Meteorological type sudden drought early warning method based on weather forecast

Abstract

The present application relates to a kind of hydrological prediction methods.The purpose is to provide a kind of meteorological sudden drought early warning method based on weather forecast, to realize the probability early warning of meteorological sudden drought, improve the early warning ability of region to sudden drought event, improve the emergency response capability of region to hydrological extreme event.Technical scheme is: a kind of meteorological sudden drought probability prediction method based on weather forecast, comprising the following steps: step 1: basic data set preparation;Step 2: the definition of meteorological sudden drought;Step 3: weather probability prediction based on generalized bayes theory;Step 4: establish sudden drought probability early warning model based on Copula function.

Description

TECHNICAL FIELD

[0001] The present application relates to a hydrological forecasting method, in particular a meteorological sudden drought early warning method based on meteorological forecasting. BACKGROUND

[0002] Sudden drought is a very special drought phenomenon, which represents a rapidly developing drought. From the perspective of hydro-meteorology, under the condition of continuous sunny and few cloudy weather, strong solar radiation can increase the potential evaporation capacity, thereby causing the actual evaporation to increase, the soil moisture to be rapidly consumed, and eventually leading to the occurrence of sudden drought events. From the above process, it can be found that in the development and evolution process of sudden drought, the energy controlling evapotranspiration dominates at the initial stage, and then the water dominates. Finally, when the soil moisture decreases to a certain threshold, the evapotranspiration capacity begins to decrease, and the soil moisture decreases at a slowing down rate, and the sudden drought may become a traditional drought.

[0003] At present, scholars at home and abroad have great controversy on the definition of sudden drought. The concept of sudden drought was first proposed in 2002 to describe a rapidly developing drought caused by severe heat wave and short-term dryness, however, the study did not give a clear definition of sudden drought. In subsequent studies, many hydrological and meteorological scholars based on their own understanding of the concept of sudden drought have proposed a series of definitions of sudden drought as the basis for the early warning of sudden drought in the study area. Although the current academic circle has not reached a unified understanding of the causes and driving mechanisms of sudden drought, and lacks quantitative assessment of the impact and destructiveness of sudden drought, considering the risks brought by sudden drought to agriculture, forestry and water resources security, the research on the monitoring and early warning of sudden drought is very necessary and urgent. However, there is no mature sudden drought early warning system at home and abroad at present.

[0004] Although the current research on the definition and evolution mechanism of sudden drought is still controversial, most researchers believe that the occurrence of sudden drought is related to factors such as temperature, precipitation, soil moisture, evaporation, etc. From the perspective of hydro-meteorology, temperature and precipitation are the main driving factors of changes in soil moisture and evapotranspiration. At the same time, with the continuous improvement of meteorological forecasting ability, it is possible to use precipitation forecast and temperature forecast data for meteorological sudden drought early warning. However, although the accuracy and forecast period of numerical weather prediction have shown great progress in recent years, due to the chaotic and complex nature of the atmospheric system, errors are inevitable in the results of meteorological forecasting, and the uncertainty of the drought early warning system based on meteorological forecasting is objective. Therefore, when using meteorological forecast data for meteorological sudden drought early warning, the uncertainty of meteorological forecast must be considered.

[0005] In summary, domestic and foreign researchers have carried out relevant research work in the identification and analysis of sudden drought, but the definition of sudden drought has not been clearly defined and a reliable sudden drought warning system has not been established. Therefore, it is necessary to define meteorological sudden drought based on meteorological forecast data; based on precipitation forecast and temperature forecast data, a sudden drought warning model is established, and the uncertainty existing in the sudden drought warning is fully considered to realize the probability warning of sudden drought. SUMMARY

[0006] The purpose of the present application is to overcome the deficiencies of the above background art, provide a meteorological sudden drought warning method based on meteorological forecast, to realize the probability warning of meteorological sudden drought, improve the warning ability of the region to sudden drought events, and improve the emergency response ability of the region to hydrological extreme events.

[0007] The technical scheme provided by the present application is:

[0008] A meteorological sudden drought probability prediction method based on meteorological forecast, comprising the following steps:

[0009] Step 1: Preparation of basic data set

[0010] Collecting meteorological observation data of the study area; the meteorological observation data includes measured data and forecast data of pentad average precipitation and pentad average temperature of the study area;

[0011] Step 2: Definition of meteorological sudden drought

[0012] The definition of water shortage type sudden drought proposed by Mo and Lettenmaier is: pentad average temperature anomaly > 1 standard deviation, and pentad average precipitation percentile < 40% is meteorological sudden drought. Based on the above definition, the present application determines the corresponding values of the mean value μ T and standard deviation σ T of pentad average temperature and the 40% percentile R 40 of pentad precipitation according to the measured precipitation and temperature data of the study area; determine: when pentad climate > μ T + σ T and pentad precipitation < R 40 , it is meteorological sudden drought.

[0013] Step 3: Meteorological probability prediction based on generalized Bayesian theory

[0014] The generalized Bayesian statistical model is a model for describing the uncertainty of meteorological prediction, which was proposed by Cai et al. in 2019 for precipitation probability prediction model. This model can not only effectively handle discrete, continuous random variables, but also handle mixed random variable probability prediction problems, and has high precision and reliability. Therefore, the present application uses the generalized Bayesian model to make probability prediction of pentad precipitation and pentad temperature.

[0015] (1) Prior distribution

[0016] Bayes formula mainly includes three parts, namely, prior distribution, likelihood function and posterior distribution. The first step of the forecast of pentad precipitation and pentad temperature is to estimate their prior distribution. Generally, the prior distribution can be determined according to expert opinion or historical data. For the prior distribution of pentad precipitation and pentad temperature variables, the marginal distribution of historical observed pentad precipitation and pentad temperature data can be used as the prior distribution of the model. Among them, pentad temperature can be regarded as a continuous random variable Y T , while precipitation is a mixed random variable composed of a discrete part and a continuous part. The discrete part of the precipitation probability distribution is equivalent to the proportion of rainless (precipitation is 0) days in the total number of observations, and the continuous part can be determined by fitting a commonly used non-negative distribution or a non-parametric distribution. The probability distribution of the precipitation random variable is shown in Figure 1 and equation 1.

[0017] Let Y R represent the precipitation random variable in the study area, y R its corresponding value, and its sample space is [0, +∞). Its probability distribution function can be expressed as follows:

[0018]

[0019] In the formula: F(y R ) represents the probability distribution function; P represents the probability of the corresponding event occurring.

[0020] As can be seen from equation (1), the precipitation random variable is a distribution that is not continuous at the point 0, and some traditional probability and statistical analysis tools such as Bayes formula are difficult to apply directly. The generalized Bayes model based on the generalized probability density function effectively solves this problem. By introducing the Dirac delta function and defining the generalized density function, the distribution law of discrete random variables and the probability density function of continuous random variables are unified in form. The Dirac delta function, usually denoted as δ(x), is one of the most commonly used generalized functions in hydrology and is applied in the calculation of instantaneous unit hydrograph. δ(x) is equal to 0 at all points except x = 0; and the integral of the δ function over the entire domain is 1, as shown in Figure 2 , which can be expressed as follows:

[0021]

[0022] From the above concepts of generalized probability density function and equation (1), the generalized probability density function of the precipitation random variable Y R is:

[0023]

[0024] In the formula, Y = 0 R P{Y R > 0} = 1 - a0.

[0025] Thus, the prior distribution of the random variable Y R of the forecasted precipitation can be expressed by equation (3), while the prior distribution of the random variable Y T of the forecasted temperature is a continuous distribution, which can be directly described by the probability density function

[0026] (2) Likelihood function

[0027] The likelihood function is a function of the parameters of a statistical model in statistics, which represents the likelihood of the model parameters, and can be understood as the inverse of the conditional probability. In the generalized Bayesian model, the likelihood function is obtained in the form of the model prediction error.

[0028] Let X R and X T represent the random variables of the forecasted precipitation and temperature, respectively, and x R and x T represent the specific values of the two. In the generalized Bayesian model, when the actual forecasted precipitation or temperature value Y R = y R or Y T = y T is known, the relationship between the forecasted precipitation random variable X R and X T and the respective prediction errors ε R (y R ) and ε T (y T ) can be expressed as:

[0029]

[0030] Thus, when Y R = y R or Y T = y T is known, the likelihood functions and can be derived from the distributions of ε R (y R ) and ε T (y T ).

[0031]

[0032] where: β 0,0 = P{X R = 0 | Y R = 0} and

[0033] (3) Posterior distribution

[0034] From the above definition of the generalized density function and the generalized conditional probability density function and the conditional probability formula, the posterior probability density function of the forecasted rainfall and the forecasted temperature can be obtained, that is, the generalized Bayes formula:

[0035]

[0036] In the formula, Y is a random variable of the true value of the variable to be predicted (in the application, the true value of the forecasted rainfall and the forecasted temperature); X is a random variable of the predicted value of the variable to be predicted (in the application, the predicted value of the forecasted rainfall and the forecasted temperature); y and x respectively represent the corresponding values of the random variables Y and X; t is an integral variable; f Y|X (y|X=x) is the posterior generalized probability density function; f Y (y) represents the prior generalized probability density function; f X|Y (x|Y=y) is the generalized likelihood function.

[0037] Although the generalized Bayes formula (6) is the same in form as the Bayes formula of continuous random variables, it has a wider meaning. The generalized Bayes formula unifies the Bayes formulas of discrete random variables, continuous random variables and mixed random variables, and widens the application range of the traditional Bayes formula.

[0038] Through the generalized Bayes model, the uncertainty of the forecasted rainfall and the forecasted temperature is expressed, and finally the probability prediction result and

[0039] Step 4: Establishing a drought probability early warning model based on a Copula function

[0040] The Copula function is often used to describe the correlation between variables, and can be used to construct the joint distribution function of different variables according to the marginal distribution function of different variables. In the application, the Copula function is used to construct the joint distribution between the probability prediction result and and the forecasted temperature, and the fitting precision of different Copula functions is judged through the AIC information criterion (formula (7)), and the optimal Copula function is selected.

[0041] AIC = 2k - 2ln(L) (7)

[0042] where k is the number of parameters, and L is the likelihood function.

[0043] When the optimal Copula function is determined, the probability of drought occurrence is estimated in the form of joint distribution function according to the drought threshold determined in step 2, so as to establish a drought probability early warning model and realize drought probability early warning.

[0044] Probability of drought occurrence P D = F(Y R < R 40 , Y T > μ T + σ T | X R = x R , X T = x T ) (8)

[0045] The pentad average precipitation and the pentad average air temperature refer to pentad five-day average precipitation and pentad five-day average air temperature values.

[0046] The present application has the beneficial effects that: the present application aims at the problem that current meteorological drought lacks definite definition and early warning model, defines the meteorological drought through meteorological forecast, generalized Bayesian model and Copula function, and realizes the probability early warning of the meteorological drought. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 It is a probability distribution function schematic diagram of the present application.

[0048] Figure 2 It is a Dirac delta function schematic diagram in the present application.

[0049] Figure 3 It is a flow chart of the present application.

[0050] Figure 4 It is a drought probability early warning result schematic diagram of the present application. DETAILED DESCRIPTION

[0051] The idea of the present application is: using meteorological data, the definition of meteorological sudden drought is given; based on the forecast of the candidate precipitation and the candidate air temperature, the sudden drought probability warning model is constructed through the generalized Bayesian model and the Copula function. Based on the definition of meteorological sudden drought, the method can effectively improve the warning ability of meteorological sudden drought, and provide reference for regional water resources management. The implementation method of the idea is: first, collect the measured value and the forecast value data of precipitation and air temperature in the study area; then, according to the definition of meteorological sudden drought, the threshold of meteorological sudden drought is determined; then, the generalized Bayesian model is used to generate the probability prediction results of candidate precipitation and candidate air temperature; finally, the Copula function is used to establish the sudden drought probability warning model, and the sudden drought probability prediction is realized.

[0052] The present application will be further described in detail through the accompanying drawings and specific embodiments.

[0053] As shown in the meteorological drought probability warning method based on meteorological forecast, taking the Xixian basin above the Huaihe River basin as an example, the occurrence probability of sudden drought under different temperature and precipitation forecast conditions is analyzed by using the present application. Figure 3

[0054] I. Overview of the study area and data set preparation.

[0055] The Xixian basin above the Huaihe River basin is located in the upper reaches of the Huaihe River, and is one of the most important sub-basins in the Huaihe River basin. In this embodiment, the 0.5° grid daily average temperature and daily precipitation data from 1979 to 2020 published by China Meteorological Data Network are selected as the measured data, and the candidate average (5-day average) temperature and precipitation are calculated daily; the CMA (China Meteorological Agency) data in the S2S (Sub-seasonal to seasonal prediction) data set published by the European Centre for Medium-Range Weather Forecasts is selected as the meteorological forecast data, and the precipitation and temperature forecast data are also processed to the candidate average data.

[0056] II. Definition and threshold of meteorological sudden drought.

[0057] According to the definition of meteorological sudden drought of the present application, that is, the candidate average air temperature anomaly is greater than 1 standard deviation, and the candidate average precipitation percentile is less than 40%, the threshold of meteorological sudden drought is determined based on the long series of measured data in the study area. According to the measured candidate average temperature and precipitation data, the definition of meteorological sudden drought in this embodiment is that the candidate average temperature is greater than 24.8℃, and the candidate average precipitation is less than 1mm.

[0058] ​III. Meteorological probability forecast based on generalized Bayesian model According to the principle of generalized Bayesian model, the prior distribution, likelihood function and posterior distribution of two random variables, i.e. the pentad precipitation and the pentad temperature, are estimated. The discrete part of the prior distribution and the likelihood function of the pentad precipitation can be determined by the ratio of the number of rainless days to the total number of days in history. The continuous part and the prior distribution and the likelihood function of the pentad temperature can be selected by Kolmogorov-Smirnov test (K-S test) from a plurality of different continuous probability distributions. The selected distribution type of each variable in the prior distribution and the likelihood function is shown in the following table according to the measured and predicted values of the pentad average precipitation and temperature:

[0059] Table 1 Distribution selection table of generalized Bayesian model

[0060]

[0061] When all the distributions are determined, the probability forecast results of the pentad precipitation and the pentad temperature are generated according to the equations (1) to (6).

[0062] IV. Probability early warning of sudden drought based on Copula function

[0063] The joint distribution of the two distributions is established by Copula function with the probability forecast results generated by the generalized Bayesian model as input. The AIC information criterion is used as the discrimination condition to determine the most suitable Copula function type. After comparison, the Gumbel Copula function is used in this embodiment. Through the joint distribution, the probability of the occurrence of meteorological sudden drought in the region under the condition of different precipitation and temperature prediction values is determined, and the probability early warning model of meteorological sudden drought is established. The probabilities of the occurrence of meteorological sudden drought in the Huaihe River Basin above Xixian Basin under different combinations of pentad average precipitation prediction and pentad average temperature prediction are calculated by using different pentad precipitation prediction and pentad temperature prediction in this embodiment, and the results are shown in Figure 4 The size of the probability is represented by color in the figure (where 0-12% is different shades of blue, and 22-42% is different shades of red). The deeper the red color, the greater the probability of the occurrence of sudden drought.

Claims

1. A weather-based sudden drought probability forecasting method based on weather forecast, comprising the following steps: Step 1: Preparation of basic data set Collecting weather observation data of the study area; the weather observation data includes measured data and forecast data of the study area pentad average precipitation and pentad average air temperature; Step 2: Definition of weather-based sudden drought According to the observed precipitation and air temperature data in the study area, when the air temperature and the precipitation are defined as meteorological type drought, wherein: is the mean of the average temperature of the pentad, is the standard deviation of the average temperature of the pentad, is the 40th percentile of the pentad precipitation; Step 3: Weather probability forecast based on generalized Bayesian theory Carrying out probability forecast of pentad precipitation and pentad air temperature by using generalized Bayesian model, Probability forecast result ; In the formula: respectively represent the forecasted precipitation random variable and the forecasted temperature random variable of the candidate, respectively represent specific values of the two; respectively represent the precipitation random variable and the temperature random variable of the candidate, respectively represent specific values of the two; the sample space of the forecasted precipitation random variable and the precipitation random variable of the candidate is , and the sample space of the forecasted temperature random variable and the temperature random variable of the candidate is ; Step 4: Establishment of sudden drought probability early warning model based on Copula function Using the Copula function, probabilistic prediction results are constructed. The joint distribution between them is determined by the AIC information criterion (7), and the fitting accuracy of different Copula functions is judged to select the optimal Copula function. （7） In the formula, k is the number of parameters, and L is the likelihood function; After the optimal Copula function is determined, the probability of sudden drought occurrence is estimated in the form of joint distribution function according to the sudden drought threshold value determined in step 2, so as to establish a sudden drought probability early warning model and realize sudden drought probability early warning. Probability of sudden drought occurrence (8).

2. The weather-based meteorological drought probability forecasting method based on weather forecast according to claim 1, characterized in that: The pentad average precipitation and pentad average air temperature refer to five-day average precipitation and five-day average air temperature values.

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