Rainfall level integrated forecasting method based on Bayesian formula and evidence theory

Abstract

The invention relates to a weather forecasting method, in particular to a rainfall level integrated forecasting method based on a Bayesian formula and an evidence theory. The invention aims to provide a rainfall level integrated forecasting method based on a Bayesian formula and an evidence theory, and provides a firm and reliable technical support for further improving the rainfall forecasting precision and promoting the application of the rainfall forecasting method in flood and drought disaster early warning and water resource scheduling. According to the technical scheme, the rainfall level integrated forecasting method based on the Bayesian formula and the evidence theory comprises the following steps of 1, rainfall forecasting and actually measured data collection; step 2, rainfall level determination; 3, determining and calculating Bayesian formula distribution; step 4, evidence fusion; and 5, integrating forecast evaluation.

Description

Technical Field

[0001] This invention relates to a weather forecasting method, specifically an integrated forecasting method for rainfall magnitude based on Bayesian formulas and evidence theory. Background Technology

[0002] Rainfall forecasts are one of the most important products of numerical weather prediction and a crucial reference for flood and drought disaster early warning and water resource allocation. Currently, the accuracy of rainfall forecasts still falls short of the practical needs of flood and drought disaster forecasting and water resource allocation in the hydrological field, severely limiting the role rainfall forecasts can play in hydrological applications. To address this, meteorologists have proposed combining rainfall forecasts from different models or different initial values ​​from the same model, a process known as ensemble forecasting. Since the concept of ensemble forecasting was proposed, from simple equal-weighted ensemble averaging to complex statistical learning methods, an increasing number of statistical regression analysis methods have been applied to ensemble forecasts of different meteorological variables. Ensemble forecasts often provide a better forecast result than individual members.

[0003] Based on the concept of integrated forecasting, its essence is to integrate forecasting... Rainfall forecasts from different institutions or models Through a linear or nonlinear function Combined into a new forecast value Therefore, the forecast results of each member of the integrated forecast can be combined. These are considered as evidence from different sources, and the multi-source evidence fusion method in evidence theory is used to fuse the forecast results of each member to generate an integrated forecast result. Theoretically, it is feasible to use evidence theory to achieve integrated rainfall forecasting, but two problems still need to be solved.

[0004] First, evidence theory requires defining an identification framework, that is, the set of things or objects being examined and judged, defined as a non-empty set. It contains Each pair of mutually exclusive events. For example, Consists of two mutually exclusive events and Composition, that is, having Then there are power sets For rainfall forecasting, its value can be: For any value within the interval, there are infinitely many pairwise mutually exclusive events, resulting in infinitely many power sets, making the computation of evidence theory difficult. Another problem is how to assign credibility. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the above-mentioned technical background and propose an integrated forecasting method for rainfall magnitude based on Bayes' formula and evidence theory, which provides solid and reliable technical support for further improving the accuracy of rainfall forecasting and promoting its application in flood and drought disaster early warning and water resource allocation.

[0006] The technical solution provided by this invention is: an integrated forecasting method for rainfall magnitude based on Bayesian formula and evidence theory, comprising the following steps: Step 1: Rainfall Forecast and Measured Data Collection: Collect rainfall forecast data and corresponding measured rainfall data issued by multiple meteorological agencies in the study area during a certain historical period; Step 2: Determining the rainfall level: Based on the national standard "Rainfall Levels" (GB / T 28592-2012), formulate corresponding rainfall level classification standards, and calculate the rainfall forecast data collected in the previous step from different institutions and the corresponding measured rainfall values ​​to their respective levels; Step 3: Bayesian Formula Distribution Determination and Calculation: Using the rainfall forecast level issued by a meteorological agency as a condition, calculate the probability of different measured rainfall levels occurring using the Bayesian formula; specifically, assume that a certain weather forecast... The random variable for the magnitude of rainfall forecast over a given period is: The corresponding real-order random variable is , and Both are discrete random variables, and according to Bayes' theorem, we have: (1) In the formula, Indicates in When it happens The conditional probability of occurrence, i.e., the posterior distribution; express The probability distribution of occurrence, i.e., the prior distribution; Indicates in When it happens The conditional probability of occurrence, i.e., the likelihood function; express The probability distribution of occurrence is used for normalization.

[0007] Based on the above formula, we need to first determine , and .in, Let be the prior distribution, representing our estimate of the actual rainfall magnitude at a future time when there is no rainfall forecast. In this invention, a uniform distribution is used, meaning that when no forecast is made, it is assumed that the probability of each magnitude occurring is equal (Equation 2). is the distribution function of the rainfall forecast magnitude, which can be estimated based on the historical rainfall forecast magnitude distribution data collected (Equation 3). The likelihood function can be estimated based on different measured rainfall levels and their corresponding rainfall forecast levels from collected historical data (Equation 4). The specific calculation formula is as follows: Assume that rainfall is divided into A quantity, and denoted as ,Right now and The range of values ​​is .

[0008] (2) (3) (4) In the formula, The total number of samples is the number of rainfall forecast levels (or actual measurement levels, which correspond one-to-one). The rainfall forecast level is the [number]. The number of orders of magnitude; The measured rainfall level was [number]. The magnitude is [number], while the rainfall forecast magnitude is [number]. The number of orders of magnitude.

[0009] Step 4: Evidence Fusion: The probabilities calculated using the Bayesian formula above are used as the credibility assignment function for the evidence. For example, suppose rainfall is divided into only two levels: no rain and rain, and there is a forecasting agency whose posterior distributions for the actual rainfall levels (rain and no rain) are as follows: and According to evidence theory, the identification framework is now in place. It contains two mutually exclusive events: the measured rainfall level indicates that there will be rain. The measured rainfall level was no rain. That is, forming a power set. This invention does not consider ambiguity between orders of magnitude; therefore, a set of multiple events, such as... The confidence assignment function is 0, meaning that the measured rainfall level cannot be both no rain and rainy. Therefore, when the agency's forecast is rainy, the confidence assignment function... for: (5) According to Bayesian statistical theory Therefore, Equation 5 satisfies the requirements of the credibility assignment function; Following this logic, if precipitation is divided into... Each order of magnitude is denoted as... Then the credibility assignment function for: (6)

[0010] Therefore, based on the above steps, the credibility allocation function of each institution is determined, and the evidence fusion calculation is performed using the following formula (Equation 7) to calculate the probability of different precipitation levels occurring.

[0011] (7) In the formula, For evidence fusion operators; Assign a function to the credibility of the merged event; Evidence respectively The corresponding credibility assignment function is a normalization constant, which can be calculated using the following formula: (8) Step 5: Integrated Forecast Evaluation The effectiveness of the integrated forecast in this invention can be evaluated using the multi-class Brier score. The Brier score is applicable to both binary and multi-class classification problems and is an effective method for assessing the predictive reliability and discriminative power of probabilistic results. The Brier score ranges from 0 to 1; a value of 0 indicates a perfect forecast, while a value of 1 indicates a forecast with no discriminatory power. The formula for calculating the multi-class Brier score is as follows: (9) In the formula: Represents the total number of forecasts; It represents the total number of possible categories; Indicates the first The forecast result is The probability of; This represents the actual occurrence and is a one-hot encoding, meaning that only the magnitude of the actual occurrence is 1, while the other magnitudes are 0.

[0012] The beneficial effects of this invention are: Based on Bayes' theorem and evidence theory, this invention proposes a new integrated rainfall forecasting method, which can effectively improve the accuracy and reliability of rainfall forecasts, thereby enabling it to play a more important role in hydrological applications such as flood and drought disaster early warning and water resource allocation. Attached Figure Description

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

[0014] This invention employs evidence theory to achieve integrated rainfall forecasting, and addresses two existing problems by providing the following solutions: First, for rainfall forecasting, its value can be: Any value within a given interval represents an infinite number of mutually exclusive pairwise events, resulting in an infinite number of power sets, making the computation of evidence theory difficult. However, in practical applications, it is usually sufficient to know a certain range of rainfall values, rather than the specific values ​​themselves, to conduct flood and drought disaster early warnings or water resource allocation to a certain extent. Therefore, this invention uses the national standard "Rainfall Levels" (GB / T 28592-2012) as a benchmark, classifying rainfall forecast values ​​and actual values ​​into seven levels: trace rainfall (sporadic light rain), light rain, moderate rain, heavy rain, torrential rain, extremely heavy rain, and exceptionally heavy rain. The levels corresponding to the rainfall forecast values ​​obtained from different models are used as evidence to construct an identification framework, and the rainfall level is used as the final output of the integrated forecast.

[0015] Second, regarding how to assign credibility; the credibility assignment function. Also known as the mass function, it is a function that extracts data from a set. arrive The mapping, let For identification framework any subset (i.e. ), and satisfy .

[0016] This invention introduces Bayesian statistical theory to derive the credibility assignment function for different modes that meet the requirements.

[0017] The underlying idea of ​​this invention is (see...) Figure 1 To address the practical need for improving rainfall forecast accuracy, this paper applies Bayesian formulas to evidence theory to construct a new integrated rainfall forecasting method. The method's implementation involves: first, collecting rainfall forecast data and corresponding measured rainfall data from multiple meteorological agencies over a historical period in the study area; then, establishing rainfall level classification standards based on the national standard "Precipitation Levels"; next, calculating the probability of different measured rainfall levels occurring under known forecast levels using Bayesian formulas; then, integrating the rainfall forecasts from multiple agencies using the evidence fusion formula in evidence theory and obtaining the integrated rainfall forecast result; finally, evaluating the integrated forecast result.

[0018] The present invention will be further described in detail below with reference to the embodiments.

[0019] An integrated rainfall magnitude forecasting method based on Bayesian formulas and evidence theory is proposed. Using rainfall forecast data from four institutions—the European Centre for Medium- and Long-Term Weather Forecasts, the Canadian Centre for Environment and Seasonal Change, the Japan Meteorological Agency, and the U.S. National Center for Environmental Prediction—along with measured rainfall data from a rain gauge station in southern my country, this invention integrates rainfall forecasts to generate more accurate rainfall forecasts.

[0020] I. Basic Information The rainfall forecast data used in this embodiment are all from the Global Interactive Ensemble Forecasting System (TIGGE) dataset, a core product of the global ensemble forecasting project initiated by the World Meteorological Organization's Observational Systems Research and Predictability Experimentation Programme. This dataset, initiated in 2005, aims to provide high-quality ensemble forecast data to support research and improvement of weather forecasting. Through multi-model ensemble forecasting techniques, it enhances the accuracy and reliability of numerical weather forecasts to serve meteorological research, disaster warning, and operational climate applications. Simply put, TIGGE integrates operational numerical weather forecasts from different countries or institutions to form a multi-institutional numerical weather forecast dataset. The TIGGE dataset contains 10 members; this embodiment selects daily rainfall forecast data from four institutions: the European Centre for Medium- and Long-Range Weather Forecasts, the Canadian Centre for Environment and Seasonal Change, the Japan Meteorological Agency, and the U.S. National Center for Environmental Prediction. The selected data covers the period from January 1, 2020 to October 31, 2024, with forecast times all at 00:00 UTC and a lead time of one day.

[0021] In this embodiment, the measured rainfall data comes from a surface rain gauge station, and the selected time range is also from January 1, 2020 to October 31, 2024. Meanwhile, since the rain gauge data is point data, while the rainfall forecasts from various institutions in the TIGGE dataset are stored in raster format, to ensure consistency between the two types of data, this embodiment uses the rainfall forecast data of the raster grid points where the rain gauge station's latitude and longitude are located for subsequent integrated forecasting.

[0022] II. Rainfall Level Classification Considering that rainfall of less than 1 mm has a very small impact on actual hydrological runoff, this embodiment makes certain adjustments to the 24-hour rainfall classification standard in the "Rainfall Classification", classifying events with daily rainfall of less than 1 mm as no-rain events. The specific classification standard is shown in the table below: Table 1 Classification of 24-hour rainfall levels III. Bayesian Theorem Distribution Determination and Calculation Based on historical rainfall forecasts and measured values, and in accordance with the above-mentioned classification criteria, the rainfall forecast magnitudes and corresponding measured magnitudes for various institutions at different historical periods were calculated, thereby obtaining statistical results. , and (Equations 2-4), and then the posterior distribution is derived based on Equation 1. various institutions The calculation results are shown in the table below. It should be noted that the probability of actual rainfall levels of heavy rain or torrential rain in Table 2 is mostly 0. This is because heavy rain and torrential rain occur relatively infrequently, and the time range selected in this embodiment is limited (only from January 1, 2020 to October 31, 2024), during which there may not have been any instances of rainfall forecasts or actual measurements reaching the levels of heavy rain or torrential rain.

[0023] Table 2. Calculation Results of Bayes' Theorem for Each Institution IV. Evidence Integration Using the probability distribution calculated above as the credibility allocation function, evidence fusion was performed on the rainfall forecast magnitudes of various institutions on a daily basis. Due to space limitations, this invention selected two dates as samples to briefly introduce the results of evidence fusion. The dates of the two samples, the rainfall forecast values ​​and corresponding magnitudes of each institution, and the actual rainfall values ​​and corresponding magnitudes at each station are as follows: Table 3. Summary of selected sample dates, rainfall forecasts and corresponding magnitudes for each institution, and measured rainfall values ​​and corresponding magnitudes at each station. Based on the evidence fusion formulas (Equations 7 and 8), the probabilities of each magnitude occurring after the fusion of these two sample evidences can be calculated as shown in the table below: Table 4. Evidence fusion results of selected samples Therefore, the fusion results show that the four institutional evidences on January 29, 2020, indicate that the rainfall on that day had the highest probability of being a light rain (scattered light rain), while the rainfall on April 18, 2020, had the highest probability of being a light rain (level 2). The level of the highest probability of occurrence in both forecasts was the same as the actual rainfall level.

[0024] V. Integrated Forecast Evaluation Brier scores for the original forecasts from each agency and the integrated forecasts were calculated according to Equation 9, as shown in the table below. The results show that the Brier scores using the original forecasts from each agency range from 0.71 to 0.82, while the Brier score for the integrated forecast using the method of this invention is 0.58, significantly lower than the Brier scores of the original forecasts from each agency. Since a Brier score closer to 0 indicates better forecast accuracy and reliability, it can be concluded that the method of this invention effectively improves the accuracy and reliability of rainfall forecasts.

[0025] Table 5. Evaluation Table of Integrated Rainfall Forecast

Claims

1. A method for integrated forecasting of rainfall magnitude based on Bayesian formula and evidence theory, comprising the following steps: Step 1: Rainfall Forecast and Measured Data Collection: Collect rainfall forecast data and corresponding measured rainfall data issued by multiple meteorological agencies in the study area during a certain historical period; Step 2: Determining the rainfall level: Establish corresponding rainfall level classification standards, and calculate the rainfall forecast data collected in the previous step from different institutions and the corresponding measured rainfall values ​​to their respective levels; Step 3: Bayesian formula distribution determination and calculation: Using the rainfall forecast level issued by a certain meteorological agency as a condition, calculate the probability of different measured rainfall levels occurring using the Bayesian formula; Specifically, suppose a certain weather forecast... The random variable for the magnitude of rainfall forecast over a given period is: The corresponding real-order random variable is According to Bayes' theorem, we have: （1） In the formula: Indicates in When it happens The conditional probability of occurrence, i.e., the posterior distribution; express The probability distribution of occurrence, i.e., the prior distribution, is specifically a uniform distribution; Indicates in When it happens The conditional probability of occurrence, i.e. the likelihood function, is specifically estimated based on the different measured rainfall levels and their corresponding rainfall forecast levels in the collected historical data. express The probability distribution of occurrence is used for normalization, specifically estimated based on the collected historical rainfall forecast magnitude distribution. Step 4: Evidence fusion: The probability calculated by the Bayes formula above is used as evidence. The credibility allocation function of each institution is determined by Equation 6, and the evidence fusion is performed by Equation 7 to calculate the probability of different precipitation levels occurring. Credibility assignment function for: （6） （7） In the formula: For evidence fusion operators; Assign a function to the credibility of the merged event; Evidence respectively The corresponding credibility assignment function; K is the normalization constant, calculated using Equation 8: （8）。 2. The integrated rainfall magnitude forecasting method based on Bayesian formula and evidence theory according to claim 1, characterized in that: The specific calculation formula for step 3 is as follows: Rainfall is divided into A quantity, and denoted as ,Right now and The range of values ​​is ; （2） （3） （4） In the formula, The total number of samples represents either the number of rainfall forecast levels or the number of actual rainfall levels, with a one-to-one correspondence between the two. The rainfall forecast level is the [number]. The number of orders of magnitude; The measured rainfall level was [number]. The magnitude is [number], while the rainfall forecast magnitude is [number]. The number of orders of magnitude.

3. The integrated rainfall magnitude forecasting method based on Bayesian formula and evidence theory according to claim 2, characterized in that: The method for determining the credibility assignment function in step 4 is as follows: Assuming rainfall is divided into two levels: no rain and rain, and given that when a forecasting agency predicts rain, the posterior distributions of the actual rainfall levels for rain and no rain are respectively... and According to evidence theory, the identification framework at this point... It contains two mutually exclusive events: the measured rainfall level indicates that there will be rain. The measured rainfall level was no rain. ; Then the credibility assignment function for: （5） Following this logic, if precipitation is divided into... Each order of magnitude is denoted as... Then the credibility assignment function for: （6）。

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