Rainfall multi-model ensemble prediction method based on average mutual information decomposition

Abstract

The application provides a rainfall multi-mode integrated forecasting method based on average mutual information decomposition, and belongs to the field of rainfall multi-mode integrated forecasting. First, quality evaluation is performed on single rainfall forecasting products to determine the forecasting products participating in integration; second, based on the selected single forecasting products, the product combination mode participating in integration is determined; then, according to the selected integrated forecasting product combination, the normalized average mutual information decomposition term of each product is calculated; then, based on the decomposition term of each forecasting product at each level, the integrated weight of each product is calculated in combination with the real-time forecasting level of each product; integrated forecasting is performed based on the determined weight; finally, the integrated forecasting result is evaluated; the application can fully consider the characteristics of the forecasting products in forecasting rainfall at each level, effectively reduce the missed report events in the main flood season and the empty report events in the post-flood season under the premise of guaranteeing that the overall error does not increase, and provide high-quality rainfall forecasting input for safe implementation of flood control forecasting and dispatching.

Description

Technical Field

[0001] This invention belongs to the field of multi-model integrated forecasting of rainfall, and relates to a multi-model integrated forecasting method for rainfall based on average mutual information decomposition. Background Technology

[0002] Currently, rainfall forecast information can extend the lead time and improve the flood control or water storage benefits of reservoirs. However, forecast information inevitably contains forecast errors, which may introduce decision-making risks while improving benefits. Furthermore, the higher the forecast accuracy, the more significant the improvement in scheduling efficiency. Therefore, improving rainfall forecast accuracy is key to enhancing forecast-driven scheduling efficiency. Integrating multiple rainfall forecast products is an effective way to improve the utilization level of rainfall forecasts and reduce forecast errors. Traditional integrated rainfall forecasting research mainly integrates different products based on their overall accuracy, which improves the overall quality of rainfall forecasts to some extent.

[0003] However, in actual reservoir operation, the main operation objectives and key rainfall forecast indicators differ at different times. During the main flood season, the primary objective of reservoir operation is to ensure flood control safety. Decision-makers focus on whether forecasts of minor rainfall events will miss major rainfall events, thus posing a flood risk, and strive to minimize the underreporting rate at all levels. In the post-flood season, the primary objective is to ensure water storage safety. Decision-makers focus on whether forecasts of major rainfall events will be false alarms, resulting in water storage losses, and strive to minimize the false alarm rate at all levels.

[0004] Related studies have shown that for single rainfall forecast products, the forecast accuracy varies significantly across different rainfall levels. Traditional multi-model integrated rainfall forecasting studies focus on improving the overall quality of rainfall forecasts, neglecting the differences in forecast accuracy among various rainfall forecast products at different levels. This approach fails to leverage the advantages of different products at different levels and does not fully meet the needs of reducing missed forecasts during the main flood season and reducing false alarms during the post-flood season.

[0005] In conclusion, under the premise of ensuring that the overall error does not increase, making full use of the advantages of different rainfall forecast products at different levels and improving the quality of rainfall forecasts at each level in a targeted manner is an urgent problem to be solved in reservoir flood control forecasting and scheduling. Summary of the Invention

[0006] To address the problems of existing technologies, this invention provides a multi-model integrated rainfall forecasting method based on average mutual information decomposition. This method addresses the characteristics of high accuracy and high probability of occurrence for small-scale rainfall events, and low accuracy but high information content for large-scale rainfall events. It utilizes both uncertainty decomposition and information content decomposition methods of average mutual information to decompose the average mutual information between actual rainfall and the forecast rainfall of each product. The weight of each product at each forecast level is determined based on the size of the decomposed terms. In practical application, the weights are determined by combining the real-time forecast rainfall levels of each product. Uncertainty decomposition is used to determine the weights during the main flood season, while information content decomposition is used to determine the weights during the post-flood season, further calculating the integrated rainfall. This invention fully considers the characteristics of forecast products at each rainfall level, effectively reducing missed forecasts during the main flood season and false alarms during the post-flood season without increasing the overall error. The rationality of this invention is verified using the integrated rainfall forecast of the Dahuo Reservoir in the Hunhe River Basin as an example.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-model ensemble forecasting method for rainfall based on average mutual information decomposition is proposed. This method first evaluates the quality of individual rainfall forecast products to determine the forecast products to be integrated; second, based on the selected individual forecast products, it determines the product combination method for integration; and third, based on the selected ensemble forecast product combination, it calculates the normalized average mutual information decomposition term for each product. and Next, based on the decomposition items of each forecast product at each level, and combined with the real-time forecast level of each product, the integration weight of each product is calculated; further, integrated forecasts are performed based on the determined weights; finally, the integrated forecast results are evaluated. The calculation flowchart is attached. Figure 1 As shown. The specific steps are as follows: Step 1: Quality evaluation of single rainfall forecast products choose M There are several rainfall forecast products, and the forecast values ​​for each product can be obtained from the website or the official website of the corresponding meteorological forecasting center. The quality of these products is evaluated based on three aspects: missed reporting index, false reporting index, and mean absolute error. Specifically: 1) Underreporting indicators The forecast rainfall is the first At the level of false negatives, the false negative rate Total number of missed reports The calculation formulas are as follows:

[0008] In the formula, For the first The number of missed reports at each level Forecast rainfall level is Total number of timesk =1, 2, …, K -1, This refers to the number of rainfall forecast levels. Underreporting rate. The range is [0,1], and the total number of missed reports is [0,1]. The range is The classification of rainfall forecast levels can be determined by combining the meteorological department's rainfall classification standards and the needs of reservoir operation.

[0009] 2) Empty reporting indicators false alarm rate Total number of false alarms The calculation formula is as follows:

[0010] In the formula, For the first Number of false alarms at each level Forecast rainfall level is Total number of times k =2, 3, …, K False alarm rate The range is [0,1], and the total number of empty reports is [0,1]. The range is .

[0011] 3) Mean Absolute Error The mean absolute error between forecasted rainfall and observed rainfall ( The calculation formula is as follows:

[0012] In the formula, , They are respectively Forecasted rainfall and observed rainfall at specific times. This is the total duration. The MAE range is... .

[0013] For all three categories of indicators, lower values ​​are better. Based on the evaluation results, if some products are significantly worse than other products in all three categories, it indicates that these products are of significantly lower quality and need to be eliminated.

[0014] Step 2: Determine the combination of forecast products to be integrated Elimination in step 1 n After receiving a rainfall forecast product of significantly poor quality m A single forecast product, where 0≤ n < M , M - n = mFurther comprehensive evaluation of the remaining rainfall forecast products will determine the initial combination of rainfall forecast products to be integrated.

[0015] Different individual forecast products can be combined into various integrated schemes, which can be analyzed using an exhaustive method. However, the comparative analysis process is relatively cumbersome and not conducive to expansion to a large number of product integration schemes. Therefore, it is necessary to conduct preliminary screening of forecast product combinations. This invention uses the Normalized Average Mutual Information (NMI) index shown in formula (6) as the evaluation index to conduct preliminary screening of product combination schemes.

[0016] In the formula, To observe rainfall, To forecast rainfall; To obtain the average mutual information between observed rainfall and forecasted rainfall; It is the actual rainfall. The entropy value; Indicates the total number of forecast levels. Actual rainfall The number of categories; This indicates that the forecast rainfall is the [number]th [item / item]. The probability of each level, The actual rainfall was the first The probability of each level, Forecasting rainfall belongs to the first category The level is [level] and the actual rainfall belongs to [level]. The probability of each level.

[0017] The specific filtering method is as follows: First, calculate The NMI index of each individual forecast product is sorted from largest to smallest based on the NMI value: , , , …, ; Next, the forecast products to be integrated can be determined by combining the product ranking and the number of products to be integrated. The number of products can be arbitrarily selected within the range of 2 to m. The products are integrated, and the product portfolio involved in the integration is { , , , …, }; Finally, select the first few from the sorted list. One product ( =2, 3, …, Combining these, we get the following: One forecast product portfolio option: { ,}, { , , }, …, { , , , …, }

[0018] In the introduction of steps 3-6, the selection of all product combination scenarios is discussed. , , , …, Let's take} as an example to illustrate.

[0019] Step 3: Calculate the normalized average mutual information decomposition term and 1) Decomposition terms of the normalized average mutual information between forecasted and actual rainfall It is determined based on the uncertainty decomposition method of mutual information, and the calculation formula is:

[0020] In the formula, This indicates that the forecast rainfall is the [number]th [item / item]. The probability of each level; This indicates that the normalized average mutual information NMI obtained using uncertainty decomposition method A is in the th... The decomposition terms at each level are calculated using formula (8):

[0021] In the formula, This indicates that the forecast rainfall is the [number]th [item / item]. k Each level; This indicates that the forecast rainfall is the [number]th [item / item]. The actual rainfall corresponding to each level; Let be the conditional entropy, representing the condition after receiving the first . Rainfall information by grade forecast After that, there is still an average uncertainty regarding future rainfall.

[0022] The entropy value in formula (8) and It can be calculated using formulas (9) and (10) respectively.

[0023] in, For forecasting rainfall, the first At level one, the actual rainfall was level two. j The posterior probability of each level is calculated using formula (11):

[0024] Generally speaking, the accuracy of forecasts for small-scale rainfall is higher than that for large-scale rainfall. Therefore, considering the physical meaning of uncertainty decomposition method A, it can be concluded that forecasts for small-scale rainfall are more accurate. The decomposition term is greater than the decomposition term of the large-scale rainfall.

[0025] 2) Normalized average mutual information decomposition term between forecasted and actual rainfall It is determined based on the information content decomposition method of mutual information, and the calculation formula is as follows:

[0026] In the formula, Normalized average mutual information According to the information content decomposition method, in the... The decomposition terms of the level are calculated by the following formula:

[0027] In the formula, for and Mutual information between them, i.e., forecasting rainfall This brings information about actual rainfall. The amount of information; This represents the prior probability distribution of actual rainfall; This indicates that the forecast rainfall is the [number]th [item / item]. The probability distribution of actual rainfall at each level is the posterior probability distribution. express and The KL distance (Kullback-Leibler Divergence), also known as relative entropy, is calculated by the following formula:

[0028] Compared to minor rainfall, major rainfall has a lower probability of occurrence but a greater amount of information. Therefore, based on information decomposition method B, it can be seen that the forecast of major rainfall... The decomposition term is larger than the decomposition term of the smaller order of magnitude.

[0029] Step 4: Calculate the weight of each forecast rainfall product 1) For all rainfall forecast products involved in the integration, calculate the normalized average mutual information decomposition term for each product at each rainfall forecast level. and ,in, =1, 2, …, , To forecast the total number of products; =1, 2, …, Further construct the matrix of the normalized average mutual information decomposition terms. and ,like Figure 2 As shown in (a) and (b).

[0030] 2) Due to the matrix Each average mutual information decomposition term The range of values ​​is Since it is inconvenient to directly calculate the weights in subsequent steps, it is normalized and converted into a normalized matrix. :

[0031] In the formula, and They are matrices The minimum and maximum values ​​in.

[0032] because All values ​​greater than 0 can omit the matrix comparison. Normalization processing.

[0033] 3) Based on the calculated matrix , The first can be calculated by combining formulas (16) and (17). i Integration weight of individual products :

[0034] In the formula, For the first Each product The rainfall forecast level at any given time can be obtained by combining the product's forecast value with the rainfall forecast level classification standard. , From the matrix respectively , Selected forecast products as Forecast level is The normalized average mutual information decomposition term (or the normalized decomposition term), with the denominator being the forecast levels of all products participating in the integration. The sum of mutual information.

[0035] Step 5: Calculate the integrated rainfall forecast results 1) t Based on the forecast results of each product, determine the level of the forecast value of each rainfall forecast product, and then determine the weights determined in step 4. Furthermore, the integration weights also change when the forecast level changes at different times.

[0036] 2) This invention considers two scenarios in the integrated forecasting process: correcting and not correcting the system bias of each forecast product.

[0037] a. If the system bias of each product is not considered, the integrated forecast product in Forecast value of time for:

[0038] In the formula, It is an integrated forecasting product in Forecast value for the time; It is the first Each product Forecast value for the time.

[0039] b. If the systematic bias of each product is taken into account, the bias correction for each forecast level of each product can be performed according to formula (19):

[0040] In the formula, It is the first after deviation correction Each product Forecast value for the time; Forecast value The rainfall forecast level is obtained from step 4 above; for t Real-time rainfall forecast products in the first The mean of all forecast values ​​for the grade; for t Rainfall forecast at the specified time is the first The mean of all observations corresponding to the grade.

[0041] After considering system bias, the forecast values ​​of the integrated forecast products are... for:

[0042] For the above-mentioned ensemble forecasting methods based on the two decomposition methods of average mutual information, in order to reduce the missed rate, an ensemble forecasting method based on uncertainty decomposition method A can be adopted; in order to reduce the false alarm rate, an ensemble forecasting method based on information content decomposition method can be adopted.

[0043] Step 6: Evaluate the integrated rainfall forecast results The integrated forecast results are evaluated using the missed reports, false reports, and mean absolute error indices determined in step 1.

[0044] Compared with the prior art, the present invention has the following advantages and effects: This invention proposes a multi-model ensemble rainfall forecasting method based on average mutual information decomposition. This method combines the advantages of high accuracy due to high probability of small-scale rainfall events and high information content despite low incidence of large-scale rainfall events. It utilizes two decomposition methods based on average mutual information to measure the reduction in uncertainty and the amount of future rainfall information brought by the rainfall forecast product, and constructs ensemble weights. Compared with traditional ensemble methods, this proposed method can effectively reduce missed forecasts during the main flood season and false alarms during the post-flood season, while ensuring that the overall error does not increase. This provides high-quality rainfall forecast input for the safe implementation of flood control forecasting and scheduling. Attached Figure Description

[0045] Figure 1 This is a flowchart of the multi-model integrated calculation of rainfall based on average mutual information decomposition; Figure 2 This is a schematic diagram of the average mutual information decomposition matrix of various forecast products at different levels; Figure 2 (a) is a schematic diagram of the average mutual information decomposition term matrix based on uncertainty decomposition method A; Figure 2 (b) is a schematic diagram of the average mutual information decomposition term matrix based on information decomposition method B; Figure 3 This is a graph of the normalized average mutual information (NMI) index for each individual product; Figure 4 This is a graph showing the forecast quality assessment results of the multi-model integrated forecasting method for rainfall based on average mutual information decomposition during the main flood season; Figure 5 This is a graph showing the forecast quality assessment results of the multi-model integrated rainfall forecasting method based on average mutual information decomposition during the post-flood season. Detailed Implementation

[0046] The present invention will be further described below with reference to specific embodiments.

[0047] This invention takes the integrated 24-hour rainfall forecast for the Hunhe River Basin as an example, covering the period from 2007 to 2021 (May to October). The current time is assumed to be 8:00 AM on October 24, 2007. The forecast grading standards are L1 (0~9.9 mm), L2 (10.0~24.9 mm), and L3 (≥25 mm). The specific implementation method is described in detail with reference to the technical solution and accompanying drawings, and includes the following steps: Step 1: Quality evaluation of single rainfall forecast products Each individual rainfall forecast product was evaluated using the indicators corresponding to formulas (1) to (5). Overall, no single product performed best or worst in all indicators, and there was no significant difference in the rainfall forecast level among the products. Therefore, it can be considered that each product has reached a reasonable forecast level. Thus, all five products are suitable for multi-model integrated rainfall forecasting in this study area.

[0048] Step 2: Determine the combination of forecast products to be integrated Based on the forecast product portfolio setup method, this section analyzes the correlation between forecasted and observed rainfall for each forecast product using the Normalized Average Mutual Information (NMI) index, and preliminarily screens candidate product portfolios for integrated forecasting. During the training period, the NMI indices for forecasted and actual rainfall for each product are as follows: Figure 3 As shown. Based on the magnitude of the NMI index, the order of correlation between forecasted and observed rainfall for each individual product is CMA > ECMWF > UKMO > NCEP > JMA. Therefore, by sequentially adding the ranked products, this section initially identified the following four candidate combinations of integrated forecast products: {CMA,ECMWF} (number 11000), {CMA,ECMWF,UKMO} (number 11100), {CMA,ECMWF,UKMO,NCEP} (number 11110), and {CMA,ECMWF,UKMO,NCEP,JMA} (number 11111).

[0049] Step 3: Calculate the normalized average mutual information decomposition term and According to formulas (7) to (14), the average mutual information decomposition terms of different products at each level can be calculated. For example, for ECMWF products at level L3, the decomposition terms based on uncertainty decomposition method A and information content decomposition method B are -1.68 and 3.26, respectively.

[0050] Step 4: Calculate the weight of each forecast rainfall product After calculating the decomposition terms for each product at each level, the normalized average mutual information decomposition term matrix can be obtained. As shown in Table 1.

[0051] Table 1. Normalized average mutual information decomposition term matrix based on uncertainty decomposition method A.

[0052] Based on Table 1, the forecast results for each individual product (row ① of Table 2), and formula (16), the following can be calculated: Fahe The integration weights of the methods are shown in rows ② and ⑤ of Table 2.

[0053] Table 2. Rainfall multi-model ensemble forecast results based on average mutual information decomposition.

[0054] Step 5: Calculate the integrated rainfall forecast results Based on the forecast values ​​of each product and the integrated weights, unbiased and biased corrections can be obtained. Fahe The integrated forecast results of the method are shown in rows ②, ③, ⑦, and ⑧ of Table 2.

[0055] Step 6: Evaluate the integrated rainfall forecast results The assessment results of the two methods during the main flood season and the post-flood season are as follows: Figure 4 and Figure 5 As shown in the figure. The missed detection metrics include the missed detection rates for L1 and L2 levels. , Total number of missed reports (2) The air report indicators include: the air report rate of L2 and L3 levels. , Total number of false alarms (3): Mean Absolute Error .Depend on Figure 4 and Figure 5 The optimal integrated forecasting scheme for the main flood season can be determined as follows: (11111; Deviation uncorrected), all five products are integrated; the optimal integrated forecast scheme selected for the post-flood season is... (11110; bias corrected), four products—CMA, ECMWF, UKMO, and NCEP—were integrated. The optimal integrated forecast scheme was compared and analyzed with the rainfall forecast quality of each individual product, and the evaluation indicators are shown in Table 3.

[0056] Table 3. Forecast quality evaluation results of single product forecasts and ensemble forecasting methods based on average mutual information decomposition.

[0057] As shown in Table 5, during the main flood season, compared with single products, the integrated rainfall forecasting scheme... The underreporting related indicators for (11111; uncorrected deviation) showed a significant improvement. The total number of underreports decreased by 6-12, the L1 level underreporting rate decreased by 4%-9%, and the L2 level underreporting rate was similar to the average level of each individual product. In addition, its MAE was reduced by about 0.4 mm compared to the average level of each individual product.

[0058] In the post-flood season, the integrated rainfall forecasting scheme is the preferred option compared to individual forecast products. The (11110; bias corrected) model exhibits the best overall performance in terms of false alarm related indicators. Its total number of false alarms decreased by approximately 9–16, the L2 level false alarm rate decreased by 17%–30%, and the L3 level false alarm rate decreased by 15%–33%. Furthermore, its MAE is optimal, decreasing by approximately 0.4 mm compared to the average level of individual products. Therefore, the rainfall multi-model integrated forecasting method based on normalized average mutual information decomposition proposed in this invention is effective. Fahe This method can ensure that MAE reaches the average level of a single product and reduce the underreporting rate during the main flood season and the false alarm rate during the post-flood season, respectively.

[0059] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A multi-model ensemble forecasting method for rainfall based on average mutual information decomposition, characterized in that, The specific steps are as follows: Step 1: Quality evaluation of single rainfall forecast products choose M We analyzed rainfall forecast products and obtained the forecast values ​​for each product. We evaluated their quality based on three aspects: missed reports, false alarms, and mean absolute error (MAE). Lower values ​​for all three indicators were considered better. Based on the evaluation results, if some products showed significantly worse performance in all three indicators compared to other products, they were removed. The number of products to be removed was defined as... n , where 0≤ n < M , M = m + n ; Step 2: Determine the combination of forecast products to be integrated Elimination in step 1 n After receiving a rainfall forecast product of significantly poor quality m A single forecast product, for m Further comprehensive evaluation of the rainfall forecast products will determine the initial combination of rainfall forecast products to be integrated; Different single forecast products can be combined into multiple integrated schemes to conduct preliminary screening of forecast product combinations; the normalized average mutual information (NMI) index shown in formula (6) is used as the evaluation index to conduct preliminary screening of product combination schemes. In the formula, To observe rainfall, To forecast rainfall; To obtain the average mutual information between observed rainfall and forecasted rainfall; It is the actual rainfall. The entropy value; Indicates the total number of forecast levels. Actual rainfall The number of categories; This indicates that the forecast rainfall is the [number]th [item / item]. The probability of each level, The actual rainfall was the first The probability of each level, Forecasting rainfall belongs to the first category The level is [level] and the actual rainfall belongs to [level]. The probability of each level; The specific filtering method is as follows: First, calculate The NMI index of each individual forecast product is sorted from largest to smallest based on the NMI value: , , ,…, ; Next, the forecast products to be integrated are determined based on the product ranking and the number of products to be integrated; the number of products can be arbitrarily selected within the range of 2 to m. The products are integrated, and the product portfolio involved in the integration is { , , , …, }; Finally, select the first few from the sorted list. One product ( =2, 3, …, Combining these, we get the following: One forecast product portfolio option: { , }, { , , }, …, { , , , …, }; The following steps 3-6 illustrate the scenario of selecting all product combinations; Step 3: Calculate the normalized average mutual information decomposition term and 1) Decomposition terms of the normalized average mutual information between forecasted and actual rainfall It is determined based on the uncertainty decomposition method of mutual information, and the calculation formula is: In the formula, This indicates that the forecast rainfall is the [number]th [item / item]. The probability of each level; This indicates that the normalized average mutual information NMI obtained using uncertainty decomposition method A is in the th... The decomposition terms at each level are calculated using formula (8): In the formula, This indicates that the forecast rainfall is the [number]th [item / item]. k Each level; This indicates that the forecast rainfall is the [number]th [item / item]. The actual rainfall corresponding to each level; Let be the conditional entropy, representing the condition after receiving the first . Rainfall information by grade forecast Afterwards, there remains an average uncertainty regarding future rainfall; Small-volume rainfall events are more accurate than large-volume rainfall events. Therefore, combining the physical meaning of uncertainty decomposition method A, it can be seen that the forecast of small-scale rainfall... The decomposition term is larger than the decomposition term of the massive rainfall event; 2) Normalized average mutual information decomposition term between forecasted and actual rainfall It is determined based on the information content decomposition method of mutual information, and the calculation formula is as follows: In the formula, Normalized average mutual information According to the information content decomposition method, in the... The decomposition terms of the level are calculated by the following formula: In the formula, for and Mutual information between them, i.e., forecasting rainfall This brings information about actual rainfall. The amount of information; This represents the prior probability distribution of actual rainfall; This indicates that the forecast rainfall is the [number]th [item / item]. The probability distribution of actual rainfall at each level is the posterior probability distribution. express and The KL distance, or relative entropy, is calculated by the following formula: Compared to minor rainfall, major rainfall has a lower probability of occurrence but a greater amount of information; therefore, based on information decomposition method B, it can be seen that the forecast of major rainfall... The decomposition term is larger than the decomposition term of a smaller order of magnitude; In step 3, the entropy value in formula (8) and It can be calculated using formulas (9) and (10) respectively. in, For forecasting rainfall, the first At level one, the actual rainfall was level two. j The posterior probability of each level is calculated using formula (11): Step 4: Calculate the weight of each forecast rainfall product 1) For all rainfall forecast products involved in the integration, calculate the normalized average mutual information decomposition term for each product at each rainfall forecast level. and ,in, =1, 2, …, , To forecast the total number of products; =1, 2, …, Further construct the matrix of normalized average mutual information decomposition terms. and ; 2) Due to the matrix Each average mutual information decomposition term The range of values ​​is Normalize it to convert it into a normalized matrix. : In the formula, and They are matrices The minimum and maximum values ​​in; because All values ​​are greater than 0, omit matrix pairings. Normalization processing; 3) Based on the calculated matrix , Combine formulas (16) and (17) to calculate the first i Integration weight of individual products : In the formula, For the first Each product The rainfall forecast level at any given time can be obtained by combining the product's forecast value with the rainfall forecast level classification standard; , From the matrix respectively , Selected forecast products as Forecast level is The normalized average mutual information decomposition term, with the denominator being the forecast levels of all products participating in the integration. The sum of mutual information; Step 5: Calculate the integrated rainfall forecast results 1) t Based on the forecast results of each product, determine the level of the forecast value of each rainfall forecast product, and then determine the weights determined in step 4. Furthermore, the integration weights also change when the forecast level changes at different times; 2) Two scenarios are considered during the integrated forecasting process: correcting or not correcting the systematic biases of each forecast product; a. If the system bias of each product is not considered, the integrated forecast product in Forecast value of time for: In the formula, It is an integrated forecasting product in Forecast value for the time; It is the first Each product Forecast value for the time; b. If the systematic bias of each product is considered, then the bias correction is performed for each forecast level of each product according to formula (19): In the formula, It is the first after deviation correction Each product Forecast value for the time; Forecast value The rainfall forecast level is obtained from step 4 above; for t Real-time rainfall forecast products in the first The mean of all forecast values ​​for the grade; For t Rainfall forecast at the specified time is the first The mean of all observations corresponding to the grade; After considering system bias, the forecast values ​​of the integrated forecast products are... for: For the above-mentioned ensemble forecasting methods based on the two decomposition methods of average mutual information, in order to reduce the missed rate, an ensemble forecasting method based on uncertainty decomposition method A can be adopted; in order to reduce the false alarm rate, an ensemble forecasting method based on information content decomposition method can be adopted. Step 6: Evaluate the integrated rainfall forecast results The integrated forecast results are evaluated using the missed reports, false reports, and mean absolute error indices determined in step 1.

2. The multi-model integrated forecasting method for rainfall based on average mutual information decomposition according to claim 1, characterized in that, In step 1, the specific indicators for quality evaluation are as follows: 1) Underreporting indicators The forecast rainfall is the first At the level of false negatives, the false negative rate Total number of missed reports The calculation formulas are as follows: In the formula, For the first The number of missed reports at each level Forecast rainfall level is Total number of times k =1, 2, …, K -1, It refers to the number of rainfall forecast levels; the underreporting rate. The range is [0,1], and the total number of missed reports is [0,1]. The range is The classification of rainfall forecast levels can be determined by combining the meteorological department's rainfall classification standards and reservoir scheduling needs. 2) Empty reporting indicators false alarm rate Total number of false alarms The calculation formula is as follows: In the formula, For the first Number of false alarms at each level Forecast rainfall level is Total number of times k =2, 3, …, K ; false alarm rate The range is [0,1], and the total number of empty reports is [0,1]. The range is ; 3) Mean Absolute Error The mean absolute error between forecasted rainfall and observed rainfall ( The calculation formula is as follows: In the formula, , They are respectively Forecasted rainfall and observed rainfall at specific times. This is the total duration; the MAE range is... .

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