A method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts

Abstract

A method for evaluating the uncertainty of deterministic graded rainfall forecasts, belonging to the technical field of rainfall forecast product evaluation. First, the rainfall forecast grading standard and the binning standard for calculating the entropy value are determined; secondly, according to the rainfall forecast grading standard and the binning standard for calculating the entropy value, the forecast values and the observed values are graded and binned; thirdly, according to the grading and binning results, the normalized contingency table is calculated; finally, according to the normalized contingency table and the proposed index calculation formula, the index evaluation result can be obtained. The method for evaluating the uncertainty of deterministic graded rainfall forecasts proposed by the present invention is based on the mutual information theory, and respectively constructs an index for evaluating the comprehensive uncertainty of rainfall forecasts and an index for the uncertainty of each rainfall forecast level; this evaluation method has the advantage of being insensitive to extreme value deviations; by establishing the connection between the two uncertainties through these two indexes, the two uncertainty evaluation results of the present invention have the advantage of consistency.

Description

Technical Field

[0001] The present invention belongs to the technical field of rainfall forecast product evaluation, and relates to a method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts. Background Art

[0002] With the development of numerical weather prediction, various forms of rainfall forecast products have emerged and the forecast quality has been significantly improved. Generally speaking, rainfall forecasts can be divided into deterministic forecasts, probabilistic forecasts, and ensemble forecasts. Ensemble forecasts use a set of discrete forecast results to characterize the distribution characteristics of the forecast results. Therefore, ensemble forecasts are sometimes also considered another form of probabilistic forecasts. From the perspective of data form, they can be further divided into continuous forecasts and hierarchical forecasts. Probabilistic forecasts contain rich uncertainty information, but it is difficult for the public to use them correctly due to their complexity. In contrast, deterministic hierarchical rainfall forecasts are easy to understand and use, and are widely used in flash flood warnings (Economou, T., Stephenson, D.B., Rougier, J.C., Neal, R.A., & Mylne, K.R., 2016). On the use of Bayesian decision theory for issuing natural hazard warnings. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2194), 20160295.), reservoir operation (Wang Bende, Zhou Huicheng, Wang Guoli, Yuan Jingxuan, Liang Guohua, & Li Min, 2006. Theory and method of dynamic control of reservoir flood limit water level and its application. China Water Resources and Hydropower Press.), and drought management (Sigaroodi, S.K., Chen, Q., Ebrahimi, S., Nazari, A., & Choobin, B. (2014). Long-term precipitation forecast for drought relief using atmospheric circulation factors: a study on the Maharloo Basin in Iran. Hydrology and Earth System Sciences, 18(5), 1995-2006.), etc. However, rainfall forecasts inevitably have errors, which may further lead to decision-making biases, and it is necessary to evaluate the uncertainty of rainfall.

[0003] The different characteristics and usage methods of forecast data make it impossible for a single evaluation index to fully evaluate it (Mason, S.J., & Weigel, A.P. (2009). A Generic Forecast Verification Framework for Administrative Purposes. Monthly Weather Review, 137(1), 331 - 349.). Currently, there are various evaluation techniques for deterministic categorical forecasts. Common evaluation indexes include indexes such as the probability of correct prediction (PC), bias (BR), probability of detection (POD), and forecast skill score. These commonly used indexes can evaluate the quality of forecast data from aspects such as bias, accuracy, discrimination, and forecast skill respectively. However, there is less research on the evaluation of categorical rainfall forecasts from the aspect of uncertainty. Brown and Murphy (Brown, B.G., & Murphy, A.H. (1987). Quantification of Uncertainty in Fire - Weather Forecasts: Some Results of Operational and Experimental Forecasting Programs. Weather and Forecasting, 2(3), 190 - 205.) used the interquartile range (IQR) to evaluate the uncertainty in fire - weather forecasts, which is defined as the variation characteristics of the observed value distribution under the condition of a given forecast value. In addition to the IQR, the standard deviation (Std) is also a commonly used index for quantifying the variation characteristics of the distribution of research variables. However, the Std is easily affected by extreme values; the IQR only uses the information of two quartiles and cannot fully utilize the forecast and observed data. In recent years, few scholars have studied new techniques for evaluating the uncertainty of deterministic categorical forecasts. Therefore, it is necessary to develop a more accurate evaluation technique with less influence from extreme values.

[0004] As an uncertainty assessment index, information entropy has been widely applied in various fields such as water resources. Information entropy is calculated from the characteristics of sample distribution. Therefore, information entropy is not sensitive to extreme value deviations and can fully utilize rainfall forecast information. DelSole and Tippett (DelSole, T., & Tippett, M.K. (2007). Predictability: Recent insights from information theory: PREDICTABILITY. Reviews of Geophysics, 45(4).) pointed out that it is difficult to find a better method than entropy value to quantify uncertainty. Mutual information is a concept in the field of information entropy, which quantifies the amount of information that one variable X contains in another variable Y (Gong, W., Gupta, H.V., Yang, D., Sricharan, K., & Hero, A.O. (2013). Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach: ESTIMATING EPISTEMIC AND ALEATORY UNCERTAINTIES. Water Resources Research, 49(4), 2253-2273.). Mutual information has been applied to the evaluation of probabilistic forecasts, such as RMIS score and DS score. However, no study has applied mutual information to the evaluation of deterministic rainfall forecasts. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a method for evaluating the uncertainty of deterministic graded rainfall forecasts. Based on the mutual information theory, this method constructs indexes for evaluating the uncertainty of each grade and the comprehensive uncertainty of rainfall forecasts respectively. This evaluation method has the advantages of being insensitive to extreme value deviations and having consistency in the two uncertainty evaluation results. Taking the rainfall forecast data applied to the operation of the Dahuofang Reservoir in the Hunhe River Basin as an example, the rationality of the present invention is verified.

[0006] In order to achieve the above object, the technical scheme adopted by the present invention is as follows:

[0007] A method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts. First, determine the rainfall forecast classification criteria and the binning criteria for calculating entropy values; second, classify and bin the forecast values and observed values according to the rainfall forecast classification criteria and the binning criteria for calculating entropy values; third, calculate the normalized contingency table based on the classification and binning results; finally, according to the normalized contingency table and the proposed index calculation formula, the index evaluation result can be obtained. The calculation flow chart is as shown in the appendix Figure 1 as follows.

[0008] Step 1: Determine the rainfall forecast classification criteria and the binning criteria for calculating entropy values

[0009] Combined with the classification criteria of the meteorological department and the actual use, determine the classification criteria for rainfall forecast data, where L k is the k-th rainfall level, k = 1, 2, 3,..., K, where K is the total number of rainfall forecast classification levels.

[0010] When calculating the relevant entropy indicators, it is necessary to determine the bin width. There are currently various bin width calculation methods, including equal-frequency binning, equal-distance binning, and a hybrid method of equal-frequency and equal-distance. Among them, the equal-distance binning method is simple to calculate and has high efficiency, and this patent adopts this method. The calculation of the bin width is shown in formula (1),

[0011]

[0012] where W is the bin width, and σ and N are the standard deviation and the number of samples of the rainfall samples respectively.

[0013] Based on the bin width W, according to the maximum and minimum values P min in the rainfall samples, a total of NC bins are divided, and the value range of each bin is [P min , P min +W], [P min +W, P min +2W],..., [P min +jW, P min +(j + 1)W],..., [P min +(NC - 1).W, P min +NC·W], and the j-th bin is represented by C j , where j is the bin number index, j = 1, 2, 3,..., NC.

[0014] It should be noted that the calculation of the forecast classification and the bin width are independent of each other.

[0015] Step 2: Classify and bin the forecast values and observed values

[0016] Determine the classification to which the rainfall forecast value belongs according to the rainfall forecast classification standard determined in step 1. Similarly, determine the bin to which the rainfall observation value belongs according to the binning standard obtained in step 1.

[0017] Step 3: Calculate the normalized contingency table of the forecast rainfall and the observed rainfall

[0018] Based on the classification results in step 2, the probability p that the actual rainfall is in the bin level C k under the rainfall forecast level L j can be statistically calculated. Similarly, the probability that the rainfall forecast is at level L k，j and the probability p that the actual rainfall occurs in the bin C k can also be statistically calculated. As shown in Table 1, this table characterizes the probability distribution characteristics of the classified forecast and the observed values. j j

[0019] Table 1 Normalized contingency table of forecast rainfall and observed rainfall

[0020]

[0021] Among them, O represents the observed rainfall and F represents the forecast rainfall. p j represents the probability that the observed value belongs to the j-th bin, represents the probability that the forecast value belongs to the k-th level, and p k，j represents the probability that the forecast value belongs to the k-th level and the corresponding observed value belongs to the j-th bin. The classification standards L1, L2, L3, ……, L K and the binning standards C1, C2, C3, ……, C Nc are determined in step 1.

[0022] p k，j According to the classification and binning results of all the forecast and observed data in step 2, count the number n of cases where the forecast rainfall belongs to the k-th level and the corresponding observed rainfall belongs to the j-th bin k，j , then p k，j can be calculated by formula (2)

[0023]

[0024] From p k，j p j and can be calculated respectively as shown in formulas (3) and (4):

[0025]

[0026]

[0027] ​​​Step 4: Calculate the uncertainty evaluation index NMID for each level of the evaluation rainfall forecast k and the comprehensive uncertainty index NMI

[0028] The present invention first proposes the index NMID k to evaluate the uncertainty of each level of the deterministic graded rainfall forecast, as shown in formula (5):

[0029]

[0030] where: H(O) represents the entropy value of the observed rainfall O; F k represents the forecast rainfall at the k-th level; O|F k represents the observed rainfall when the forecast rainfall is F k ; H(O|F k ) is the entropy value of O|F k , which characterizes the remaining uncertainty in the measured rainfall O after obtaining the rainfall forecast information F k .

[0031] In formula (5), H(O) and H(O|F k ) can be calculated according to formulas (6) and (7) respectively, where p j is calculated in step three

[0032]

[0033]

[0034] The entropy values H(O) and H(O|F k ) are in bits; represents the conditional probability that the observed rainfall belongs to the j-th bin when the forecast rainfall belongs to the k-th level, and is calculated by formula (8):

[0035]

[0036] Combining formulas (5) to (8), the uncertainty evaluation index NMID for each rainfall forecast level can be calculated k .

[0037] Mutual information measures the degree of mutual dependence between two variables. Specifically, for two random variables, mutual information is the "amount of information" obtained by observing another random variable after obtaining the information of one random variable. The normalized mutual information NMI is the normalized form of mutual information. The present invention first applies it to evaluate the comprehensive uncertainty of all levels of the deterministic graded rainfall forecast, and the calculation formula is as follows:

[0038]

[0039] Where: H(O|F) represents the conditional entropy of the observed rainfall O given the known rainfall forecast F; I(O; F) represents the mutual information between the observed rainfall O and the forecast rainfall F, indicating the uncertainty eliminated in the observed rainfall O by observing the forecast rainfall F; therefore, NMI represents the proportion of uncertainty eliminated in the observed rainfall O by observing the forecast rainfall F.

[0040] As can be seen from formula (9), NMI is the weighted average of NMID k at each level, so NMID can be calculated by formula (5) k Substituting into formula (9), the comprehensive uncertainty evaluation index NMI can be obtained.

[0041] The index NMI proposed by the present invention can evaluate the comprehensive uncertainty of all levels of rainfall forecasts, and NMID k can evaluate the uncertainty of each level of rainfall forecasts, which can provide decision-making support for actual management workers.

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

[0043] The evaluation method for the uncertainty of deterministic graded rainfall forecasts proposed by the present invention is based on the mutual information theory, and respectively constructs the comprehensive uncertainty index NMI for evaluating rainfall forecasts and the uncertainty index NMID for each rainfall forecast level k . According to the above calculation process, it can be seen that this method calculates using the probability distribution characteristics of graded forecasts and observed values, rather than directly applying the forecast and observed values for calculation. Therefore, this evaluation method has the advantage of being insensitive to extreme value deviations; in addition, the comprehensive uncertainty evaluation index NMI proposed by the present invention is the weighted average of the uncertainty evaluation index NMID k for each level, and the connection between the two uncertainties is established through these two indexes. Therefore, the two uncertainty evaluation results of this method have the advantage of consistency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic diagram of the calculation process of the evaluation index based on mutual information;

[0045] Figure 2 is a diagram of the comprehensive uncertainty evaluation result NMI of rainfall forecasts at six rain gauges; Figure 2 (a) is a diagram of the comprehensive uncertainty evaluation result NMI of rainfall forecasts at the Yujiabaozi Station; Figure 2 (b) is a diagram of the comprehensive uncertainty evaluation result NMI of rainfall forecasts at the Muqi Station; Figure 2 (c) is a diagram of the comprehensive uncertainty evaluation result NMI of rainfall forecasts at the Yingemen Station; Figure 2 (d) is a diagram of the comprehensive uncertainty evaluation result NMI of rainfall forecasts at the Yingpan Station; Figure 2(e) is the NMI diagram of the comprehensive uncertainty assessment results of rainfall forecasts for Zhaojiabaozi Station; Figure 2 (f) is the NMI diagram of the comprehensive uncertainty assessment results of rainfall forecasts for Bianwaibaozi Station;

[0046] Figure 3 It is the NMID1 diagram of the L1-level assessment results of rainfall forecasts at six rain gauge stations; Figure 3 (a) is the NMID1 diagram of the L1-level assessment results of rainfall forecasts for Yujiabaozi Station; Figure 3 (b) is the NMID1 diagram of the L1-level assessment results of rainfall forecasts for Muqi Station; Figure 3 (c) is the NMID1 diagram of the L1-level assessment results of rainfall forecasts for Yingemen Station; Figure 3 (d) is the NMID1 diagram of the L1-level assessment results of rainfall forecasts for Yingpan Station; Figure 3 (e) is the NMID1 diagram of the L1-level assessment results of rainfall forecasts for Zhaojiabaozi Station; Figure 3 (f) is the NMID1 diagram of the L1-level assessment results of rainfall forecasts for Bianwaibaozi Station;

[0047] Figure 4 It is the NMID2 diagram of the L2-level assessment results of rainfall forecasts at six rain gauge stations; Figure 4 (a) is the NMID2 diagram of the L2-level assessment results of rainfall forecasts for Yujiabaozi Station; Figure 4 (b) is the NMID2 diagram of the L2-level assessment results of rainfall forecasts for Muqi Station; Figure 4 (c) is the NMID2 diagram of the L2-level assessment results of rainfall forecasts for Yingemen Station; Figure 4 (d) is the NMID2 diagram of the L2-level assessment results of rainfall forecasts for Yingpan Station; Figure 4 (e) is the NMID2 diagram of the L2-level assessment results of rainfall forecasts for Zhaojiabaozi Station; Figure 4 (f) is the NMID2 diagram of the L2-level assessment results of rainfall forecasts for Bianwaibaozi Station;

[0048] Figure 5 It is the NMID3 diagram of the L3-level assessment results of rainfall forecasts at six rain gauge stations; Figure 5 (a) is the NMID3 diagram of the L3-level assessment results of rainfall forecasts for Yujiabaozi Station; Figure 5 (b) is the NMID3 diagram of the L3-level assessment results of rainfall forecasts for Muqi Station; Figure 5 (c) is the NMID3 diagram of the L3-level assessment results of rainfall forecasts for Yingemen Station; Figure 5 (d) is the NMID3 diagram of the L3-level assessment results of rainfall forecasts for Yingpan Station; Figure 5 (e) is the NMID3 diagram of the L3-level assessment results of rainfall forecasts for Zhaojiabaozi Station; Figure 5 (f) is the NMID3 diagram of the L3-level assessment results of rainfall forecasts for Bianwaibaozi Station; Detailed implementation manners

[0049] The present invention will be further described below in conjunction with specific embodiments.

[0050] Taking the Hunhe River Basin as an example, the time range is from 2007 to 2018 (from May to October). The specific implementation manners will be described in detail in combination with the technical solution and the drawings, which specifically include the following steps:

[0051] Step 1: Determine the rainfall forecast classification standard and the binning standard for calculating the entropy value

[0052] The classification standard of the China Meteorological Administration is shown in Table 2. According to the classification standard of the China Meteorological Administration and the observation data, the sample numbers of each level can be statistically obtained, as shown in Table 3. Since the sample numbers of heavy rain and above levels in the Hunhe River Basin are relatively small, they are merged into one level; in addition, during the reservoir operation process, no rain and light rain are often classified into the same level. Therefore, the forecast classification adopted in this patent is shown in Table 4:

[0053] Table 2 Rainfall forecast classification standard of the China Meteorological Administration

[0054]

[0055] Table 3 Observation sample numbers of each level at each rain gauge station

[0056]

[0057] Table 4 Rainfall forecast classification

[0058]

[0059] According to formula (1), the bin widths calculated for each station are shown in Table 5.

[0060] Table 5 Bin widths calculated for each rain gauge station (mm)

[0061]

[0062] Combining the bin width with the maximum observed rainfall at the rain gauge station, the binning standard can be obtained. For example, the maximum observed rainfall at the Muqi Station is 190.4 mm, then the corresponding binning standard is: C1 [0, 2.8), C2 [2.8, 5.6), C3 [5.6, 8.4),......, C 67 [188.1, 190.9).

[0063] Step 2: Classify and bin the forecast values and the observed values

[0064] According to the forecast grading standard and the calculation result of the bin width, the grading and binning results of each rain gauge can be obtained. The results corresponding to Muqi Station, ECMWF product, and a 1-day lead time are shown in Table 6.

[0065] Table 6 Grading and Binning Results of Rainfall Forecast and Observed Values (Muqi Station; ECMWF Product; 1-day Lead Time)

[0066]

[0067] Step 3: Calculate the normalized contingency table of forecast rainfall and observed rainfall

[0068] According to the grading and binning results of the forecast and observed values, through statistical analysis and combined with Formulas (2) - (4), the normalized contingency table can be obtained, as shown in Table 7.

[0069] Table 7 Calculation Results of the Normalized Contingency Table of Forecast Rainfall and Observed Rainfall (Muqi Station; ECMWF Product; 1-day Lead Time)

[0070]

[0071] Step 4: Calculate the uncertainty evaluation index NMID for each grade of the evaluated rainfall forecast k And the comprehensive uncertainty index NMI

[0072] Combined with Formulas (5) - (9), NMI and NMID can be calculated. k . Among them, the calculation result of the comprehensive uncertainty evaluation index NMI is as Figure 2 shown; the calculation results of the uncertainty evaluation indexes NMID for each grade k are as Figure 3 , 4 , and 5 shown.

[0073] From Figure 2 and Figure 3 , it can be seen that the variation trends of NMI and NMID1 of any product with the lead time show great similarity. The reasons are as follows. From Table 3, it can be seen that the rainfall samples of Level L1 (no rain, light rain) account for about 89% of the total samples. Therefore, the trends of NMI and NMID1 are similar. The results reflect the advantage that the comprehensive uncertainty calculated by the proposed method is consistent with the uncertainty of each grade.

[0074] To analyze the sensitivity of NMI and NMID k to extreme value deviations, the following experiment is designed. As shown in Table 8, when the forecast deviation changes from -24.2 mm to {-50, -100, -150, -200} mm (corresponding to Experiments 1 - 4 respectively), NMI and NMID k (taking NMID1 as an example) also change accordingly. NMI in the tablep and NMID1 p respectively represent the percentage changes of NMI and NMID1. As can be seen from the table, when the extreme value deviation changes to -200 mm, NMI and NMID 1 only increase by 6% and 3% respectively. Therefore, NMI and NMID k are not sensitive to extreme value deviation.

[0075] Table 8 Sensitivity analysis results of NMI and NMID k to extreme value deviation (Muqi Station; ECMWF product; 1-day prediction period)

[0076]

[0077] The above-described embodiments only represent the implementation modes of the present invention, but should not be construed as limiting the scope of the present invention patent. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts, characterized in that, The specific evaluation method is as follows: First, determine the rainfall forecast grading standard and the binning standard for calculating the entropy value; second, grade and bin the forecast values and observed values according to the rainfall forecast grading standard and the binning standard for calculating the entropy value; Third, calculate the normalized contingency table according to the grading and binning results, specifically as follows: Based on the classification and binning results, the rainfall forecast level L can be calculated k The actual rainfall is in bin level C. j The probability p k,j , the rainfall forecast can also be calculated as L k Probability of level And the actual rainfall occurs in bin C j The probability p j , as shown in Table 1, which characterizes the probability distribution characteristics of graded forecasts and observations; Table 1 Normalized contingency table of forecast rainfall and observed rainfall where O represents the observed rainfall and F represents the forecast rainfall; p j represents the probability that the observed value belongs to the j-th bin, represents the probability that the forecast value belongs to the k-th level, and p k,j represents the probability that the forecast value belongs to the k-th level and the corresponding observed value belongs to the j-th bin; the classification criteria L1, L2, L3, ……, L K and the binning criteria C1, C2, C3, ……, C NC are determined by step 1; Finally, according to the normalized contingency table and the proposed index calculation formula, the index evaluation results can be obtained. The specific calculation for evaluating the uncertainty evaluation index NMID of each level of rainfall forecast is as follows k and the comprehensive uncertainty index NMI; Through the uncertainty evaluation index NMID k , to evaluate the uncertainty of each rainfall forecast level of the deterministic graded rainfall forecast, as shown in formula (5): Where: H(O) represents the entropy value of the observed rainfall O; F k represents the predicted rainfall at the k-th level; O|F k represents the observed rainfall when the predicted rainfall is F k ; H(O|F k ) is the entropy value of O|F k , representing the remaining uncertainty in the measured rainfall O after obtaining the rainfall prediction information F k ; Apply the normalized mutual information NMI to evaluate the comprehensive uncertainty of all levels of deterministic graded rainfall forecasts. The calculation formula is as follows: Where: H(O|F) represents the conditional entropy of the observed rainfall O given the rainfall forecast F; I(O; F) represents the mutual information between the observed rainfall O and the forecast rainfall F, indicating the uncertainty eliminated in the observed rainfall O by observing the forecast rainfall F; therefore, NMI represents the proportion of uncertainty eliminated in the observed rainfall O by observing the forecast rainfall F; As can be seen from formula (9), NMI is the weighted average of NMID k at each level, so NMID calculated from formula (5) k is substituted into formula (9) to obtain the comprehensive uncertainty evaluation index NMI; the index NMI can evaluate the comprehensive uncertainty of all levels of rainfall forecasts, and NMID k can evaluate the uncertainty of each level of rainfall forecasts and provide decision-making support for actual managers.

2. The method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts according to claim 1, characterized in that, It includes the following steps: Step 1: Determine the rainfall forecast grading standard and the binning standard for calculating the entropy value Combined with the grading standards of the meteorological department and the actual use, determine the grading standards for rainfall forecast data, L k is the k-th rainfall level, where k = 1, 2, 3, ……, K, and K is the total number of rainfall forecast grades; When calculating the relevant indicators of entropy, it is necessary to determine the bin width W; based on the bin width W, according to the maximum and minimum values P in the rainfall samples min , it is divided into NC bins in total, and the value range of each bin is [P min , P min + W], [P min + W, P min + 2W], ……, [P min + jW, P min + (j + 1)W], ……, [P min + (NC - 1)·W, P min + NC·W], and the j-th bin is represented by C j , where j is the bin number index, and j = 1, 2, 3, ……, NC; Step 2: Grade and bin the forecast values and observed values According to the rainfall forecast grading standard determined in Step 1, determine the grade to which the rainfall forecast value belongs; Similarly, according to the binning standard obtained in Step 1, determine the bin to which the rainfall observed value belongs; Step 3: Calculate the normalized contingency table of forecast rainfall and observed rainfall Step 4: Calculate the uncertainty evaluation index NMID for each level of the evaluation rainfall forecast k and the comprehensive uncertainty index NMI.

3. The method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts according to claim 2, characterized in that, The calculation methods of the bin width in Step 1 include equal-frequency binning, equal-distance binning, and equal-frequency and equal-distance hybrid method.

4. The method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts according to claim 2, characterized in that, The p in step 3 described above k,j According to the classification and binning results of all the forecast and observation data in step 2, count the number n of cases where the forecast rainfall belongs to the k-th level and the corresponding observed rainfall belongs to the j-th bin k,j , then p k,j is calculated by formula (2): From p k,j p can be calculated j and See formulas (3) and (4) respectively:

5. The method for evaluating the uncertainty of deterministic hierarchical rainfall forecasts according to claim 2, characterized in that, In the formula (5) of step 4 described above, H(O) and H(O|F k ) can be calculated according to formulas (6) and (7) respectively, where p j is calculated from step 3 Among them, represents the conditional probability that when the predicted rainfall belongs to the k-th level, the observed rainfall belongs to the j-th bin, which is calculated by formula (8):

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