CN111507517A - Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability - Google Patents

Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability Download PDF

Info

Publication number
CN111507517A
CN111507517A CN202010286552.9A CN202010286552A CN111507517A CN 111507517 A CN111507517 A CN 111507517A CN 202010286552 A CN202010286552 A CN 202010286552A CN 111507517 A CN111507517 A CN 111507517A
Authority
CN
China
Prior art keywords
typhoon
probability
time
occurrence
indicates
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202010286552.9A
Other languages
Chinese (zh)
Inventor
刘桂林
陈柏宇
李笑
李宝才
崔柯
刘春鹏
聂驰
徐鹏飞
王莉萍
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
HEILONGJIANG PROV ELECTRONIC TECHNOLOGY INSTITUTE
Ocean University of China
Original Assignee
HEILONGJIANG PROV ELECTRONIC TECHNOLOGY INSTITUTE
Ocean University of China
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by HEILONGJIANG PROV ELECTRONIC TECHNOLOGY INSTITUTE, Ocean University of China filed Critical HEILONGJIANG PROV ELECTRONIC TECHNOLOGY INSTITUTE
Priority to CN202010286552.9A priority Critical patent/CN111507517A/en
Publication of CN111507517A publication Critical patent/CN111507517A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01W—METEOROLOGY
    • G01W1/00—Meteorology
    • G01W1/10—Devices for predicting weather conditions
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/10—Services
    • G06Q50/26—Government or public services
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Landscapes

  • Business, Economics & Management (AREA)
  • Engineering & Computer Science (AREA)
  • Tourism & Hospitality (AREA)
  • Economics (AREA)
  • Human Resources & Organizations (AREA)
  • Strategic Management (AREA)
  • Environmental & Geological Engineering (AREA)
  • Theoretical Computer Science (AREA)
  • Development Economics (AREA)
  • Marketing (AREA)
  • General Physics & Mathematics (AREA)
  • Physics & Mathematics (AREA)
  • General Business, Economics & Management (AREA)
  • General Health & Medical Sciences (AREA)
  • Ecology (AREA)
  • Health & Medical Sciences (AREA)
  • Educational Administration (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Atmospheric Sciences (AREA)
  • Biodiversity & Conservation Biology (AREA)
  • Primary Health Care (AREA)
  • Environmental Sciences (AREA)
  • Game Theory and Decision Science (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Operations Research (AREA)
  • Quality & Reliability (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention provides a method for predicting typhoon occurrence probability, occurrence frequency probability and continuity probability. The method firstly describes that the typhoon occurrence frequency in a certain period of time accords with a certain random process model, strictly proves the typhoon occurrence frequency, further provides the dependence relationship and time interval distribution of the typhoon occurrence in different periods of time, and carries out more reasonable statistical inference and prediction on the typhoon occurrence rule through the analysis of the occurrence probability, the occurrence frequency probability and the continuity probability of the typhoon frequency in different periods of time.

Description

Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability
Technical Field
The invention relates to the technical field of atmospheric science, in particular to a method for predicting typhoon occurrence probability, occurrence frequency probability and continuity probability.
Background
Frequent natural disasters often result in significant casualties and economic losses. According to the statistics of Munich Re Group disaster database, in the ten years of 2009-2018, a natural disaster causes 37.1 million people to die, and the economic loss is 18580 hundred million dollars, wherein the meteorological disaster accounts for about 60%. In all meteorological disasters, typhoons (hurricanes) seriously threaten the survival and development of human beings due to the frequent occurrence, huge destructive power and various disaster causing modes. As the earth warms up, the frequency of strong typhoons/hurricanes tends to increase (see fig. 1), and marine disasters caused by typhoons/hurricanes are more severe and frequent than ever. In 2013, typhoon "haiyan" swiftly passes through philippines, the maximum wind speed in the center of typhoon reaches about 105 m/s, and 90% of buildings in Takroban city are leveled into flat ground. In 2017, tropical storm Daibe is used as a temporary foundation for the ancient northern Australia and a plurality of towns in Kunlanzhou are full-meshed and round-grained. According to statistics, nearly 300 million people in China are in disaster, 1200 houses collapse in excess, the disaster area of crops is 174.4 kilo hectares, and the direct economic loss is 52 hundred million yuan; the philippines 74 are in distress and the economic loss may reach 6.6% of GDP, or over $ 200 billion. Storm, heavy wave, storm surge and indirect landslide and debris flow caused by typhoon often cause serious casualties and social and economic losses. At present, a qualitative method is mostly adopted to analyze the typhoon occurrence rule, but the accuracy of the result is not high, and the practicability is not strong.
Therefore, a quantitative method for forecasting and early warning the typhoon activity in a certain period of time in the future is needed.
Disclosure of Invention
In view of the above, the present invention provides a method for predicting the occurrence probability, occurrence frequency probability and continuity probability of typhoon, which can predict or warn typhoon activity in a certain period of time in the future.
The invention provides a method for predicting typhoon occurrence probability, which is characterized by comprising the following steps: the method comprises the following steps: establishing a one-dimensional distribution function corresponding to a random process K (t) of whether the typhoon happens or not at a certain time, wherein the one-dimensional distribution function comprises a probability function of the occurrence of the typhoon at the certain time and a probability function of the non-occurrence of the typhoon at the certain time:
the probability function of typhoon occurring at a certain time is as follows:
Figure BDA0002448734650000021
wherein K (t) indicates whether a typhoon occurs at time t, and when K (t) takes 1, it indicates that a typhoon occurs, m (t) indicates a random variable, K indicates that a variable K is 0, 1,2 …, λ indicates an average number of times of occurrence of a typhoon per unit time, and h indicates an angle variable;
the probability function that no typhoon occurs at a certain moment is as follows:
Figure BDA0002448734650000022
where K (t) indicates whether or not a typhoon occurs at time t, and when K (t) takes 1, it indicates that a typhoon occurs, m (t) indicates a random variable, K indicates that a variable K is 0, 1,2 …, λ indicates the average number of times of occurrence of a typhoon per unit time, and h indicates an angle variable.
Further, said m (t) is a poisson distribution over time intervals (0, t):
Figure BDA0002448734650000023
where m (t) represents a random variable, t represents time, m represents a random variable with time t, and λ represents the average number of typhoons occurring in a unit time.
Correspondingly, the invention discloses a method for pre-estimating typhoon occurrence frequency probability, which is characterized by comprising the following steps: the method comprises the following steps: constructing a model for estimating the probability of the occurrence times of the typhoon, wherein the model comprises the following steps:
Figure BDA0002448734650000031
where K denotes a random variable, n (t) denotes the number of occurrences of typhoon in a certain time interval, and λ denotes the average number of occurrences of typhoon per unit time.
Correspondingly, the invention also provides a method for predicting the typhoon continuity probability, which is characterized by comprising the following steps: the method comprises the following steps: constructing a distribution function of the arrival time intervals of the typhoon, wherein the function is as follows:
Figure BDA0002448734650000032
wherein, TnA sequence of intervals at which typhoon occurs, wherein n is 1,2, 3 …, t represents time, and λ represents the average number of typhoon occurrences per unit time;
the probability P (T is less than or equal to T) of typhoon occurring in the time T is determined by the following method:
Figure BDA0002448734650000033
wherein P (T ≦ T) represents the probability that typhoon occurred within time T, FTn(t) represents a distribution function of arrival time intervals of typhoons, t represents time, and λ represents an average number of typhoons occurring per unit time.
The invention has the beneficial technical effects that: the method and the device quantitatively analyze the typhoon risk in a certain period of time in the future, and obtain a quantitative result through establishing the model of the occurrence probability, the occurrence frequency probability and the continuity probability of the typhoon frequency in different periods of time, so that the typhoon activity condition in a certain period of time in the future can be more reasonably predicted.
Drawings
The invention is further described below with reference to the following figures and examples:
FIG. 1 is a sample function diagram of an observation of a typhoon process according to the present invention.
FIG. 2 is a sample curve and a schematic diagram of a sample curve of an embodiment of the present invention.
FIG. 3 is a graph showing a probability distribution of the number of typhoons occurring in month 5 of 2000-2016 in accordance with an embodiment of the present invention.
FIG. 4 is a graph of comparative analysis of probability distributions for an embodiment of the present invention.
Fig. 5 is a cumulative distribution diagram of typhoon occurrence time intervals according to the embodiment of the invention.
Fig. 6 is a probability distribution diagram of occurrence of a typhoon in time t according to an embodiment of the present invention.
FIG. 7 is a diagram illustrating the distribution function of the interval T according to an embodiment of the present invention.
FIG. 8 is a diagram illustrating a probability density function of the interval T according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings in which:
the invention provides a method for predicting typhoon occurrence probability, which is characterized by comprising the following steps: the method comprises the following steps: establishing a one-dimensional distribution function corresponding to a random process K (t) of whether the typhoon happens or not at a certain time, wherein the one-dimensional distribution function comprises a probability function of the occurrence of the typhoon at the certain time and a probability function of the non-occurrence of the typhoon at the certain time:
the probability function of typhoon occurring at a certain time is as follows:
Figure BDA0002448734650000041
wherein K (t) indicates whether a typhoon occurs at time t, and when K (t) takes 1, it indicates that a typhoon occurs, m (t) indicates a random variable, K indicates that a variable K is 0, 1,2 …, λ indicates an average number of times of occurrence of a typhoon per unit time, and h indicates an angle variable;
the probability function that no typhoon occurs at a certain moment is as follows:
Figure BDA0002448734650000042
where K (t) indicates whether or not a typhoon occurs at time t, and when K (t) takes 1, it indicates that a typhoon occurs, m (t) indicates a random variable, K indicates that a variable K is 0, 1,2 …, λ indicates the average number of times of occurrence of a typhoon per unit time, and h indicates an angle variable.
M (t) is taken as the number of sign changes in (0, t) time accompanying the number of typhoon occurrences per month, which is a random variable. Whether a typhoon occurs at time t can be described by a random process k (t) which takes only two values of +1 or-1. K (t) takes +1 when m takes 0 or even number, and K (t) takes-1 when m takes odd number. When K (t) takes 1, typhoon will occur, and when K (t) takes +1, typhoon will not occur.
m (t) is a set of random variables that vary with time, which is a measurable function defined in the sample space Ω, taking real values. The number of sign changes m (t) caused by the occurrence and non-occurrence times of typhoon is the poisson process. In time interval (0, t), m (t) is the poisson distribution, i.e.:
said m (t) is a poisson distribution over a time interval (0, t):
Figure BDA0002448734650000051
where m (t) represents a random variable, t represents time, m represents a random variable with time t, and λ represents the average number of typhoons occurring in a unit time.
Correspondingly, the invention also provides a method for pre-estimating the probability of the occurrence times of typhoon, which is characterized by comprising the following steps: the method comprises the following steps: constructing a model for estimating the probability of the occurrence times of the typhoon, wherein the model comprises the following steps:
Figure BDA0002448734650000052
where K denotes a random variable, n (t) denotes the number of occurrences of typhoon in a certain time interval, and λ denotes the average number of occurrences of typhoon per unit time.
The proof procedure for equation (4) is given below:
we consider the number of typhoon occurrences in a certain period of time as a random process to build a mathematical model of it. And taking an observed value of the occurrence frequency of the typhoon every time T, wherein a series of observed values obtained at the same time T form a group of random variables. For each observation
Figure BDA0002448734650000053
A time t is specified, then
Figure BDA0002448734650000054
The deterministic function can be denoted as n (t). Consider all observations at different times
Figure BDA0002448734650000055
The typhoon occurrence times N (t) represent a function family, the function family represented by N (t) is called a one-dimensional random process, the one-dimensional random process is a family of one-dimensional random variables depending on a time parameter t, and the typhoon occurrence times N (t) in a certain period of time are mathematically described based on engineering reality:
constructing a counting process N (t) of typhoon occurrence in a certain period of time, and taking the counting process N (t) as the measurement of the natural physical process of the frequency of typhoon occurrence in a certain period of time in a certain sea area, and according to engineering implementation, making the following assumptions:
(1) zero initial value: n (0) ═ 0.
(2) Independent augmentative Properties: the number of typhoons occurring in any two non-overlapping time intervals is independent of each other.
(3) The timeliness: at (t)1,t2) The number of typhoons occurring at time intervalsAnd the length t of the time interval2-t1Related to the starting time t1Is irrelevant.
(4) The universality; in a sufficiently small time interval, typhoons occur only once at most. Namely: with pk(Δ t) denotes the probability of k typhoons occurring within the time interval Δ t, then there is a positive integer λ, so that for a sufficiently small Δ t there is:
p0(Δ t) ═ 1- λ Δ t + o (Δ t) (the probability of no typhoon occurring within a sufficiently small time interval is 1- λ Δ t);
p1(Δ t) ═ λ Δ t + o (Δ t) (λ Δ t is the probability of a typhoon occurring once in a sufficiently small time interval);
Figure BDA0002448734650000061
(it is almost impossible for typhoons to occur twice or more in a sufficiently small time interval).
Let λ be the average number of typhoons occurring per unit time, i.e. λ represents the intensity or rate of the typhoon process.
The typhoon counting process N (t), t ∈ [ t ] can be known from engineering facts0,∞)(t0Not less than 0) has the following properties:
(1) n (t) takes non-negative integer values;
(2) if t1＜t2Then N (t)1)-N(t2)＜0；
(3) N (t) is a right-continuous step function at [0, ∞);
(4) for t1＜t2，
Figure BDA0002448734650000062
Expressed as a time period (t)1,t2) Number of occurrences of typhoon.
It is easy to see that each observation of the typhoon process in a limited interval is continuous and can be tiny everywhere except for a limited point. The shape of the sample function of each typhoon observation is a step function, the length of each step is 1, and the occurrence time of the steps is random, as shown in fig. 1.
If typhoon is inThe number of times { N (t) ≧ 0} occurring within a certain time interval is the counting process given by the above definition, and N (t) is a Poisson process with intensity λ t, i.e., with intensity λ t
Figure BDA0002448734650000071
Consider the probability p of k typhoons occurring within [0, t + Δ t) ]k(t + Δ t), dividing [0, t + Δ t) into two non-overlapping intervals [0, t) and [ t, t + Δ t), and then the independent increment, time alignment and total probability formula of N (t) is:
Figure BDA0002448734650000072
(1) following evidence p0(t)＝e-λtWhere k is 0 in the above formula,
Figure BDA0002448734650000073
let Δ t → 0 have
LetΔt→0,
Figure BDA0002448734650000074
Solving the differential equation to obtain p0(t)＝Ce-λt. By no typhoon, i.e. p, occurring at time t-00(0) P { N (0) ═ 0} ═ 1, and C is substituted into 1. Therefore, it is
p0(t)＝e-λt(4-3)
(2) When k is greater than or equal to 1, there are
Figure BDA0002448734650000081
Figure BDA0002448734650000082
Let Δ t → 0 have
LetΔt→0,
Figure BDA0002448734650000083
For k is 1, there are
Figure BDA0002448734650000084
By solving this equation, the
p1(t)＝λte-λt(4-6)
In the formula (4-4), let k be 2 and use p obtained1(t) can determine p2(t) of (d). So as to solve
Figure BDA0002448734650000085
After the syndrome is confirmed.
Correspondingly, the invention also provides a method for predicting the typhoon continuity probability, which is characterized by comprising the following steps: the method comprises the following steps: constructing a distribution function of the arrival time intervals of the typhoon, wherein the function is as follows:
Figure BDA0002448734650000086
wherein, TnA sequence of intervals at which typhoon occurs, wherein n is 1,2, 3 …, t represents time, and λ represents the average number of typhoon occurrences per unit time;
the probability P (T is less than or equal to T) of typhoon occurring in the time T is determined by the following method:
Figure BDA0002448734650000091
wherein P (T ≦ T) represents the probability that typhoon occurred within time T, FTn(t) represents a distribution function of arrival time intervals of typhoons, t represents time, and λ represents an average number of typhoons occurring per unit time.
Let { N (T), T ≧ 0} be the Poisson process with parameter λ, { T ≧ 0nN is not less than 1, is the corresponding n-1 th typhoon generation to the nThe sequence of time intervals in which a typhoon occurs, then the time interval TnN 1,2. independently and obey an exponential distribution with a mean value of 1/λ, i.e. TnE (. lamda.). Because of T1Indicating the time required before the first appearance of a typhoon, { T1T indicates that typhoon has not occurred within (0, t), for t ≧ 0:
Figure BDA0002448734650000092
therefore, it is not only easy to use
P{T1≤t}＝1-P{T1＞t}＝1-e-λt,t≥0
P{T1≤t}＝0,t＜0 (6-2)
T1The distribution function of (a) is:
Figure BDA0002448734650000093
this is the mean value of
Figure BDA0002448734650000094
Is used as the index distribution of (1). And due to T2For the time interval between the first occurrence of an event and the second occurrence, then similarly:
P{T2＞t|T1＝s1p { at(s) }1,s1+ T) no typhoon occurs | T1＝s1}
P { in(s)1,s1+ t) no typhoon present }
Due to the independence of the increments:
＝P{N(s1+t)-N(s1)＝0}
＝P{N(t)-N(0)＝0} (6-4)
since the poisson process is an odd independent incremental process:
＝P{N(t)＝0}＝e-λt(6-5)
visible T2Also obey mean value of
Figure BDA0002448734650000101
Is distributed exponentially of, and T2And T1Independently and equally distributed.
In general, for n > 1 and t, s1,s2,...,sn-1Not less than 0, including:
P{Tn≥t|T1＝s1，T2＝s2，...，Tn-1＝sn-1}
p { in(s)1+…+sn-1，s1+…+sn-1+ T) no typhoon occurs | T1＝s1，T2＝s2，...，Tn-1＝sn-1}
P { in(s)1+…+sn-1，s1+…+sn-1+ t) no typhoon present }
＝P{N(s1+…+sn-1+t)-N(s1+…+sn-1)＝0}
＝P{N(t)-N(0)＝0}＝P{N(t)＝0}＝e-λt
I.e. the time interval of arrival Tn(n ≧ 1) are independent and identically distributed random variables, all obeying a mean value of
Figure BDA0002448734650000102
The distribution function of the arrival time intervals of the typhoon is as follows:
Figure BDA0002448734650000103
the following is illustrated by an example:
the maximum wind speed when typhoon lands is used as an index for describing the typhoon intensity, and the maximum wind speed on the ground near the center of the typhoon is selected as a standard for judging whether the typhoon occurs. According to the standards issued by the China weather service, tropical cyclones are divided into six levels by comparing the central wind speed, and the six levels are shown in Table 1. As is known from the standard, when the maximum average wind speed near the center of the bottom reaches 17.2 m/s, the tropical cyclone is defined as a Tropical Storm (TS), and a typhoon blue warning signal is issued at this time. Therefore, the wind speed set herein is considered to be typhoon occurrence at 17.2 m/s or more, and is considered not to be typhoon occurrence at 17.2 m/s or less.
TABLE 1 Tropical cyclone Classification criteria
Figure BDA0002448734650000111
The method selects typhoon frequency data of 16 years in 1960 and 2000-2016 (2004 and 2007) of the Chinese Yuexi sea area Salamador station, and establishes a mathematical model by taking the typhoon occurrence frequency in a certain period of time as a random process. The set of all sub-observation components of a typhoon is called the sample space, denoted as Ω. Thus, every time T (taking the unit of T as month or season), the number of typhoon occurrences is taken as an observed value, and a series of observed values obtained at the same time T form a set of random variables.
Firstly, selecting typhoon data of logging in the Salicomia in 1960, and judging that 3 typhoons occur in total in 1960 by using the standard given above for whether the typhoon occurs or not in 1 month unit, wherein the occurrence time and duration of each typhoon are respectively as follows: for the first time: 1960, 06, month 02, day-1960.06.17; and (3) for the second time: 1960.06.21-1960.07.01; and thirdly: 1960.09.29-1960.10.13. Typhoon occurs twice in 6 months, which is the difference between the observed value of the number of typhoon occurrences in 6 months and the observed value in 5 months: t is6-T 52, namely the increment of the number of the 6-month typhoon occurrences is 2; similarly, 1 typhoon occurs in 10 months, which is the difference between the observed value of the number of typhoon occurrences in 10 months and the observed value in 9 months: t is10-T 91, namely the increment of the number of the 10-month typhoon occurrences is 1; the number of typhoon occurrences in a certain period of time, for example, 6 to 9 months, is the difference between the observed value of the number of typhoon occurrences in 9 months and the observed value in 5 months: t is9-T5And 3, namely, the increment of the typhoon occurrence number in the time period is 3. The increment of the typhoon occurrence number in the 12-month period in 1960 follows a poisson distribution with the mean value λ 3/12 0.25, i.e. its typhoon occurrence number n (t) follows a poisson process with the parameter λ 0.25/month, and the sample curves and diagrams of n (t) are shown in fig. 2.
As shown in FIG. 2, N (,)t0,t1]) The number of typhoons n (t) is poisson process with mean λ ═ 0.25 times/month, and the one-dimensional distribution function of n (t) is:
Figure BDA0002448734650000121
therefore, the finite dimensional family of probability distributions for N (t) is:
Figure BDA0002448734650000122
let m (t) be the number of sign changes in 1960. Typhoon occurs twice in 6 months, and the number is changed for 3 times, which is the difference between the observed value of the number of change times in 6 months and the observed value in 5 months: t is6-T53, i.e. the number of 6 month sign changes is increased by 3. The increment of the number of sign changes m within the 12-month period in 1960 obeys the mean value of lambda1A poisson distribution of 0.5 when 6/12. It is known that m (t) is also a poisson process.
Whether typhoon occurs or not K (t) is a random process only taking +1 or-1, and in the time interval (0, t), the number change time point m (t) is the mean value of lambda1When 6/12 is 0.5 poisson process, the one-dimensional distribution of k (t) is:
Figure BDA0002448734650000123
Figure BDA0002448734650000124
with the different values of t, the probability of whether the typhoon occurs in different time periods can be obtained.
The site of observation of the saliferous is located on the island of saliferous, and due to the topographic relationship with the peninsula of leizhou caused by the specific geographical location of the site of observation of the saliferous, the number of landings in west of saliferous is historically small in the tropical cyclone which has a large influence on the saliferous, and the number of landings in south and east of the saliferous is large in the tropical cyclone, so that the number and frequency of typhoons occurring tend to be enhanced from 5 months and concentrated in 5-9 months. The typhoon frequency of 5 to 9 months of salami generated in 2000-2016 (2004, 2007) each year is subject to the poisson process with the parameter lambda, and the intensity of each corresponding poisson process is shown in table 2:
TABLE 2 Poisson intensity for typhoon occurrences in 5 to 9 months per year
Figure BDA0002448734650000125
The statistical characteristics of the number of typhoons occurring in different periods of months from 5 to 9 months of salami are examined below. As can be seen from the measured data, in the year of 2000-2016, only one typhoon occurs in the month 5 in 2006, and no typhoon occurs in the other months, so that the probability that the typhoon does not occur in the month 5 and the typhoon occurs in 1 time in the months 5 to 9 is considered. Focusing on the occurrence of typhoon in 2000, according to formula (4), there are:
Figure BDA0002448734650000131
this gives a probability of 21.65% for no typhoon occurrence for month 5 and 1 typhoon occurrence in total for months 5 to 9. Then the probability of no typhoon occurrence in 5 months per year in 2000-2016 and 1 typhoon occurrence in total in 5 to 9 months is shown in table 3, the probability of no typhoon occurrence in 5 months per year in 2000-2016 and 2, 3, 4 typhoons occurrence in total in 5 to 9 months are shown in tables 4 to 6, respectively:
TABLE 3 probability of total 1 typhoon occurrence in 5 to 9 months per year
Figure BDA0002448734650000132
TABLE 4 probability of total occurrence of 2 typhoons in 5 to 9 months per year
Figure BDA0002448734650000133
TABLE 5 probability of total occurrence of 3 typhoons in 5 to 9 months per year
Figure BDA0002448734650000134
TABLE 6 probability of total 4 typhoons occurring in 5 to 9 months per year
Figure BDA0002448734650000141
As shown in FIG. 3, the probability distribution graph of no typhoon occurrence in 5 months of the year and 1,2, 3, 4 typhoons occurrence in 5 to 9 months in total is given in 2000-2016. As can be seen from the graph, when no typhoon occurs in month 5, the probability of occurrence of typhoon in month 5 to 9 decreases with the increase of the number of occurrences; in addition, the fluctuation of the typhoon occurrence probability is gradually reduced and tends to be stable.
The probability of no typhoon occurrence in month 5 every year in year 2000-2016 and the probability of no typhoon occurrence and typhoon occurrence in the next four months are shown in tables 7 and 8, respectively:
TABLE 7 probability of no typhoon occurrence in 6 to 9 months per year
Figure BDA0002448734650000142
TABLE 8 probability of 1 typhoon occurrence in 6 to 9 months per year
Figure BDA0002448734650000143
Fig. 4 shows the results of comparing the probability distributions in tables 7 and 8 with those in table 3. When no typhoon occurs in month 5, the typhoon distribution situation of the next four months is considered separately, a large deviation occurs in 2010, and compared with the probability distribution obtained by considering the influence of the typhoon occurrence situation in month 5 in fig. 4, the stability of the prediction result is poor; similarly, the probability of 1 typhoon occurrence in months 6 to 9 is about 10% lower than the result obtained without considering the time factor by considering the influence of the typhoon occurrence in month 5. According to the above discussion, the probability values corresponding to the typhoon occurrence times in each time period can be obtained. Table 9 is the probability that no typhoon occurred in month 5 and typhoons occurred at least twice in months 6 to 7.
TABLE 9 probability of twice typhoon
Figure BDA0002448734650000144
Knowing that the number of typhoon occurrences { N (T) ≧ 0} in months 5 to 9 is the Poisson process with parameter λ, take { T ≧ 0}nN is more than or equal to 1 is the time interval sequence from the n-1 th typhoon generation to the n-th typhoon generation, the random variable T isn N 1,2. independently obey an exponential distribution with a mean value of 1/λ, i.e. TnE (. lamda.). As can be seen from equation (5), the distribution function of the time intervals of typhoon occurrence is equation (5), and the cumulative distribution graph is shown in fig. 5:
Figure BDA0002448734650000151
the probability of the typhoon occurring within the time t is 1 minus the above equation (5), and the distribution function is equation (6), and the distribution function is shown in fig. 6.
Figure BDA0002448734650000152
As the time interval becomes longer, the occurrence probability of typhoon sharply decreases, and exponentially decays. If typhoon occurs 0.6 times per month on average, the probability that the typhoon occurs at an interval of four months next time is 9.07% as calculated above, and then the probability of interval of 7 months and 8 months is close to 0. The probability that typhoon will occur in the next week is P (T ≦ 0.25) ═ 1-e-0.6×0.25≈0.1393。
Between the next week and 2 weeks, the probability of typhoon occurrence is 11.99%.
Figure BDA0002448734650000153
The distribution function and probability density function of the interval time T are:
Figure BDA0002448734650000154
Figure BDA0002448734650000155
the probability that the time interval T between two typhoons is greater than or equal to one month is P { T ≧ 1} -, 1-F can be obtained from the equation (5-1)T(1)＝e-0.6≈0.5488
The values of the distribution function and the density function for different values of t are shown in table 10, and the distribution function graph and the probability density graph are shown in fig. 7 and 8, respectively:
TABLE 10 distribution function value and Density function value
Figure BDA0002448734650000161
From fig. 7, it can be seen that the probability of occurrence of typhoon in the next week, i.e., when t is 0.25, is 13.93%, and the probability of occurrence of typhoon in the next 1 to 2 weeks is FT(0.5)-FT(0.25) ═ 25.92% to 13.93% ═ 11.99%, and when t is 1, FT(1) 0.4512, the probability of the time interval t between two typhoons being greater than or equal to one month is 54.88%. Therefore, the duration probability of the typhoon under various conditions can be reasonably predicted through the time interval distribution of the occurrence of the typhoon, and a basis is provided for the forecast and early warning of typhoon activities.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (4)

1. A method for predicting typhoon occurrence probability is characterized by comprising the following steps: the method comprises the following steps: establishing a one-dimensional distribution function corresponding to a random process K (t) of whether the typhoon happens or not at a certain time, wherein the one-dimensional distribution function comprises a probability function of the occurrence of the typhoon at the certain time and a probability function of the non-occurrence of the typhoon at the certain time:
the probability function of typhoon occurring at a certain time is as follows:
Figure FDA0002448734640000011
wherein K (t) indicates whether a typhoon occurs at time t, and when K (t) takes 1, it indicates that a typhoon occurs, m (t) indicates a random variable, K indicates that a variable K is 0, 1,2 …, λ indicates an average number of times of occurrence of a typhoon per unit time, and h indicates an angle variable;
the probability function that no typhoon occurs at a certain moment is as follows:
Figure FDA0002448734640000012
where K (t) indicates whether or not a typhoon occurs at time t, and when K (t) takes 1, it indicates that a typhoon occurs, m (t) indicates a random variable, K indicates that a variable K is 0, 1,2 …, λ indicates the average number of times of occurrence of a typhoon per unit time, and h indicates an angle variable.
2. The method of predicting the occurrence probability of typhoon as claimed in claim 1, wherein: said m (t) is a poisson distribution over a time interval (0, t):
Figure FDA0002448734640000013
where m (t) represents a random variable, t represents time, m represents a random variable with time t, and λ represents the average number of typhoons occurring in a unit time.
3. A method for pre-estimating the probability of the occurrence frequency of typhoon is characterized in that: the method comprises the following steps: constructing a model for estimating the probability of the occurrence times of the typhoon, wherein the model comprises the following steps:
Figure FDA0002448734640000021
where K denotes a random variable, n (t) denotes the number of occurrences of typhoon in a certain time interval, and λ denotes the average number of occurrences of typhoon per unit time.
4. A method for predicting the continuity probability of typhoon is characterized by comprising the following steps: the method comprises the following steps: constructing a distribution function of the arrival time intervals of the typhoon, wherein the function is as follows:
Figure FDA0002448734640000022
wherein, TnA sequence of intervals at which typhoon occurs, wherein n is 1,2, 3 …, t represents time, and λ represents the average number of typhoon occurrences per unit time;
the probability P (T is less than or equal to T) of typhoon occurring in the time T is determined by the following method:
Figure FDA0002448734640000023
wherein P (T ≦ T) represents the probability that typhoon occurred within time T, FTn(t) represents a distribution function of arrival time intervals of typhoons, t represents time, and λ represents an average number of typhoons occurring per unit time.
CN202010286552.9A 2020-04-13 2020-04-13 Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability Pending CN111507517A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010286552.9A CN111507517A (en) 2020-04-13 2020-04-13 Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010286552.9A CN111507517A (en) 2020-04-13 2020-04-13 Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability

Publications (1)

Publication Number Publication Date
CN111507517A true CN111507517A (en) 2020-08-07

Family

ID=71875983

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010286552.9A Pending CN111507517A (en) 2020-04-13 2020-04-13 Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability

Country Status (1)

Country Link
CN (1) CN111507517A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117036983A (en) * 2023-10-08 2023-11-10 中国海洋大学 Typhoon center positioning method based on physical reinforcement deep learning

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117036983A (en) * 2023-10-08 2023-11-10 中国海洋大学 Typhoon center positioning method based on physical reinforcement deep learning
CN117036983B (en) * 2023-10-08 2024-01-30 中国海洋大学 Typhoon center positioning method based on physical reinforcement deep learning

Similar Documents

Publication Publication Date Title
CN109086935B (en) Regional geological disaster trend prediction method
Bao et al. Coupling ensemble weather predictions based on TIGGE database with Grid-Xinanjiang model for flood forecast
CN108508505A (en) Heavy showers and thunderstorm forecasting procedure based on multiple dimensioned convolutional neural networks and system
US20070185653A1 (en) Method and system for automated location dependent probabilistic tropical cyclone forecast
CN113191644B (en) Urban waterlogging risk evaluation method based on spontaneous-induced risk evaluation model
CN111897030A (en) Thunderstorm early warning system and method
KR101646587B1 (en) Hybrid seasonal prediction of the Western North Pacific Tropical Cyclone Activity
CN112949953B (en) Rainstorm forecasting method based on PP theory and AF model
CN113327022B (en) Lightning protection safety risk management system and method
CN116151483B (en) Regional rainfall landslide probabilistic prediction method and prediction terminal
CN107067683B (en) A kind of transmission line forest fire clusters quantitative forecast method and system
CN113657732A (en) Disaster degree index calculation method and equipment based on analytic hierarchy process
CN113711156A (en) Predicting the impact of tropical cyclones
CN113836808A (en) PM2.5 deep learning prediction method based on heavy pollution feature constraint
CN112819064A (en) Terminal area time sequence meteorological scene identification method based on spectral clustering
CN109784720B (en) Power distribution network risk assessment method based on space-time grid association under typhoon disaster
CN111507517A (en) Method for pre-estimating typhoon occurrence probability, occurrence frequency probability and continuity probability
Fernández-Alvarez et al. Evaluation of precipitation forecast of system: numerical tools for hurricane forecast
CN112785876B (en) Intelligent identification system for terminal area time sequence meteorological scene
CN114463947A (en) Convective disaster-causing strong wind early warning and forecasting method based on space-time network convolution model
Garba et al. Extreme rainfall characterisation under climate change and rapid population growth in the city of Niamey, Niger
CN112232689A (en) Ecological geological vulnerability evaluation method for tea leaf continuous planting area
CN108957594B (en) Method and system for forecasting and correcting total cloud amount of satellite orbit
CN116777079A (en) Desertification intrusion disaster prediction method based on Bayesian interlayer structure model
CN109784602A (en) A kind of disaster-ridden kind of coupling physical vulnerability assessment method based on PTVA model

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination