Medium and long term hydrological forecasting method and system based on Bayesian discrimination

Abstract

The invention relates to the technical field of medium-and-long-term hydrological forecasting, in particular to a medium-and-long-term hydrological forecasting method and system based on Bayesian discrimination, and the method comprises the following steps: S1, selecting related forecasting factors for a forecasting object; s2, dividing runoff categories according to the runoff data; s3 and S4, according to the classification of the runoff, calculating the prior and posterior probabilities of each class of runoff; s5, calculating an optimal combined forecasting result according to the forecasting result calculated by each forecasting factor; and S6, scoring the forecasting result of each forecasting factor and the combined forecasting result. The medium-and-long-term hydrological forecasting system based on Bayesian discrimination comprises the medium-and-long-term hydrological classification and probability forecasting model obtained according to the forecasting method. According to the medium and long-term hydrological forecasting method and system, the precision of a medium and long-term hydrological forecasting result is improved, the capability of meeting actual production activity requirements is improved, decision makers are enabled to consider decision-making risks, organic combination of forecasting and decision-making is realized, and the method and system are more suitable for current water resource management requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of medium- and long-term hydrological forecasting, and in particular to a medium- and long-term hydrological forecasting method based on Bayesian discrimination. Background Art

[0002] The statements in this section merely provide background art related to the present disclosure and do not necessarily constitute prior art.

[0003] Accurate and timely medium- and long-term hydrological forecasts are of great significance for striving for the initiative in flood control and drought relief, formulating scientific water resources scheduling plans, ensuring the safety of water conservancy facilities and exerting their economic benefits. There are many medium- and long-term forecasting methods at present, but the forecast results are generally deterministic, that is, point forecasts. The hydrological cycle system is affected by many factors such as astronomy, meteorology, underlying surface, and human activities. To some extent, it is a complex giant system with natural, social, open and dynamic variability. The study of this open complex giant system must process a large amount of information and knowledge, which is both deterministic and uncertain. At the same time, the hydrological forecast model is only a simulation of the objective hydrological process, which is not very accurate. Therefore, the forecast value as the output of the model is also uncertain. The medium- and long-term hydrological process is affected by various deterministic and uncertain factors during the long period of influence. The deterministic forecast form restricts the analysis and utilization of uncertain information. The application of deterministic forecast results often cannot obtain the optimal decision.

[0004] Probabilistic hydrological forecasting uses probability values ​​instead of definite forecast values ​​to indicate the possibility of occurrence of hydrological forecast quantities. It can make full use of various information in the forecasting process, describe the uncertainty of hydrological forecasting in the form of probability distribution, and give the mean value of hydrological forecast variables and the interval forecast value of the specified probability, so as to measure the degree of uncertainty of the occurrence of hydrological variables. Probabilistic hydrological forecasting reflects both the certainty of changes in hydrological elements and the uncertainty and degree of uncertainty of changes in hydrological elements. In practical applications, this form of forecasting allows decision makers to consider decision risks and realize the organic combination of forecasting and decision-making, so it can better meet the current needs of water resources management.

[0005] The current medium- and long-term hydrological forecast results have low accuracy, are unable to measure corresponding risks, and cannot meet the needs of actual production activities. Summary of the invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a method that first uses the kernel density estimation theory to improve the distribution density function estimation in the Bayesian discriminant method, and on this basis, a medium- and long-term hydrological forecasting method based on medium- and long-term hydrological classification probability forecast and continuous probability forecast is proposed.

[0007] The technical solution adopted by the present invention is: a medium- and long-term hydrological forecasting method based on Bayesian discrimination, characterized in that it includes the following steps:

[0008] S1. Select relevant prediction factors for the prediction object and implement screening prediction factors;

[0009] S2. According to the runoff data, the runoff categories are divided, the forecast objects are sorted from large to small, the corresponding empirical frequencies are calculated, and the runoff is divided into three categories of abundant, normal and dry runoff according to the runoff abundant and dry classification standards in Table 01;

[0010] Table 01 Classification of three types of runoff

[0011]

[0012] S3. According to the classification of runoff, calculate the prior probability of each category of runoff;

[0013] S4. According to the classification of runoff, calculate the posterior probability of each category of runoff;

[0014] S5. Calculate the optimal combined forecast result based on the forecast results calculated for each forecast factor;

[0015] S6. Score the forecast results of each forecast factor and the combined forecast results.

[0016] In this technical solution, the medium- and long-term hydrological forecasting method is a classification forecasting method. In step S2, the runoff categories are divided into three categories to calculate the prior probability rate p of each category. i (i=1,2,3), , and .

[0017] In the specific implementation process, in the formula: Q1 is the runoff value corresponding to the frequency P=75%, which is the critical value of runoff dryness; Q0 is the runoff value corresponding to the frequency P=25%, which is the critical value of runoff abundance; Q is the runoff value corresponding to any frequency P.

[0018] In this technical solution, in step S3, the corresponding prediction factors are divided into three categories, and for each prediction factor and prediction object, a prediction model is established using the Bayesian discriminant method BDA to calculate the posterior probability of different types of runoff occurring when the prediction factor appears. , the formula is as follows:

[0019] (1);

[0020] In formula (1): Q iare various types of runoff, r is the number of runoff categories, X is the prediction factor, and f i (x) is the probability density function of the corresponding category predictor, p i is the prior probability for each category.

[0021] In this technical solution, the optimal combination forecast result P OCF The calculation formula is:

[0022] (2);

[0023] Where: m is the number of prediction factors, a i are the optimized parameters for each predictor, is the posterior probability predicted by each predictor, where the parameters of each predictor are optimized using an accelerated genetic algorithm.

[0024] In this technical solution, when the forecast results are scored in step S6, the Half-Brier scoring method is used to score the forecast results of each forecast factor and the combined forecast results:

[0025] (3);

[0026] Where: B is the Half-Brier score result, and its value range is from 0 to 0.5. When B=0, it means that the prediction is completely accurate. When B=0.5, it means that the prediction effect is the worst, which is equivalent to completely random guessing. The smaller the B value, the higher the prediction accuracy. N is the data year of runoff, r is the number of runoff classifications, ϕ ij is the probability of an event occurring in category j; δ ij is 1 or 0, depending on whether the event occurs in category j: when the event occurs entirely in category j, δ ij is 1; when the event does not occur in category j at all, δ ij is 0.

[0027] In this technical solution, the medium- and long-term hydrological forecasting method is a probabilistic forecasting method. When classifying runoff categories in step S2, the runoff values ​​are sorted from large to small, the empirical frequency of the corresponding runoff is calculated, and then any runoff value is given. , divide the runoff sequence into and less than of two categories.

[0028] In this technical solution, in step S3, according to the runoff category divided in step S2, the runoff value Q i (i=1,2,…,n) corresponding empirical frequencies, calculate the prior probabilities of the two categories ;in:

[0029] and .

[0030] In the technical solution, in step S3, the corresponding prediction factors are divided into two categories, and for each prediction factor, the density function f of the two categories of prediction factors is estimated using the kernel density estimation method. i (x), and then use the following formula to calculate the posterior probability of belonging to the two categories under the condition of the occurrence of the predictor , the formula is as follows:

[0031] (1);

[0032] Where: Q i are various types of runoff, r is the number of runoff categories, X is the prediction factor, and f i (x) is the probability density of the corresponding category predictor, is the prior probability for each category.

[0033] In this technical solution, when the forecast results are scored in step S6, the LEPS scoring method is used to score the results of the continuous probability forecast:

[0034] (4);

[0035] In formula (4): P f and P v are the predicted cumulative probability and the actual value cumulative probability respectively: when P f =P v =0 or P f =P v =1, The maximum value is 2; when P f =1,P v =0 or P f =0,P v =1, The minimum value is -1.

[0036] In this technical proposal, the average LEPs scoring method is defined as:

[0037] (5);

[0038] Where SK is the average LEPS score result, ranging between -100% and 100%;

[0039] The value depends on Positive and negative:

[0040] if is positive, then is the sum of all the best predictions in the data, that is, the cumulative probability of the forecast P f Equal to the cumulative probability P of the actual value v correspond If is negative, then It is the sum of all the worst predictions in the data, that is, the cumulative probability of the forecast P f Equal to 1 or 0 corresponds to The sum.

[0041] A medium- and long-term hydrological forecasting system based on Bayesian discriminant, a medium- and long-term hydrological classification forecasting model and a medium- and long-term hydrological probability forecasting model obtained according to the medium- and long-term hydrological forecasting method based on Bayesian discriminant.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. Using the kernel density estimation theory, the estimation of the distribution density function in the Bayesian discriminant method was improved, and on this basis, the medium- and long-term hydrological classification probability forecast and continuous probability forecast based on Bayesian discriminant were proposed, and a probability forecast model and a classification forecast model with good stability were established. The accuracy of both simulation and trial forecasting is satisfactory, especially for the wet and dry characteristics in the forecast year.

[0044] 2. Moreover, the probabilistic forecasting model still shows a certain forecasting ability. The annual forecast is a continuous probability of exceeding, so it can also give interval forecasts with different probabilities. This form of forecasting allows decision makers to consider decision risks, achieve an organic combination of forecasting and decision-making, and better meet the current needs of water resources management.

[0045] In summary, the medium- and long-term hydrological forecasting method and system based on improved Bayesian discriminant of the present invention improve the accuracy of medium- and long-term hydrological forecast results and their ability to meet the needs of actual production activities. It enables decision makers to consider decision risks, achieve an organic combination of forecasting and decision-making, and better adapt to current water resources management needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A flowchart of an embodiment of a medium- and long-term hydrological forecasting method based on Bayesian discrimination;

[0047] Figure 2 A flowchart of another embodiment of a medium- to long-term hydrological forecasting method based on Bayesian discrimination;

[0048] Figure 3The probability density function diagram of different prediction factors for a certain reservoir classification prediction, the vertical coordinate PDF is the probability density function, where: (a) is the probability density function diagram of the prediction factor 100hPa height field (100hpa_4_252); (b) is the probability density function diagram of the prediction factor 500hPa height field (500hpa_4_105); (c) is the probability density function diagram of the prediction factor Pacific sea temperature field (SST_3_418), (d) is the probability density function diagram of the prediction factor circulation characteristic (74_11_47);

[0049] Figure 4 The probability density function diagram of the forecast factor in another reservoir classification forecast, the ordinate PDF is the probability density function, where: (a) is the probability density function diagram of the forecast factor 100hPa height field (100hpa_4_218), (b) is the probability density function diagram of the forecast factor 500hPa height field (500hpa_8_164), (c) is the probability density function diagram of the forecast factor North Pacific sea temperature field (SST_10_494), (d) is the probability density function diagram of the forecast factor circulation characteristic (74_3_60);

[0050] Figure 5 is the forecast exceedance probability of a certain reservoir forecast factor in 1955, where: (a) is the forecast exceedance probability of the forecast factor 100hPa height field (100hpa_4_252); (b) is the forecast exceedance probability of the forecast factor 500hPa height field (500hpa_4_105); (c) is the forecast exceedance probability of the forecast factor North Pacific sea temperature field (SST_3_418); (d) is the forecast exceedance probability of the forecast factor circulation characteristic (74_11_47);

[0051] Figure 6 is the forecast exceedance probability of a certain reservoir forecast factor in 1996, where: (a) is the forecast exceedance probability of the forecast factor 100hPa height field (100hpa_4_218), (b) is the forecast exceedance probability of the 500hPa height field (500hpa_8_164), (c) is the forecast exceedance probability of the forecast factor North Pacific SST field (SST_10_494), (d) is the forecast exceedance probability of the forecast factor circulation characteristic (74_3_60);

[0052] Figure 7 This is a comparison between the simulated and measured values ​​of runoff inflow to a reservoir in September from 1952 to 2000. The vertical axis is in billion m 3 ;

[0053] Figure 8 This is a comparison between the simulated and measured values ​​of inflow to another reservoir in July from 1957 to 2000. The vertical axis unit is m3 / s. DETAILED DESCRIPTION

[0054] Embodiments of the present invention are described in detail below. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 (d) Figure 4 (a) Figure 4 (b) Figure 4 (c) Figure 4 The vertical axis PDF in (d) is the probability density function, namely Probability Density Function.

[0055] The basic idea of ​​the Bayesian discriminant method is: assuming that there is a certain understanding of the object of study, the prior probability distribution is often used to describe this understanding; then a sample is drawn, and the sample is used to correct the existing prior probability distribution to obtain the posterior probability distribution. Combined with the misclassification loss function, the expected misclassification loss can be obtained. The discriminant method that minimizes the average loss ECM (expected cost of misclassification) is called the Bayesian discriminant method.

[0056] The medium- and long-term hydrological forecasting methods based on Bayesian discrimination, such as Figure 1 As shown, the following steps are included:

[0057] S1. Relevant prediction factors selected for the prediction object;

[0058] S2. Classify runoff categories based on runoff data;

[0059] S3. According to the classification of runoff, calculate the prior probability of each category of runoff;

[0060] S4. According to the classification of runoff, calculate the posterior probability of each category of runoff;

[0061] S5. Calculate the optimal combined forecast result based on the forecast results calculated for each forecast factor;

[0062] S6. Score the forecast results of each forecast factor and the combined forecast results.

[0063] like Figure 2It can be seen from the flowchart shown that the medium- and long-term hydrological forecasting method of the present invention includes two forecast types: classification forecasting and probability forecasting. Regardless of the forecast type, it includes the selection of forecast objects, classification, prior distribution and posterior distribution, forecast result combination, and forecast result evaluation. The difference between the two forecast types is the number of types of forecast types, the calculation of posterior probability in posterior distribution, the calculation method of optimal combination forecast results, and the result scoring method.

[0064] Example

[0065] The embodiments take the inflow runoff forecast of a certain reservoir and another reservoir in Longtou upstream of Wujiang River as examples, and use the above two forecasting methods to forecast them: one reservoir focuses on the inflow runoff in September during the autumn flood season, while the other reservoir focuses on the inflow runoff in July during the flood season.

[0066] The prediction factors used in the embodiment include three element fields: the North Pacific sea temperature field (SST), the monthly average height field of 100hpa in the Northern Hemisphere (H100hPa), the monthly average height field of 500hpa in the Northern Hemisphere (H500hPa) and 74 meteorological prediction factors of circulation characteristics as screening influencing prediction factors. In addition, considering the correlation of runoff in the early stage, the runoff in the early stage is also used as an alternative prediction factor to establish a prediction factor set for runoff prediction. The prediction factor set basically reflects the general trend of the formation and development of previous weather processes and has a good physical background.

[0067] 1.1 Determination of prediction factors

[0068] The selection of forecasting factors is the process of selecting effective forecasting factors from a large number of physical forecasting factors. By analyzing the correlation coefficients between the inflow runoff of a certain reservoir and another reservoir and the various influencing forecasting factors in the previous period, the factors with larger correlation coefficients and exceeding a certain degree of confidence are selected as candidate forecasting factors. This embodiment uses the grid data of three fields, SST, 500hpa, and 100hpa, 74 items of circulation characteristic data, and previous runoff data to conduct a relevant census with the inflow runoff of a certain reservoir in September and the inflow runoff of another reservoir in July. During the census, all forecasting factors from January of the previous year to one month before the forecast month were correlated with the runoff of the forecast month to select effective forecasting factors. The basic forecasting factor set for the runoff forecast of a certain reservoir in September is shown in Table 1, and the basic forecasting factor set for the runoff forecast of Hongjiadu in July is shown in Table 2.

[0069] Table 1 Basic prediction factor set of runoff in a reservoir in September

[0070]

[0071] Table 2 Basic prediction factor set of runoff in July for another reservoir

[0072]

[0073] 1.2 Classification prediction model

[0074] (1) Prediction factor analysis

[0075] The runoff series is classified according to the discrimination criteria in the classification forecast of the Bayesian discrimination method, and then the classification forecast model is established using the forecast factors selected in the previous section. Because this embodiment uses four different forecast factor fields, the effective information provided by different forecast factors is also different. In order to make full use of the effective forecast information of each forecast factor, this embodiment adopts the method of first selecting a single forecast factor for classification forecast, and then using a linear combination method to optimally combine the classification forecasts of each forecast factor.

[0076] In order to show the classification forecasting ability of different forecasting factors for forecast objects, the probability density function diagrams of different forecasting factors for classification forecasting of a certain reservoir and another reservoir are drawn below. Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 (d) and Figure 4 (a) Figure 4 (b) Figure 4 (c) Figure 4 (d) in.

[0077] Depend on Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 As can be seen from (d) in the figure, for a certain reservoir, among the four prediction factor fields, the 500hPa height field prediction factor has a high prediction ability for all three categories. When the density function is biased to the left, that is, the height value is small, it will lead to abundant runoff. When the density function is biased to the right, that is, the height value is large, it will lead to dry runoff. When the density function is in the middle, the runoff tends to be normal in the later period. The 100hPa height field prediction factor has a strong ability to predict abundant runoff and normal years, but has poor prediction performance for dry years. The prediction ability of the North Pacific SST prediction factor and the circulation characteristic quantity is similar. They can effectively predict the abundant state of runoff, but cannot distinguish between dry and normal states.

[0078] Depend on Figure 4 (a) Figure 4 (b) Figure 4 (c) Figure 4As can be seen from (d) in the figure, for another reservoir, among the four prediction factor fields, the 500hPa height field and the circulation characteristic prediction factor have better prediction performance for years with abundant runoff, but poor prediction ability for years with runoff below normal. The 100hPa height field and the North Pacific SST field have better prediction ability for years with low runoff, but cannot distinguish between years with runoff above normal.

[0079] (2) Analysis of forecast results

[0080] From the above analysis, it can be seen that the classification forecasting capabilities of different forecasting factors are different. Therefore, this embodiment adopts a classification combination forecasting model to perform the optimal combination forecasting on the forecasting results of each forecasting factor. First, the Half-Brier scoring method is used to evaluate the classification forecasting results of each forecasting factor, and the forecasting factors with higher scores are selected as the optimal combination forecasting factors. The parameters of each forecasting factor in the optimal combination model are optimized using the accelerated genetic algorithm (RAGA). Finally, 5 optimal forecasting factors were selected for a certain reservoir, and 6 optimal forecasting factors were selected for Hongjiadu. The following Tables 3 and 4 are the optimized parameters of the optimal forecasting factors of the two reservoirs.

[0081] Table 3 Optimization coefficients of the best forecasting factors for a reservoir runoff forecast

[0082] Table 4 Optimization coefficients of the best forecasting factors for runoff forecast of another reservoir

[0083] Based on the established model, a simulation and classification forecast of the inflow volume of a reservoir in September from 1952 to 2000 was carried out. The output results are shown in Table 5. At the same time, the model was tested from 2001 to 2008, and the results are shown in Table 6.

[0084] Table 5 Results of simulation and classification forecast of runoff of a certain reservoir from 1952 to 2000

[0085] Table 6 Results of runoff classification forecast for a reservoir from 2001 to 2008

[0086] It can be seen from Tables 5 and 6 that for the classified forecast of a certain reservoir, there were 5 years with errors in the 49 years of simulation, and the qualified rate of fitting was 89.8%. In the 8 years of the test period, only 2008 was wrong, and the qualified rate was 87.5%. From the classification of errors, 4 of the 5 years with errors in the simulation period were in the state of runoff being low, and the runoff in 2008 during the test period was also low, which shows that the forecast model has a higher forecast effect for the state of abundant runoff of a certain reservoir, but the forecast performance is slightly worse for the state of low runoff.

[0087] Similarly, based on the established model, the July inflow of another reservoir from 1953 to 2000 was classified and forecasted, and the output results are shown in Table 7. At the same time, the model was tested from 2001 to 2006, and the results are shown in Table 8.

[0088] Table 7 Results of runoff simulation and classification forecast for another reservoir from 1953 to 2000

[0089] Table 8 2001-2006 runoff classification forecast results of another reservoir

[0090]

[0091] It can be seen from Tables 7 and 8 that for the classification forecast of another reservoir, there were 7 years of errors in the 48 years of simulation period, and the qualified rate of fitting was 85.4%. There was 1 year of error in the 6 years of verification period, and the qualified rate was 83.3%. From the classification of errors, 4 of the 7 years of errors in the simulation period were in a state of runoff dryness, 3 years were in a state of runoff abundance, and the runoff in 2005, the year of error in the verification period, was in a state of dryness, indicating that the classification forecast model is slightly less effective in predicting the abnormal state of inflow of another reservoir.

[0092] In addition, in order to compare the forecast performance of the single predictor forecast model and the combined forecast model for the two reservoirs, the Half-Brier score table for the runoff forecast of one reservoir and another reservoir is listed below, see Table 9 and Table 10.

[0093] Table 9 Half-Brier score table for runoff forecast of a reservoir

[0094] Table 10 Half-Brier score table for runoff forecast of another reservoir

[0095]

[0096] It can be seen from Tables 9 and 10 above that in the runoff forecast of various forecast factors of a certain reservoir, the 500hPa height field forecast factor and the sea temperature forecast factor have better prediction effects, and the forecast performance of the 100hPa height field and the circulation characteristic quantity is second; in the runoff forecast of various forecast factors of another reservoir, the forecast effects of different forecast factor fields are different, and the forecast effects of various forecast factors in the 500hPa height field are also different, among which the 500hPa height at 164 points in August of the previous year has the best forecast effect; the combined forecast combines the forecast advantages of each forecast factor, and its effect is better than that of a single forecast factor.

[0097] 1.3 Probabilistic forecast model

[0098] (1) Prediction factor analysis

[0099] This embodiment also uses four different forecast factor fields. In order to make full use of the effective forecast information of each forecast factor, this embodiment first selects a single forecast factor for probability forecasting, and then uses a linear combination method to optimally combine the probability forecast results of each forecast factor. The forecast results of each year are described in the form of exceedance probability. Due to the large number of years, only the forecast exceedance probability of each forecast factor of a reservoir in 1955 and the forecast exceedance probability of each forecast factor of a reservoir in 1996 are listed below. See Figure 5 (a) Figure 5 (b) Figure 5 (c) and Figure 5 (d) in the above, and Figure 6 (a) Figure 6 (b) Figure 6 (c) and Figure 6 (d) in.

[0100] According to the forecast results of the past two years:

[0101] ① For the runoff forecast of a certain reservoir, the forecast performance of different forecast factors is different. If the runoff value corresponding to the probability of more than 50% is published as the forecast value, the forecast performance of the 500hPa height field is the best, followed by the forecast performance of the 100hPa height field and the circulation characteristic quantity. The forecast performance of the North Pacific SST field is basically not improved compared with the prior probability.

[0102] ② For the runoff forecast of another reservoir, the forecast performance of each forecast factor is relatively consistent. If the runoff value corresponding to the probability of more than 50% is published as the forecast value, the forecast performance of each forecast factor is greatly improved compared with the prior distribution.

[0103] (2) Analysis of forecast results

[0104] This embodiment also uses a combination method to perform the optimal combination forecast on the forecast results of each forecast factor. The LEPS scoring method is used to score the probability forecast results of each forecast factor, and the four best-scoring forecast factors are selected from the four fields as forecast factors, and then the accelerated genetic algorithm is used to optimize the parameters of each forecast factor in the optimal combination model.

[0105] According to the established model, the runoff value corresponding to the probability of exceeding 50% is published as the forecast value, and the runoff inflow of a reservoir in September from 1952 to 2000 is simulated. Figure 5-6 Comparison between measured and simulated runoff values ​​from September 1952 to 2000.

[0106] For the mid- to long-term forecast of runoff in September during the autumn flood season at Danjiangkou, the predicted values ​​fit the measured values ​​well. In order to evaluate the simulation performance of the model, the indicators in Section 3.5.4 were used to evaluate the simulation and test results. The following Table 11 shows the evaluation results.

[0107] Table 11 Evaluation of the runoff simulation and trial report results of a reservoir in September

[0108] From the evaluation of the simulation results in Table 11, it can be seen that the runoff forecast value corresponding to the probability of more than 50% can simulate the historical runoff process well, and the results of each evaluation index are satisfactory. The model is used to test the runoff from 2001 to September 2008, and the accuracy is evaluated using relative error. The results are shown in Table 12.

[0109] Table 12 Result of runoff forecast for a certain reservoir from 2001 to 2008

[0110] According to the accuracy evaluation results of relative error, two of the eight years of trial forecasts failed, and the qualified rate of trial forecasts was 75%. Overall, the established forecast model has good stability, and the accuracy of both simulation and trial forecasts is satisfactory, especially for the characteristics of flood and drought in the forecast years.

[0111] Similarly, based on the established forecast model, the runoff value corresponding to the probability of exceeding 50% was published as the forecast value, and the inflow of another reservoir in July from 1953 to 2000 was simulated. Figure 5-Figure 7 Comparison between measured and simulated flow values ​​from 1953 to July 2000.

[0112] In order to evaluate the simulation performance of the forecast model, the simulation and test results are evaluated using indicators. Table 13 shows the evaluation results.

[0113] Table 13 Evaluation of runoff simulation and trial report results of another reservoir in July

[0114] from Figure 8 The evaluation of the fitting and simulation results in Table 13 shows that the runoff forecast value corresponding to the probability of more than 50% simulates the historical runoff process well. The model was used to test the runoff from 2001 to July 2006, and the accuracy was evaluated using relative errors. The results are shown in Table 14.

[0115] Table 14 2001-2006 runoff forecast results of another reservoir

[0116]

[0117] According to the accuracy evaluation results of relative error, 3 out of 6 years of trial forecasts failed, and the qualified rate of trial forecasts was 50%. This shows that the prediction performance of the model needs to be improved, especially for the dry year of 2005, there was a deviation, but the forecast for the abundant water year of 2001 was satisfactory.

[0118] Overall, the forecast model still shows good forecasting performance for the flow forecast of another reservoir in July during the flood season.

[0119] (1) The kernel density estimation theory is used to improve the estimation of the distribution density function in the Bayesian discriminant analysis method. On this basis, medium- and long-term hydrological classification probability forecasting and continuous probability forecasting models based on the improved Bayesian discriminant are proposed.

[0120] (2) The medium- and long-term hydrological classification probability forecast model based on improved Bayesian discriminant was used to analyze the forecast factors and classify the runoff inflow into a certain reservoir in September during the autumn flood season and the runoff inflow into another reservoir in July during the flood season. The forecast factor analysis results showed that among the forecast factors of a certain reservoir, the 500hPa height field forecast factor had a high forecast ability for the three classifications (flood, normal, and dry), and the 100hPa height field forecast factor had a strong forecast ability for the years with abundant runoff and normal years. The North Pacific SST forecast factor and the circulation characteristic quantity had similar forecast abilities and could effectively predict the abundant runoff state. Among the forecast factors of another reservoir, the 500hPa height field and the circulation characteristic quantity forecast factor had better forecast performance for the abundant runoff, and the 100hPa height field and the North Pacific SST field had better forecast performance for the years with dry runoff.

[0121] The forecast results show that the qualified rate of the classification forecast simulation period of a certain reservoir is 89.8%, and the qualified rate of the inspection period is 87.5%; the qualified rate of the classification forecast simulation of another reservoir is 85.4%. The qualified rate of the inspection period is 83.3%. The Half-Brier score shows that the combined forecast combines the forecast advantages of each forecast factor, and its effect is better than the forecast of a single forecast factor.

[0122] (3) The medium- and long-term hydrological probability forecasting model based on improved Bayesian discriminant was used to analyze the forecast factors and predict the continuous exceedance probability of the inflow into a certain reservoir in September during the autumn flood season and the inflow into another reservoir in July during the flood season.

[0123] The results of the forecast factor analysis show that the forecast performance of different forecast factors for runoff forecast of a certain reservoir is different, while the forecast performance of each forecast factor for runoff forecast of another reservoir is relatively consistent. According to the established model, the runoff value corresponding to the probability of more than 50% is published as the forecast value. The qualified rate of runoff simulation of a certain reservoir is 91.8%, and the qualified rate of trial report is 75%. The qualified rate of runoff simulation of another reservoir is 93.7%, and the qualified rate of trial report is 50%.

[0124] The embodiments of the present invention disclose preferred embodiments, but are not limited thereto. A person skilled in the art can easily understand the spirit of the present invention based on the above embodiments and make different extensions and changes. However, as long as they do not deviate from the spirit of the present invention, they are all within the protection scope of the present invention.

Claims

1. A medium- and long-term hydrological forecasting method based on Bayesian discrimination, characterized in that: The following steps are involved: S1. Relevant prediction factors selected for the prediction object; S2. Classify runoff categories based on runoff data; S3. According to the classification of runoff, calculate the prior probability of each category of runoff; S4. According to the classification of runoff, calculate the posterior probability of each category of runoff; S5. Calculate the optimal combined forecast result based on the forecast results calculated for each forecast factor; S6. Score the forecast results of each forecast factor and the combined forecast results.

2. The medium- and long-term hydrological forecasting method based on Bayesian discrimination according to claim 1 is characterized in that: The medium- and long-term hydrological forecasting method is a classification forecasting method. In step S2, the runoff categories are divided into three categories to calculate the prior probability p of each category. i (i=1,2,3), , and ; Where: Q1 is the runoff value corresponding to the critical value of runoff dryness when frequency P is the critical value; Q0 is the runoff value corresponding to the critical value of runoff abundance when frequency P is the critical value; Q is the runoff value corresponding to any frequency P; In step S3, the corresponding prediction factors are divided into three categories, and for each prediction factor and prediction object, a prediction model is established using the Bayesian discriminant method to calculate the posterior probability of different types of runoff when the prediction factor appears. , the formula is as follows: ; Where: Q i are various types of runoff, r is the number of runoff categories, X is the prediction factor, and f i (x) is the probability density function of the corresponding category predictor, p i is the prior probability for each category.

3. The medium- and long-term hydrological forecasting method based on Bayesian discrimination according to claim 2 is characterized in that: When the forecast results are integrated in step S5, the optimal combined forecast result P OCF The calculation formula is: ； Where: m is the number of prediction factors, a i are the optimized parameters for each predictor, is the posterior probability predicted by each predictor, where the parameters of each predictor are optimized using an accelerated genetic algorithm.

4. The medium- and long-term hydrological forecasting method based on Bayesian discrimination according to claim 3 is characterized in that: When the forecast results are scored in step S6, the forecast results of each forecast factor and the combined forecast results are scored using the Half-Brier scoring method: ； Where: B is the Half-Brier score result, and its value range is from 0 to 0.

5. When B=0, it means that the prediction is completely accurate. When B=0.5, it means that the prediction effect is the worst, which is equivalent to completely random guessing. The smaller the B value, the higher the prediction accuracy. N is the data year of runoff, r is the number of runoff categories, ϕ ij is the probability of an event occurring in category j; δ ij is 1 or 0, depending on whether the event occurs in category j: when the event occurs entirely in category j, δ ij is 1; when the event does not occur in category j at all, δ ij is 0.

5. The medium- and long-term hydrological forecasting method based on Bayesian discrimination according to claim 1 is characterized in that: The medium- and long-term hydrological forecasting method is a probabilistic forecasting method. When classifying runoff categories in step S2, the runoff values ​​are sorted from large to small, the empirical frequency of the corresponding runoff is calculated, and then any runoff value Q is given. i (i=1,2,…,n), divide the runoff sequence into i and less than Q i of two categories.

6. The medium- and long-term hydrological forecasting method based on Bayesian discrimination according to claim 5 is characterized in that: In step S3, according to the runoff category classified in step S2, the runoff value Q i (i=1,2,…,n) corresponding empirical frequencies, calculate the prior probabilities of the two categories , ;in: and ; And in step S3, the corresponding prediction factors are divided into two categories, and for each prediction factor, the probability density function f of the two categories of prediction factors is estimated using the kernel density estimation method. i (x), and then use the following formula to calculate the posterior probability of belonging to the two categories under the condition of the occurrence of the predictor , the formula is as follows: ； Where: Q i are various types of runoff, r is the number of runoff categories, X is the prediction factor, and f i (x) is the probability density of the corresponding category predictor, is the prior probability for each category.

7. The medium- and long-term hydrological forecasting method based on Bayesian discrimination according to claim 6 is characterized in that: When scoring the forecast results in step S6, the LEPS scoring method is used to score the results of the continuous probability forecast: ; Where: is the LEPS score result, and its value range is from -1 to 2. =2, indicating that the prediction is completely accurate. =-1, indicating the worst prediction effect, which is completely random guessing; P f and P v are the predicted cumulative probability and the actual value cumulative probability respectively: when P f =P v =0 or P f =P v =1, The maximum value is 2; when P f =1,P v =0 or P f =0,P v =1, The minimum value is -1.

8. The medium- and long-term hydrological forecasting method based on Bayesian discrimination according to claim 7 is characterized in that: Define the average LEPs scoring method: ； Where SK is the average LEPS score result, ranging between -100% and 100%; The value depends on Positive and negative: If is positive, then is the sum of all the best predictions in the data, that is, the cumulative probability of the forecast P f Equal to the cumulative probability P of the actual value v correspond of and; if is negative, then It is the sum of all the worst predictions in the data, that is, the cumulative probability of the forecast P f Equal to 1 or 0 corresponds to The sum.

9. The medium- and long-term hydrological forecasting system based on Bayesian discrimination is characterized by: It comprises a medium- and long-term hydrological classification forecast model obtained by the medium- and long-term hydrological forecast method based on Bayesian discrimination according to any one of claims 1 to 5.

10. The medium- and long-term hydrological forecasting system based on Bayesian discrimination is characterized by: It includes a medium- and long-term hydrological probability forecast model obtained according to the medium- and long-term hydrological forecast method based on Bayesian discrimination according to any one of claims 6 to 8.

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