Rainfall forecast precision evaluation method based on fuzzy mathematics

Abstract

The invention relates to a weather forecast precision evaluation method, in particular to a rainfall forecast precision evaluation method based on fuzzy mathematics. The invention aims to provide a rainfall forecast precision evaluation method based on fuzzy mathematics so as to better evaluate the precision of rainfall forecast. According to the technical scheme, the rainfall forecast precision evaluation method based on fuzzy mathematics comprises the following steps: step 1, preparing a basic data set; 2, selecting a membership function; and step 3, calculating a fuzzy accurate report rate, a fuzzy missing report rate and a fuzzy empty report rate.

Description

Technical Field

[0001] The present invention relates to a weather forecast accuracy assessment method, in particular to a precipitation forecast accuracy assessment method based on fuzzy mathematics. Background Art

[0002] Precipitation, as a primary input variable in hydrological models, directly impacts the reliability of flood forecasts. In recent years, with the rapid development of numerical weather prediction (NWP), an increasing number of hydrologists have begun exploring the integration of precipitation forecasts into hydrological forecasting to extend the forecast horizon. Although the accuracy of NWP has made significant progress over the past half century, limited by the chaotic nature of the atmospheric system, whether precipitation forecast accuracy can meet the needs of basin / regional hydrological forecasting remains a hot topic in hydrometeorological research. To this end, hydrometeorologists have proposed a series of evaluation metrics to assess precipitation forecast accuracy, the most representative of which are the confirmation rate, omission rate, and false alarm rate. The confirmation rate refers to the proportion of forecasts where the predicted precipitation magnitude is the same as the actual magnitude; the omission rate refers to the proportion of forecasts where the predicted precipitation magnitude is less than the actual magnitude; and the false alarm rate refers to the proportion of forecasts where the predicted precipitation magnitude is greater than the actual magnitude. However, in reality, because precipitation forecast levels are artificially demarcated, the impact of two confirmed, missed, or false positives on hydrological forecasts can be significantly different. For example, suppose the precipitation forecast for event 1 is 2 mm, which is considered light rain, but the actual precipitation is 51 mm, which is considered heavy rain, resulting in a missed event. For event 2, the precipitation forecast is 49 mm, which is considered heavy rain, but the actual precipitation is 51 mm, also considered heavy rain, also a missed event. However, for hydrological forecasts, event 1 will clearly result in a smaller predicted flood peak, while the impact of event 2 is relatively minor. This difference between confirmed, missed, and false positives is not reflected in traditional confirmation, missed, and false positive rates.

[0003] In reality, the definitions of confirmed reports, missed reports, and false alarms all share a clear connotation but fuzzy boundaries. For example, while the definition of confirmed reports is clear—that is, a precipitation forecast is accurate—however, there's no definitive answer to what constitutes an accurate forecast, or the difference between the forecast and the actual value. This fuzziness in the boundaries is therefore crucial when applying the confirmed report rate, false alarm rate, and missed alarm rate in practice, in order to better assess precipitation forecast accuracy. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the above-mentioned background technology and provide a precipitation forecast accuracy evaluation method based on fuzzy mathematics to better evaluate the accuracy of precipitation forecasts.

[0005] The technical solution provided by the present invention is:

[0006] A precipitation forecast accuracy evaluation method based on fuzzy mathematics includes the following steps:

[0007] Step 1: Basic dataset preparation

[0008] Collect precipitation forecast data for a period of time in the study area and its corresponding precipitation measured data.

[0009] Step 2: Membership function selection

[0010] The membership function is the key to fuzzy mathematics. To apply fuzzy mathematics in practice, a membership function that conforms to the actual situation must be established. However, there is currently no unified standard for selecting a membership function. The present invention comprehensively selects a membership function based on its own definition and the connotations of fuzzy positive reports, fuzzy missed reports, and fuzzy false reports.

[0011] (1) Membership function definition requirements

[0012] According to the relevant definition of fuzzy mathematics, assuming that the entire domain space is Ω, it can be divided into n fuzzy sets, which are respectively Then for any fuzzy set The membership function The following requirements should be met:

[0013] ① The value range of is [0,1];

[0014] ②For the same x, The sum of the membership functions should be 1, that is:

[0015]

[0016] (2) Requirements for ambiguous reporting, missed reporting, and empty reporting

[0017] ① According to the relevant definitions of confirmed, missed, and false alarms, the membership function of a confirmed alarm should be inversely proportional to the gap between the measured and predicted values, that is, the larger the gap, the smaller the confirmed membership; the membership function of a missed alarm should be directly proportional to the gap between the two values ​​when the measured value is greater than the predicted value; the membership function of a false alarm should be directly proportional to the gap between the two values ​​when the measured value is less than the predicted value;

[0018] ② Considering the impact of actual events on hydrological model simulations, the membership function for confirmed predictions is not only related to the difference between the measured and predicted values, but also to the measured values ​​themselves. For example, if the predicted value for event 1 is 1 mm and the measured value is 11 mm, the absolute error between the two is 10 mm; if the predicted value for event 2 is 250 mm and the measured value is 260 mm, the absolute error between the two is also 10 mm; however, the impacts of events 1 and 2 on hydrological forecasts are completely different.

[0019] (3) Determination of membership function

[0020] Based on the above requirements, the present invention proposes corresponding membership functions for fuzzy positive alarm, fuzzy missed alarm and fuzzy false alarm based on the concept of relative error.

[0021] Assuming that each precipitation forecast value is y and its corresponding measured value is x, the domain of the relationship between the two can be divided into three fuzzy sets, namely fuzzy confirmation sets Fuzzy missed set and fuzzy empty report set The membership function of the forecast belonging to three different fuzzy sets can be expressed as:

[0022] Fuzzy confirmation membership function:

[0023] Where μ Q (x,y) is the fuzzy confirmation membership function.

[0024] Fuzzy omission membership function:

[0025] Where μ L (x,y) is the fuzzy missing membership function.

[0026] Fuzzy null membership function:

[0027] Where μ K (x,y) is the fuzzy null membership function.

[0028] Step 3: Calculation of fuzzy positive alarm rate, fuzzy missed alarm rate and fuzzy false alarm rate

[0029] According to the membership function, the membership of each forecast value and the corresponding measured value in a period of time to fuzzy confirmed alarm, fuzzy missed alarm and fuzzy false alarm is calculated, and the average value of the membership is used as the fuzzy confirmed alarm rate, fuzzy missed alarm rate and fuzzy false alarm rate.

[0030] The specific formula is as follows:

[0031] Assume that the number of precipitation forecast values ​​for this period is m, recorded as F = [f1, f2, ..., f m], and the m measured precipitation values ​​corresponding to the precipitation forecast values ​​are recorded as O = [o1, o2,…, o m ], then the fuzzy confirmation rate is

[0032]

[0033] The fuzzy false negative rate is

[0034] The fuzzy null alarm rate is

[0035] The beneficial effects of the present invention are as follows: the proposed precipitation forecast accuracy assessment method can better assess the accuracy of precipitation forecasts, and provide technical means and theoretical support for subsequent applications in hydrological forecasts. DETAILED DESCRIPTION

[0036] The idea behind this invention is to propose a precipitation forecast accuracy assessment method based on fuzzy mathematics, providing technical means and theoretical support for accurately evaluating precipitation forecast accuracy and facilitating its subsequent application in hydrological forecasting. First, historical precipitation forecasts for the study area and their corresponding measured precipitation values ​​are collected. Then, based on a defined membership function, the membership of each precipitation forecast value and its corresponding measured value to three fuzzy sets (fuzzy positive, fuzzy negative, and fuzzy false positive) is calculated. Finally, the fuzzy positive, negative, and false positive rates are statistically calculated.

[0037] The present invention is further described in detail below through specific examples.

[0038] The precipitation forecast accuracy evaluation method based on fuzzy mathematics takes an artificially set data set and Example 1 (Meishan Reservoir Basin in the Huaihe River Basin) as an example, and uses the method of the present invention to evaluate and analyze its precipitation forecast accuracy.

[0039] 1. Artificially set data sets

[0040] To further illustrate the difference between the precipitation forecast accuracy assessment method proposed in the present invention and the traditional confirmation rate, omission rate and false alarm rate, the present invention first performs calculation and analysis by artificially setting multiple relatively extreme data. At the same time, since the traditional confirmation rate, omission rate and false alarm rate are determined according to the precipitation level, in this example analysis, the 24h precipitation grade classification standard issued by the China Meteorological Administration is adopted, as shown in Table 1. The membership function selects the fuzzy confirmation, fuzzy omission and fuzzy false alarm membership functions provided in step 2, thereby calculating the fuzzy confirmation membership, fuzzy omission membership, fuzzy false alarm membership and the number of confirmations, omissions and false alarms between the forecast values ​​of each time in this period (the period in Table 1 is 20 times) and the corresponding measured values. The specific calculation results are shown in Table 2.

[0041] Table 1 24-hour precipitation level classification table

[0042]

[0043] Table 2 Data of artificial data set and calculation of fuzzy positive rate

[0044]

[0045]

[0046] According to the data in the above table, in conjunction with the definition of fuzzy confirmed alarm rate, fuzzy omission rate and fuzzy null alarm rate among the present invention, the fuzzy confirmed alarm rate that calculates is 0.449, the fuzzy omission rate is 0.276, and the fuzzy null alarm rate is 0.276; And adopt traditional method, then in 20 forecast data, only have 4 forecasts to be judged as confirmed alarm, and confirmed alarm rate, omission rate and null alarm rate are respectively 0.2,0.4 and 0.4. In fact, sequence number is that the forecast data several times of 4,7,14 and 16 are relatively close and should not be classified as omission or null alarm category. Practical significance and advantage of the present invention have also been illustrated by above-mentioned comparatively extreme data set.

[0047] 2. Example 1

[0048] Step 1: Basic dataset preparation

[0049] This case study uses the Meishan Reservoir Basin as the research area. The Meishan Reservoir Basin is located in the upper reaches of the Shihe River, a tributary of the Huaihe River in my country. The total length of the river above the Meishan Reservoir is 86 km, and the basin area is 1970 km. 2 , accounting for approximately one-third of the total area of ​​the Shihe River basin. The Dabie Mountain area, where the Meishan Reservoir basin is located, enjoys a typical subtropical humid monsoon climate, with abundant rainfall, averaging 1405.3 mm of precipitation and 738 mm of runoff depth. Precipitation within the basin varies significantly throughout the year, with the flood season from May to September accounting for two-thirds of the annual total. Due to this concentration of annual precipitation within the basin, floods frequently occur in flood reservoirs from May to September, with peak floods of significant magnitude.

[0050] This example first collects measured precipitation data and precipitation forecast data for the Meishan Reservoir basin (specific data omitted). The measured precipitation data comes from surface rain gauges, while the precipitation forecast data comes from the European Centre for Medium- and Long-Range Weather Forecasts. The data collected in this example covers the flood season (May to September) from 2015 to 2019, with a time step of one day and a forecast horizon of one day.

[0051] Step 2: Membership function selection

[0052] The membership functions used in this example are still the fuzzy positive alarm, fuzzy missed alarm and fuzzy empty alarm membership functions provided in step 2.

[0053] Step 3: Calculation of fuzzy positive alarm rate, fuzzy missed alarm rate and fuzzy false alarm rate

[0054] Based on the measured precipitation and forecast data collected in Step 1, combined with the fuzzy membership function in Step 2, we calculated a fuzzy confirmation rate of 0.41, a fuzzy omission rate of 0.09, and a fuzzy false alarm rate of 0.50. This compares to the corresponding traditional confirmation rate of 0.67, omission rate of 0.11, and false alarm rate of 0.22. This shows that the introduction of fuzzy mathematics theory significantly differs from the traditional confirmation rate, omission rate, and false alarm rate, especially in the confirmation and false alarm rates. This suggests that the precipitation forecast collected this time significantly overestimates precipitation.

Claims

1. A precipitation forecast accuracy assessment method based on fuzzy mathematics, comprising the following steps: Step 1: Basic dataset preparation Collect precipitation forecast data and corresponding precipitation measured data for a period of time in the study area; Step 2: Membership function selection The membership function of the three different fuzzy sets for the forecast in this period can be expressed as: Fuzzy confirmation membership function: Where, is the fuzzy confirmation membership function; Fuzzy omission membership function: Where, is the fuzzy omission membership function; Fuzzy null membership function: Where, is the fuzzy empty report membership function; Where: each precipitation forecast value is y, and its corresponding measured value is x; Step 3: Calculation of fuzzy positive alarm rate, fuzzy missed alarm rate and fuzzy false alarm rate According to the membership functions of different fuzzy sets described in step 2, calculate the membership of each forecast value and the corresponding measured value to fuzzy confirmed alarm, fuzzy missed alarm and fuzzy false alarm, and use the average value of the membership as the fuzzy confirmed alarm rate, fuzzy missed alarm rate and fuzzy false alarm rate.

2. The precipitation forecast accuracy assessment method based on fuzzy mathematics according to claim 1, characterized in that: The specific calculation formulas for the fuzzy confirmed alarm rate, fuzzy missed alarm rate and fuzzy false alarm rate are as follows: The fuzzy confirmation rate is The fuzzy false negative rate is The fuzzy null alarm rate is Where: m is the number of precipitation forecast values ​​in the period, denoted as F = [f1, f2, ..., f m ]; O=[o1,o2,…,o m ] are the m measured precipitation values ​​corresponding to the precipitation forecast values.

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