CN112016051B - Probability analysis method and system for encounter in multi-source flood process - Google Patents

Probability analysis method and system for encounter in multi-source flood process Download PDF

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CN112016051B
CN112016051B CN202010819757.9A CN202010819757A CN112016051B CN 112016051 B CN112016051 B CN 112016051B CN 202010819757 A CN202010819757 A CN 202010819757A CN 112016051 B CN112016051 B CN 112016051B
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徐高洪
陈璐
仇红亚
徐长江
邴建平
戴明龙
李妍清
齐尧乐
葛林松
张冬冬
陈玺
刘冬英
黄燕
李立平
王含
汪青静
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Bureau of Hydrology Changjiang Water Resources Commission
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Abstract

The invention provides a probability analysis method and a probability analysis system for encounter in a multi-source flood process, which belong to the field of hydrologic analysis and calculation in hydrology, and comprise the following steps: collecting and screening annual maximum N-day flood process data in a river basin by adopting an annual maximum method, and obtaining flood rise time, flood end time and annual maximum N-day flood value of the annual maximum N-day flood process; a brand new definition method for encountering the multi-source flood process is provided; and establishing a main and branch flow and upstream and downstream multi-source flood process encounter model comprehensively considering flood occurrence time and magnitude. The method comprehensively considers practical factors such as time lag, correlation of flood magnitude and the like in the multi-source flood process, breaks through the technical bottleneck that the existing flood process encounter method is difficult to evaluate the encounter probability of 3-dimensional and above flood processes, is simple in modeling and small in error, and provides scientific basis and effective support for improving flood control capacity of a drainage basin and guaranteeing the safety of flood control objects.

Description

Probability analysis method and system for encounter in multi-source flood process
Technical Field
The invention belongs to the field of hydrological analysis and calculation, and particularly relates to a method and a system for analyzing probability encountered in a multi-source flood process.
Background
Large floods in a drainage basin are usually formed by flood encounters of upstream and downstream main branches and branch flows, and flood peaks or flood volumes are superposed to different degrees when the flood encounters. The current common flood encounter calculation method is still the statistical analysis of the synchronous historical data, and the encounter probability of flood in T years cannot be estimated. The flood encounter problem is essentially a multivariable frequency combination problem and can be researched by adopting a multivariable hydrological analysis and calculation method. In the existing method, a Copula function is usually adopted to establish multivariate joint distribution for calculation, but most researches aim at establishing joint distribution for flood peaks or flood volumes and research the probability of occurrence of high flood at peak height.
In engineering practice, flood encounters occur only when peak-height flood occurs simultaneously in the main branch and upstream and downstream. Therefore, students establish joint distribution of flood occurrence time and magnitude, but research is only limited to flood events such as flood peaks or flood volumes. Historically, flood water usually lasts for 15 days or even 1 month, and the essential characteristics of flood encounters can be better characterized by adopting a flood process analysis method. However, the current flood process encounter research only aims at the two-river encounter situation, when a plurality of main and branch flood encounters are involved, the existing flood process encounter method needs to calculate the time interval between floods of any two rivers, taking the three-river flood encounter as an example, the time interval between flood occurrences of any two of 3 rivers needs to be calculated, considering the correlation of the flood occurrence time, three-dimensional joint distribution needs to be established, and in addition, the influence of the correlation of the magnitude of the flood magnitude needs to be established, 6-dimensional joint distribution needs to be established, the dimension of multivariate modeling is obviously increased, and great difficulty and errors are brought to the evaluation of encounter probability. Therefore, a probability analysis theory and a method system for solving the problem encountered in the multi-source flood process are urgently needed to be established.
Disclosure of Invention
Aiming at the defects or requirements of the prior art, the invention aims to provide a method and a system for analyzing the probability of the multi-source flood process encounter, so that the technical problems of complex modeling and large error in the process of calculating the probability of the multi-source flood process encounter in the prior art are solved.
To achieve the above object, as an aspect of the present invention, there is provided a method for analyzing probability of encounter in a multi-source flood process, comprising the steps of:
(1) acquiring annual maximum flood generation time in N days and annual maximum flood value in N days by adopting an annual maximum sampling method;
(2) when the coincidence time of the multi-source flood process exceeds N/2 days, the multi-source flood process is considered to be encountered, and the coincidence time ToExpressed as: t iso＝Te-TsWherein, TeIndicating the end time, T, of the latest flood process in a multisource floodsRepresenting the rise time of the earliest flood process in the multi-source flood;
(3) establishing a multi-source flood process encounter model representing the probability of the occurrence of the multi-source flood process encounter based on the obtained flood occurrence time and flood value and the multi-source flood process encounter definition;
when the flood coincidence time and the flood volume value have a correlation, the model is expressed as:
Figure BDA0002634034670000021
when the flood coincidence time and the flood value do not have a correlation, the model is represented as:
Figure BDA0002634034670000022
wherein, Wi(i-1, 2, …, N) represents the annual maximum N daily flood variable for i river, wi(i is 1,2, …, n) represents the flood volume of i river greater than a certain recurrence period, and n is the total number of rivers.
Further, fitting the flood occurrence time by adopting a mixed von Mises distribution, converting the flood occurrence time into a radian, and expressing as:
Figure BDA0002634034670000031
theta is more than or equal to 0 and less than or equal to 2 pi, wherein L represents the flood season time period length; l is1Represents the annual maximum flood process period length;
the probability density function expression of the flood occurrence time variable is as follows:
Figure BDA0002634034670000032
in the formula, theta is more than or equal to 0 and less than or equal to 2 pi; mu.sj、kjAnd pjRespectively is a position parameter, a scale parameter and a mixing proportion coefficient of the jth component of the mixed von Mises distribution, wherein the number is more than or equal to 0 muj≤2π，kj＞0，0≤pj≤1；I0(. h) is a first class of 0-order modified Bessel function; m is the order of the finite mixture von Mises distribution;
by integral operation, solve
Figure BDA0002634034670000033
Further, a Copula function is adopted to construct a joint distribution function of the multi-source flood volume, which is expressed as:
Figure BDA0002634034670000034
wherein F (-) is a joint distribution function of multidimensional variables,
Figure BDA0002634034670000035
is a random variable WnC is a Copula function;
thereby obtaining the joint probability P (W) of the flood volume of the multisource flood greater than a certain recurrence period1＞w1,W2＞w2,...,Wn≥wn)。
Further, when n is 3,
Figure BDA0002634034670000036
as another aspect of the present invention, there is provided a probability analysis system for encounter by a multi-source flood process, comprising:
the data acquisition module is used for acquiring annual maximum N-day flood generation time and annual maximum N-day flood value by adopting an annual maximum sampling method; when the coincidence time of the multi-source flood process exceeds N/2 days, the multi-source flood process is considered to be encountered, and the coincidence time ToExpressed as: t iso＝Te-TsWherein, TeIndicating the end time, T, of the latest flood process in a multisource floodsRepresenting the rise time of the earliest flood process in the multi-source flood;
the multi-source flood process encounter model establishing module is used for establishing a multi-source flood process encounter model which represents the probability of the occurrence of the multi-source flood process encounter based on the flood occurrence time and the flood value which are obtained by the data obtaining module and the multi-source flood process encounter definition;
when the flood coincidence time and the flood volume value have a correlation, the model is expressed as:
Figure BDA0002634034670000041
when the flood coincidence time and the flood value do not have a correlation, the model is represented as:
Figure BDA0002634034670000042
wherein, Wi(i-1, 2, …, N) represents the annual maximum N daily flood variable for i river, wi(i is 1,2, …, n) represents the flood volume of i river greater than a certain recurrence period, and n is the total number of rivers.
Further, fitting the flood occurrence time by adopting a mixed von Mises distribution, converting the flood occurrence time into a radian, and expressing as:
Figure BDA0002634034670000043
theta is more than or equal to 0 and less than or equal to 2 pi, wherein L represents the flood season time period length; l is1Represents the annual maximum flood process period length;
the probability density function expression of the flood occurrence time variable is as follows:
Figure BDA0002634034670000044
in the formula, theta is more than or equal to 0 and less than or equal to 2 pi; mu.sj、kjAnd pjRespectively is a position parameter, a scale parameter and a mixing proportion coefficient of the jth component of the mixed von Mises distribution, wherein the number is more than or equal to 0 muj≤2π，kj＞0，0≤pj≤1；I0(. h) is a first class of 0-order modified Bessel function; m is the order of the finite mixture von Mises distribution;
by integral operation, solve
Figure BDA0002634034670000051
Further, a Copula function is adopted to construct a joint distribution function of the multi-source flood volume, which is expressed as:
Figure BDA0002634034670000052
wherein F (-) is a joint distribution function of multidimensional variables,
Figure BDA0002634034670000053
is a random variable WnC is a Copula function;
thereby obtaining the joint probability P (W) of the flood volume of the multisource flood greater than a certain recurrence period1＞w1,W2＞w2,...,Wn≥wn)。
Further, when n is 3,
Figure BDA0002634034670000054
in general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
the invention fully considers the time and magnitude characteristics of the main and branch flows, the upstream and downstream peak high volume flood, provides a novel method for analyzing the probability of encountering the multi-source flood process, avoids the problem of indirectly representing the overlapping time of the multi-source flood process through the interval time of the flood process of any two rivers, overcomes the recognition limitation of single probability calculation of the encountering probability of the flood process, and provides background support for the flood control point to divide and store the flood in advance and guarantee the flood control safety. Meanwhile, the method breaks through the technical bottleneck that the existing flood process encounter method is difficult to evaluate the encounter probability of the flood process of 3-dimensional or more, and is simple in modeling and small in error.
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Fig. 1 is a schematic flow chart of a method for analyzing probability of encounter in a multi-source flood process according to the present invention.
Detailed Description
In order to make the objects and methods of the invention more clear and intuitive, the invention is described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, a schematic flow chart of a method for analyzing probability of encounter in a multi-source flood process provided by the present invention includes the following steps:
(1) collecting flood process data (specifically determined according to the size of the drainage basin) of 7 days, 15 days or 30 days at the maximum year in the drainage basin by adopting a maximum annual sampling method to obtain the flood rise time, the flood end time and the maximum annual N-day flood value in the maximum annual N-day flood process;
(2) a brand new definition method for encountering the multi-source flood process is provided;
specifically, if the maximum N-day course of multi-source flood WNThe time overlapping of more than N/2 days is the encounter of flood process, wherein N represents days, WNRepresenting the annual maximum N-day flood value. Thus, when a multi-source flood encounters, the coincidence time of the multi-source flood process can be defined as:
To＝Te-Ts
in the formula, ToThe time for overlapping the multi-source flood process; t iseRepresenting the end time of the latest flood process in the multi-source flood; t issIndicating the rise time of the earliest flooding process in the multi-source flood. Since the total days of the flood process are usually odd in the hydrologic analysis calculation, such as 3 days, 7 days, 15 days, etc., when To>And at N/2 days, the multi-source flood process water is considered to be encountered.
(3) And (3) providing a main and branch flow and upstream and downstream multi-source flood process encounter model considering flood occurrence time and magnitude, and evaluating encounter probability of flood processes with different magnitudes.
Specifically, only considering flood occurrence time, the probability encountered by the multi-source flood process is:
Figure BDA0002634034670000071
considering that the flood time variable may be unimodal or multimodal, fitting the flood occurrence time by adopting a mixed von Mises distribution, and converting the flood occurrence time into radian, wherein the conversion formula is as follows:
Figure BDA0002634034670000072
wherein L represents the flood season time period length; l is1Represents the annual maximum flood process period length; further, the probability density function expression of the flood time variable is as follows:
Figure BDA0002634034670000073
in the formula, theta is more than or equal to 0 and less than or equal to 2 pi; mu.sj、kjAnd pjRespectively is a position parameter, a scale parameter and a mixing proportion coefficient of the jth component of the mixed von Mises distribution, wherein the number is more than or equal to 0 muj≤2π，kj＞0，0≤pj≤1；I0(. h) is a first class of 0-order modified Bessel function; m is the order of the finite mixture von Mises distribution.
Flood encounters a hydrological phenomenon that can be defined as the simultaneous occurrence of major branch flows, high volume floods upstream and downstream, and thus, both with respect to the time and magnitude of flood occurrences, is a multivariable problem with respect to the time and magnitude of flood occurrences.
When the flood occurrence time and the flood occurrence magnitude have correlation, the multidimensional joint distribution of the flood occurrence time and the flood occurrence magnitude can be established for research, and the model is as follows:
Figure BDA0002634034670000074
when the flood occurrence time and the flood magnitude are independent of each other, an independent model can be adopted for solving:
Figure BDA0002634034670000075
the Copula function is a multidimensional joint distribution function with the definition domains uniformly distributed on [0,1], can flexibly connect the edge distribution of multidimensional random variables, and is not limited by the edge distribution type. According to the Sklar theory, edge distributions in any forms can be connected through a unique Copula function, and then a correlation structure among multidimensional variables is described.
Figure BDA0002634034670000081
Wherein F (-) is a joint distribution function of multidimensional variables;
Figure BDA0002634034670000082
is a random variable XiThe edge distribution function of (1); c is a Copula function.
A joint distribution function of the multi-source flood volume can be constructed by utilizing a Copula function, and the expression is as follows:
Figure BDA0002634034670000083
taking three rivers as an example, when n is 3,
Figure BDA0002634034670000084
the joint probability of the multi-source flood greater than a certain recurrence period flood based on the Copula function can be calculated by the following formula:
Figure BDA0002634034670000085
the practicability of the invention is further illustrated by taking the flood process encounter in the top 15 days of the year in Jinshajiang, Yazhenjiang and Minjiang (corresponding to hydrological stations for climbing flowers, small stones and high-rise stations, respectively) at the upper reaches of the Yangtze river as an example.
The method comprises the following steps: collecting flood process data of 15 days in maximum year in a drainage basin by adopting a maximum annual sampling method, and obtaining flood rise time and flood end time of the 15 days in maximum year and flood value of 15 days in maximum year;
step two: based on the newly proposed multi-source flood process encounter definition, a Jinshajiang, Yazhenjiang and Minjiang flood process encounter model considering time and magnitude simultaneously is established;
step three: and (4) setting a flood process under different flood combinations of Jinshajiang, Yazheng and Minjiang to obtain the flood combination of the three rivers which is most likely to occur in the flood reproduction period.
For convenience of description, W is usedp、WxAnd WgIndicating the flood volume of Panzhihua, Xiaodao and high-rise hydrological station, as Tp、TxAnd TgRepresenting the Jinshajiang, Yazhenjiang and Minjiang flood reproduction period. Correlation analysis was performed at a 5% significance level using Pearson, Kendall and Spearman coefficients, and the results calculated are shown in table 1. As can be seen from table 1, the maximum Kendall coefficient between the flood overlap time and the flood volume of each river is 0.069, which indicates that the flood overlap time and the flood volume are independent of each other. On the other hand, as can be seen from table 1, the maximum and minimum Kendall coefficients of flood pairs are 0.56 and 0.20, respectively, which indicates that there is a certain correlation between the floods of Jinshajiang, Yazhenjiang and Minjiang.
TABLE 1 correlation coefficients for different combinations of flood overlap time and magnitude
Figure BDA0002634034670000091
Table 2 shows the evaluation results of the flood process encounter in the three rivers according to the present invention. As can be seen from Table 2, the three rivers reappear period Tp＝5、Tx10 and TgThe flood encounter probability is maximum at 5, which is 2.98 × 10-2(ii) a And when T ispWhen the time is 5, the probability of encountering the flood process is TxAnd TgIs reduced and increased, and conforms to the general rule of flood occurrenceAnd (4) law.
TABLE 2 probability of flood process encounter under different combinations of recurrence periods
Figure BDA0002634034670000092
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A probability analysis method for multi-source flood process encounter is characterized by comprising the following steps:
(1) acquiring annual maximum flood generation time in N days and annual maximum flood value in N days by adopting an annual maximum sampling method;
(2) when the coincidence time of the multi-source flood process exceeds N/2 days, the multi-source flood process is considered to be encountered, and the coincidence time ToExpressed as: t iso＝Te-TsWherein, TeIndicating the end time, T, of the latest flood process in a multisource floodsRepresenting the rise time of the earliest flood process in the multi-source flood;
(3) establishing a multi-source flood process encounter model representing the probability of the occurrence of the multi-source flood process encounter based on the obtained flood occurrence time and flood value and the multi-source flood process encounter definition;
when the flood coincidence time and the flood volume value have a correlation, the model is expressed as:
Figure FDA0003034922410000011
when the flood coincidence time and the flood value do not have a correlation, the model is represented as:
Figure FDA0003034922410000012
wherein, Wi(i-1, 2, …, N) represents the annual maximum N daily flood variable for i river, wi(i ═ 1,2, …, n) represents the flood volume of i river greater than a certain recurrence period, n is the total number of rivers;
the Copula function is adopted to construct a joint distribution function of the multi-source flood volume, and the joint distribution function is expressed as follows:
Figure FDA0003034922410000013
wherein F (-) is a joint distribution function of multidimensional variables,
Figure FDA0003034922410000014
is a random variable WnC is a Copula function;
thereby obtaining the joint probability P (W) of the flood volume of the multisource flood greater than a certain recurrence period1≥w1,W2≥w2,...,Wn≥wn)。
2. The method for probability analysis of multi-source flood process encounters according to claim 1,
fitting the flood occurrence time by adopting mixed von Mises distribution, converting the flood occurrence time into radians, and expressing as follows:
Figure FDA0003034922410000021
wherein L represents the flood season time period length; l is1Represents the annual maximum flood process period length;
the probability density function expression of the flood occurrence time variable is as follows:
Figure FDA0003034922410000022
in the formula, theta is more than or equal to 0 and less than or equal to 2 pi; mu.sj、kjAnd pjRespectively is a position parameter, a scale parameter and a mixing proportion coefficient of the jth component of the mixed von Mises distribution, wherein the number is more than or equal to 0 muj≤2π，kj＞0，0≤pj≤1；I0(. h) is a first class of 0-order modified Bessel function; m is the order of the finite mixture von Mises distribution;
by integral operation, solve
Figure FDA0003034922410000023
3. The method of claim 1, wherein when n is 3,
Figure FDA0003034922410000024
4. a system for probability analysis of multi-source flood process encounters, comprising:
the data acquisition module is used for acquiring annual maximum N-day flood generation time and annual maximum N-day flood value by adopting an annual maximum sampling method; when the coincidence time of the multi-source flood process exceeds N/2 days, the multi-source flood process is considered to be encountered, and the coincidence time ToExpressed as: t iso＝Te-TsWherein, TeIndicating the end time, T, of the latest flood process in a multisource floodsRepresenting the rise time of the earliest flood process in the multi-source flood;
the multi-source flood process encounter model establishing module is used for establishing a multi-source flood process encounter model which represents the probability of the occurrence of the multi-source flood process encounter based on the flood occurrence time and the flood value which are obtained by the data obtaining module and the multi-source flood process encounter definition;
when the flood coincidence time and the flood volume value have a correlation, the model is expressed as:
Figure FDA0003034922410000031
when the flood coincidence time and the flood value do not have a correlation, the model is represented as:
Figure FDA0003034922410000032
wherein, Wi(i-1, 2, …, N) represents the annual maximum N daily flood variable for i river, wi(i ═ 1,2, …, n) represents the flood volume of i river greater than a certain recurrence period, n is the total number of rivers;
the Copula function is adopted to construct a joint distribution function of the multi-source flood volume, and the joint distribution function is expressed as follows:
Figure FDA0003034922410000033
wherein F (-) is a joint distribution function of multidimensional variables,
Figure FDA0003034922410000034
is a random variable WnC is a Copula function;
thereby obtaining the joint probability P (W) of the flood volume of the multisource flood greater than a certain recurrence period1≥w1,W2≥w2,...,Wn≥wn)。
5. The probability analysis system of multi-source flood process encounters of claim 4,
fitting the flood occurrence time by adopting mixed von Mises distribution, converting the flood occurrence time into radians, and expressing as follows:
Figure FDA0003034922410000035
wherein L represents the flood season time period length；L1Represents the annual maximum flood process period length;
the probability density function expression of the flood occurrence time variable is as follows:
Figure FDA0003034922410000041
in the formula, theta is more than or equal to 0 and less than or equal to 2 pi; mu.sj、kjAnd pjRespectively is a position parameter, a scale parameter and a mixing proportion coefficient of the jth component of the mixed von Mises distribution, wherein the number is more than or equal to 0 muj≤2π，kj＞0，0≤pj≤1；I0(. h) is a first class of 0-order modified Bessel function; m is the order of the finite mixture von Mises distribution;
by integral operation, solve
Figure FDA0003034922410000042
6. The probability analysis system of multi-source flood process encounters according to claim 4, wherein when n-3,
Figure FDA0003034922410000043
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