A method for evaluating precipitation probability forecast precision based on fuzzy event probability

Abstract

The application belongs to the technical field of hydrology prediction, and particularly relates to a precipitation probability prediction precision evaluation method based on fuzzy event probability. The method is used for precipitation probability prediction precision evaluation. The technical scheme is a precipitation probability prediction precision evaluation method based on fuzzy event probability, which comprises the following steps: step 1, collecting basic data; step 2, selecting and constructing a probability prediction model; step 3, selecting membership functions of fuzzy sure event, fuzzy false event and fuzzy empty event; step 4, calculating occurrence probabilities of fuzzy sure event, fuzzy false event and fuzzy empty event of single precipitation probability prediction; and step 5, calculating fuzzy sure rate, fuzzy empty rate and fuzzy false rate of precipitation probability prediction.

Description

Technical Field

[0001] This invention belongs to the field of hydrological forecasting technology, specifically a method for evaluating the accuracy of precipitation probability forecasts based on fuzzy event probabilities. Background Technology

[0002] Precipitation forecasting is one of the most important products of numerical weather prediction (NMR) and a crucial input factor for hydrological forecasting. However, due to the complexity of atmospheric systems, the accuracy of precipitation forecasts provided by NMR remains relatively low, failing to meet the needs of practical hydrological forecasting. To address this, hydrometeorologists have proposed probabilistic precipitation forecasting methods, which use statistical methods to describe the uncertainties in precipitation forecasts, thereby improving their accuracy and reliability. Unlike deterministic forecasts, which only provide a single forecast value, probabilistic forecasts, which use the probability distribution of forecast variables as the result, can provide the probability of precipitation occurring under different threshold conditions, offering more effective information for hydrological forecasting. Currently, probabilistic precipitation forecasting is widely used in hydrological research. However, although previous studies have demonstrated that probabilistic forecasting helps improve the accuracy of precipitation forecasts, a comprehensive evaluation of its accuracy and reliability is still necessary before applying it to hydrological forecasting to avoid inaccurate hydrological forecasts due to probabilistic precipitation forecasting.

[0003] Hydrometeorologists have proposed and applied numerous indicators for evaluating the accuracy of precipitation probability forecasts, such as the Continuous Ranked Probability Score (CRPS), based on different research objectives and subjects. However, most of these indicators only focus on the overall forecast error and cannot distinguish whether the forecast error originates from false alarms (forecast magnitude greater than actual magnitude) or missed alarms (forecast magnitude greater than actual magnitude). From a meteorological research perspective, researchers typically focus more on the overall forecast performance and overall error level of precipitation forecasts or precipitation probability forecasts, and generally do not need to strictly distinguish between false alarms and missed alarms; that is, the above approach is reasonable. However, in hydrological forecasting and hydrological application scenarios, the impact of false alarm errors and missed alarm errors on hydrological forecasting research is completely different. Taking basin flood forecasting as an example: When precipitation forecasts are false alarms, hydrological models, based on overestimated precipitation inputs, overestimate future peak flow, flood volume, and flood events. This prompts flood control decision-makers to adopt more conservative flood control measures, such as prematurely opening floodgates and organizing the early evacuation of people in threatened areas. Although the actual flood may not reach the predicted magnitude, such conservative measures can still ensure flood control safety, but they will cause reservoirs to release water prematurely, resulting in the loss of some comprehensive benefits in water resource utilization, power generation, water supply, and ecology. Conversely, when precipitation forecasts are false alarms, hydrological models, due to underestimating precipitation inputs, underestimate the future flood scale. This may lead to delays in flood control engineering scheduling, dike patrol and defense, and emergency response preparations, significantly increasing the risk of flooding and the possibility of disaster losses. Therefore, it is necessary to construct a series of new precipitation probability forecast evaluation indicators that can clearly distinguish between false alarm and false alarm errors, thereby better assessing the accuracy of precipitation probability forecasts in hydrological forecasting. Some evaluation indicators designed for deterministic precipitation forecasts, such as the three rates (confirmation rate, missed rate, and false alarm rate) and their improved form, the fuzzy three rates (existing technology), are not applicable to probability precipitation forecasts. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the above-mentioned technical background and provide a method for evaluating the accuracy of precipitation probability forecasts based on fuzzy event probabilities, which can be used for assessing the accuracy of precipitation probability forecasts.

[0005] The technical solution provided by this invention is: a method for evaluating the accuracy of precipitation probability forecasts based on fuzzy event probabilities, comprising the following steps: Step 1: Basic data collection, collecting precipitation forecast and measured precipitation data for the study area; Step 2: Selection and construction of probability forecasting model. Select a suitable precipitation probability forecasting model according to the requirements, and generate a precipitation probability distribution as the precipitation probability forecast result by combining the data collected above. make This represents a random variable in precipitation forecasting. Represents the measured precipitation random variable. and Representing random variables respectively and A specific value, Indicates when When known, random variable The probability density function, i.e., the probability forecast result of precipitation.

[0006] Step 3: Select the membership function for fuzzy confirmed events, fuzzy missed events, and fuzzy empty events.

[0007] In the fuzzy three-probability model, based on the relationship between precipitation forecast values ​​and measured precipitation values, traditional research fuzzifies confirmed reports, missed reports, and false reports, forming three fuzzy events: fuzzy confirmed reports, fuzzy false reports, and fuzzy missed reports. This invention adds a threshold to the existing membership functions of fuzzy confirmed reports, fuzzy missed reports, and fuzzy false reports, making them more in line with the needs of precipitation probability forecast assessment. Fuzzy membership function: In the formula, For fuzzy reporting of membership function, This is a forecast value for a certain precipitation event. This represents the actual precipitation value corresponding to the forecast. This is the fuzzy confirmation threshold, meaning that when the difference between the forecast and the actual precipitation value is less than this threshold, the forecast can be considered a fuzzy confirmation. This threshold can be set according to actual needs.

[0008] Fuzzy missed reporting membership function: In the formula, This is a fuzzy underreporting membership function.

[0009] Fuzzy empty report membership function: In the formula, This is the membership function for fuzzy empty reports.

[0010] Step 4: Calculate the probability of occurrence of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarms in a single precipitation probability forecast. Fuzzy event probability is a theoretical tool that integrates probability theory and fuzzy mathematics, specifically designed to address the dual uncertainties of fuzzy event boundaries and imprecise probability information in reality. Based on the precipitation forecast results obtained in Step 1 and the membership functions of the three fuzzy events (fuzzy confirmed events, fuzzy missed events, and fuzzy false alarms) constructed in Step 2, the probability of occurrence of the single precipitation forecast can be calculated. When known, the probabilities of the three fuzzy events—fuzzy confirmed report, fuzzy missed report, and fuzzy false alarm—are as follows: Fuzzy probability of confirmed events Fuzzy probability of missed events Probability of fuzzy null report event Step 5: Calculation of fuzzy prediction rate, fuzzy false alarm rate, and fuzzy missed alarm rate in precipitation probability forecasts. Based on the calculation method in the previous step, calculate the probability of occurrence of fuzzy prediction events, fuzzy missed alarm events, and fuzzy false alarm events in multiple precipitation probability forecasts. Calculate the average of the three fuzzy event probabilities from multiple precipitation probability forecasts as the fuzzy prediction rate, fuzzy false alarm rate, and fuzzy false alarm rate of the precipitation probability forecast.

[0011] Assuming the total number of precipitation forecast values ​​during this period is [number missing] The probabilities of occurrence of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events calculated in each iteration are as follows: Then, the fuzzy confirmation rate, fuzzy underreporting rate, and fuzzy false alarm rate of precipitation probability forecasts can be calculated as follows: Fuzzy positive rate Fuzzy false negative rate Fuzzy false alarm rate .

[0012] The beneficial effects of this invention are as follows: by using the above method, the fuzzy three-probability method can be extended to the field of accuracy assessment of precipitation probability forecasting, providing scientific support and decision-making basis for selecting appropriate precipitation probability forecasting methods in hydrological forecasting work. Attached Figure Description

[0013] Figure 1 This is a flowchart of an embodiment of the present invention.

[0014] Figure 2 This is a graph showing the probability forecast results for precipitation. Detailed Implementation

[0015] The idea behind this invention is to improve the membership function of the fuzzy three rates based on deterministic forecasting and combine it with the concept of fuzzy event probability to propose a method for evaluating the accuracy of precipitation probability forecasting based on fuzzy event probability. This method is used to evaluate the accuracy of precipitation probability forecasting and provides a reference for selecting appropriate precipitation probability forecasts in subsequent hydrological studies.

[0016] The specific implementation method is as follows (see...). Figure 1 First, basic data such as precipitation forecasts and measured precipitation data for the study area are collected, and a suitable precipitation probability forecast model is selected to generate precipitation probability forecast results; then, according to the research needs, an appropriate fuzzy confirmation threshold is selected. Then, substitute the values ​​into the equation; then, calculate the probability of each precipitation probability forecast fuzzy confirmed event, fuzzy missed event, and fuzzy false alarm event; finally, calculate the fuzzy confirmed rate, fuzzy missed rate, and fuzzy false alarm rate based on multiple precipitation probability forecasts.

[0017] The present invention will be further described in detail below with reference to the embodiments.

[0018] Taking data from a rain gauge station in a city in southeastern coastal my country as an example, we selected publicly released precipitation forecast data from meteorological agencies A and B, and adopted ensemble preprocessing (EPP) as the precipitation probability forecasting method. We evaluated the performance of the EPP method based on different precipitation forecasts by using fuzzy three-probability evaluation of the precipitation probability forecasts.

[0019] I. Basic Data Situation This example collects global daily precipitation forecast data from meteorological agencies A and B, as well as measured precipitation data from a surface rain gauge station in a city on the southeast coast of my country. The two sets of publicly available daily precipitation data cover the period from 2020 to 2024. The precipitation forecast data is sourced from the meteorological agencies' official websites, with forecast times at 00:00 UTC (08:00 Beijing Time) and a forecast step of 24 hours. The measured precipitation data is sourced from the China Meteorological Administration website.

[0020] II. Precipitation Probability Forecast Generation This example uses the EPP method (an existing technology) to generate probabilistic precipitation forecasts. The EPP method is a probabilistic precipitation forecasting method based on bivariate sub-Gaussian distribution and normal quantile transformation. Essentially, it estimates the marginal distributions of both the forecast precipitation and its corresponding measured precipitation based on historical data. Then, through normal quantile transformation, it transforms the two variables from their original spatial distribution to a normal spatial distribution, thus obtaining the joint probability distribution between the two non-normal variables. Using conditional probability formulas, it generates probabilistic precipitation forecasts containing uncertainty information from deterministic precipitation forecasts, which is a commonly used statistical post-processing method for precipitation. This method has been used for many years in forecast centers in multiple countries and has proven to improve the accuracy and effectiveness of weather forecasts.

[0021] This example, based on the aforementioned precipitation forecast and measured precipitation data, uses the EPP method to generate precipitation probability forecasts based on precipitation forecast data from meteorological agencies A and B, respectively. For ease of presentation, this example only displays a portion of the time period and uses the Monte Carlo method (an existing technique) to sample the results generated by the EPP method, and plots the 5% and 95% quantile lines. See details... Figure 2 .

[0022] III. Calculation of the probability of occurrence of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events in single precipitation probability forecasts Based on the fuzzy confirmed membership degree and the precipitation probability forecast results generated by the EPP method, the probabilities of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events are calculated daily. In this example, the fuzzy confirmed threshold... The value is taken as 1 mm. The following are some results as examples, showing the measured precipitation values, the deterministic precipitation forecast values ​​of the two institutions, and the calculated probabilities of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events. See Table 1 for details.

[0023] Table 1. Calculation results of the probability of occurrence of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events during a certain period. IV. Calculation of Fuzzy False Alert Rate, Fuzzy Missed Alert Rate, and Fuzzy Missed Alert Rate in Precipitation Probability Forecasts Based on the calculated probabilities of occurrence of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarms in a single precipitation probability forecast, the fuzzy confirmed rate, fuzzy false alarm rate, and fuzzy false alarm rate of the precipitation probability forecast based on meteorological agency A are 0.64, 0.18, and 0.19, respectively; while the fuzzy confirmed rate, fuzzy false alarm rate, and fuzzy false alarm rate of the precipitation probability forecast based on meteorological agency B are 0.65, 0.16, and 0.19, respectively. Therefore, in the study area, the precipitation probability forecast generated based on precipitation forecast data from meteorological agency B and the EPP method is slightly more accurate than the precipitation probability forecast generated based on precipitation forecast data from meteorological agency A and the EPP method.

Claims

1. A method for evaluating the accuracy of precipitation probability forecasts based on fuzzy event probabilities, comprising the following steps: Step 1: Basic Data Collection Collect precipitation forecast and measured precipitation data for the study area; Step 2: Selection and Construction of Probabilistic Forecasting Model Select a suitable precipitation probability forecasting model based on the requirements, process the collected data, and generate the precipitation probability forecast results as follows: That is, when When the precipitation probability forecast is known, the result is a random variable. The probability density function; where: This represents a random variable in precipitation forecasting. Represents the measured precipitation random variable. and Representing random variables respectively and A specific value that can be taken; Step 3: Selection of membership functions for fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events. Based on the existing three membership functions—fuzzy confirmed reports, fuzzy missed reports, and fuzzy empty reports—a threshold has been added, resulting in the following function: Fuzzy membership function In the formula, For fuzzy reporting of membership function, This is a forecast value for a certain precipitation event. This represents the actual precipitation value corresponding to the forecast. For fuzzy reporting thresholds; Fuzzy missed reporting membership function: In the formula, For fuzzy underreporting membership function; Fuzzy empty report membership function: In the formula, For fuzzy empty report membership function; Step 4: Calculation of the probability of occurrence of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events in a single precipitation probability forecast. Based on the precipitation forecast results obtained in step 2 and the membership functions of the three fuzzy events (fuzzy confirmed report, fuzzy missed report, and fuzzy false report) constructed in step 3, the following formula is used to calculate the precipitation forecast... Given the event, the probabilities of fuzzy confirmed reports, fuzzy missed reports, and fuzzy false alarms occurring are as follows: Fuzzy probability of confirmed events Fuzzy probability of missed events Probability of fuzzy null report event Step 5: Calculation of fuzzy prediction rate, fuzzy false alarm rate, and fuzzy missed prediction rate for precipitation probability forecast. First, calculate the probability of occurrence of fuzzy confirmed events, fuzzy missed events, and fuzzy false alarm events in multiple precipitation probability forecasts according to the calculation formula described in step 4. Then, calculate the average of the probabilities of occurrence of fuzzy confirmed events in multiple precipitation probability forecasts as the fuzzy confirmed rate of precipitation probability forecasts, the average of the probabilities of occurrence of fuzzy missed events in multiple precipitation probability forecasts as the fuzzy missed rate of precipitation probability forecasts, and the average of the probabilities of occurrence of fuzzy false alarm events in multiple precipitation probability forecasts as the fuzzy false alarm rate of precipitation probability forecasts.

2. The method for evaluating the accuracy of precipitation probability forecasts based on fuzzy event probabilities according to claim 1, characterized in that: The fuzzy reporting threshold mentioned in step 3 This threshold indicates that when the difference between the forecast and the actual precipitation value is less than this threshold, the forecast can be considered a completely fuzzy but confirmed forecast; this threshold is set according to actual needs.

3. The method for evaluating the accuracy of precipitation probability forecasts based on fuzzy event probabilities according to claim 2, characterized in that: The specific calculation formula used in step 5 is as follows: Fuzzy prediction rate of precipitation probability forecast Fuzzy underreporting rate of precipitation probability forecast Fuzzy false alarm rate in precipitation probability forecast In the formula: ; This represents the number of precipitation forecast values ​​for that period. The probability of occurrence of the fuzzy confirmed event is obtained from multiple calculations; The probability of a fuzzy missed event is calculated multiple times. The probability of the occurrence of the fuzzy false alarm event is obtained from multiple calculations.

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