random scenario in the next period Keep moving forward one period at a time, and make rolling forecasts of the conditional variance until the last period t = T set in advance, and calculate the forecast residual scenario set considering time-related uncertainty S36, Generation of runoff probability forecast scenario set considering time-dependent uncertainties; A set of forecast residual scenarios that will take into account time-dependent uncertainties The runoff forecast value series of different forecast periods superimposed on the rolling forecast of the VAR model {Q i ' ,t,τ }, calculate the runoff probability forecast scenario set considering time-dependent uncertainty predicted by the EGARCH model 5. The medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model according to claim 4 is characterized in that: In step S33, the correlation coefficient matrix R a The expression is; Where ρ(·) is the correlation coefficient.

6. The medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model according to claim 4 is characterized in that: Forecast residual scenario set considering time-dependent uncertainties The expression is: in, represents the residual of runoff forecast considering time-dependent uncertainty of the lth scenario predicted by the ith hydrological station in period t before period t-τ, It represents the conditional variance of the lth scenario of the i-th hydrological station predicted in the t-time period before the t-τ time period calculated by the EGARCH model, i=1,2,…,I,l=1,2,…,L,τ=1,2,…τ0, I is the total number of hydrological stations, L is the total number of scenarios, and τ0 is the total number of the forecast period.

7. The medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model according to claim 1 is characterized in that: Step S4 includes the following steps: S41. Joint distribution of multivariate random variables of residuals of multi-station runoff forecast based on Copula function; According to Sklar's theory, if we make the multivariate random variables (X1, X2, ..., X k ) of the joint distribution F(X1,X2,…,X k ) is expressed as the functions of its marginal distributions F1(X1), F2(X2),…, F k (X k ), name has a Copula function C that satisfies the following formula: F(X1,X2,…,X k )=C·[F1(X1),F2(X2),…,F k (X k )] If F1(X1),F2(X2),…,F k (X k ) is continuous, then the function C is uniquely determined; S42, Generation of forecast residual scenario set considering spatiotemporal correlated uncertainties; The Copula parameters are used to perform random sampling simulation on the cumulative probability distribution of uncertainty, and the quantile points corresponding to each cumulative probability distribution are obtained through marginal distribution, and a random scenario set of conditional variance based on the forecast uncertainty of the Copula function is generated. And calculate the forecast residual scenario set considering the temporal and spatial correlation uncertainties S43, generation of runoff probability forecast scenario set considering spatiotemporal related uncertainties; The forecast residual scenario set will take into account the temporal and spatial correlated uncertainties The runoff forecast value series of different forecast periods superimposed on the rolling forecast of the VAR model {Q i ' ,t,τ }, calculate the runoff probability forecast scenario set based on the Copula function forecast considering the temporal and spatial correlation uncertainty 8. A medium- and long-term runoff probability forecasting system based on a hybrid vector autoregression and GARCH-Copula model, characterized in that: include: The data processing unit is used to convert the medium- and long-term runoff sequence into a stable runoff sample sequence, perform deterministic multi-station runoff single-value forecast on the stable runoff sample sequence based on the vector autoregression VAR model, and further perform deterministic single-value rolling forecast to obtain the runoff forecast value sequence and runoff forecast residual sequence for different forecast periods; The first probability forecast unit is used to generate a random scenario set of runoff forecast residuals in different forecast periods without considering the spatiotemporal correlation of multi-station runoff forecast residuals, superimpose the forecast residual random scenario set on the runoff forecast value of the vector autoregression model, perform dynamic probability forecasting, and obtain a rolling probability forecast random scenario set; The second probability forecasting unit is used to couple the EGARCH model to eliminate the heteroscedasticity effect of the multi-station runoff forecast residual sequence under the condition of considering the correlated evolution characteristics of the time and spatial dimensions of the multi-station runoff forecast residuals, and to perform dynamic probability forecasting, thereby generating a forecast residual scenario set and a runoff probability forecast scenario set that consider time-related uncertainties; The third probability forecasting unit is used to couple the EGARCH-Copula function to improve the VAR model to describe the spatiotemporal correlation characteristics of runoff forecast residuals, taking into account the correlated evolution characteristics of the time and spatial dimensions of multi-station runoff forecast residuals, and generate a set of runoff probability forecast scenarios that take into account the temporal and spatial correlation uncertainties.

9. An electronic device, characterized in that: comprising a memory and a processor, wherein: A memory for storing computer programs that can be run on the processor; A processor is used to execute the steps of a medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model as described in any one of claims 1 to 7 when running the computer program.

10. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by at least one processor, implements the steps of a medium- and long-term runoff probability forecasting method of a hybrid vector autoregression and GARCH-Copula model as described in any one of claims 1 to 7.

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