CN108320055A - The determination method of multiple river mouth Storm Surge joint return periods - Google Patents
The determination method of multiple river mouth Storm Surge joint return periods Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及海洋科学与海洋工程技术领域,具体涉及一种多个河口风暴潮增水联合重现期的确定方法。The invention relates to the technical fields of marine science and marine engineering, in particular to a method for determining a combined return period of storm surge flooding in multiple estuaries.
背景技术Background technique
海岸工程设计中的极端高潮位是指水工建筑物在非正常工作条件下的潮位,它是结构安全设计的重要参数之一。我国《海港水文规范》规定:极端高潮位是在不少于连续20a的最高潮位实测资料的基础上,采用Gumbel分布推算的50a一遇高水位。此法是把实测水位当作随机变量进行统计的。实际上观测到的年极值水位通常不是单纯由天文因素造成的,而是由台风、寒潮等产生的增减水与天文潮组合而成的。近些年来,有学者开始将风暴潮增水当作最高潮位的主要因素来考虑,把年最大增水当作样本来进行概率计算,将其重现值迭加在平均高潮位之上,从而确定极端高潮位。The extreme high tide level in coastal engineering design refers to the tide level of hydraulic structures under abnormal working conditions, and it is one of the important parameters of structural safety design. my country's "Hydrological Standards for Seaports" stipulates that extreme high tide level is the high water level once in 50 years calculated by Gumbel distribution on the basis of the measured data of the highest tide level not less than 20 years in a row. This method treats the measured water level as a random variable for statistics. In fact, the observed annual extreme water level is usually not caused by astronomical factors alone, but by the combination of the increase and decrease of water generated by typhoons, cold waves, etc. and astronomical tides. In recent years, some scholars have begun to consider the storm surge increase as the main factor of the highest tide level, take the annual maximum increase as a sample for probability calculation, and superimpose its recurrence value on the average high tide level, so that Determine extreme orgasm levels.
受台风影响的海域,每年出现台风的路径和次数是随机的,产生的风暴潮增水的次数与强度也是随机的。台风不是每年都发生的,这就导致无台风发生的年份,存在含零项,故不能采用年极值法计算台风波高的重现值。In sea areas affected by typhoons, the path and frequency of typhoons are random every year, and the frequency and intensity of storm surges generated are also random. Typhoons do not occur every year, which leads to years without typhoons, which contain zero items, so the annual extreme value method cannot be used to calculate the recurrence value of typhoon wave heights.
对于同一场台风,其影响区域内的不同河口的风暴增水程度不同。对于一个有三个河口的区域,单独来看,每个河口都会出现较高水位的风暴增水,但是其同时出现极大风暴增水的概率较低,也就是同一台风影响区域不同河口的风暴增水具有一定的相关性,对于同一场台风,其影响区域内的不同河口的风暴增水程度不同。因此,在实际应用中,如果选用每个河口的水位极值来统计重现值,那么就忽略了同一台风影响区域不同河口的风暴增水的相关性,从而使得极端高潮位设计值偏大,会造成资源的浪费。For the same typhoon, different estuaries in the affected area have different degrees of storm surge. For an area with three estuaries, individually, each estuary will have a higher level of storm surge, but the probability of extremely large storm surge at the same time is low, that is, the storm surge in different estuaries in the same typhoon affected area. Water has a certain correlation. For the same typhoon, different estuaries in the affected area have different degrees of storm water increase. Therefore, in practical applications, if the extreme water level of each estuary is used to calculate the recurrence value, then the correlation of storm water increase in different estuaries in the same typhoon-affected area is ignored, so that the design value of the extreme high tide level is too large. It will cause a waste of resources.
发明内容Contents of the invention
本发明针对现有技术中统计极端高潮位与实际情况存在偏差的问题,提出一种更为合理的计算河口海港极端水位的联合概率方法,对于区域资源调配,实现海岸区域工程有效防灾有重要意义。The present invention aims at the problem that there is a deviation between the extreme high tide level and the actual situation in the prior art, and proposes a more reasonable joint probability method for calculating the extreme water level of estuaries and seaports, which is very important for the allocation of regional resources and the realization of effective disaster prevention in coastal areas significance.
为了实现上述目的,本发明采用如下技术方案,多个河口风暴潮增水联合重现期的确定方法,包括如下步骤,In order to achieve the above object, the present invention adopts the following technical scheme, and the method for determining the joint return period of storm surge water increase in multiple estuaries includes the following steps,
S1.统计一段时间内,所研究区域内台风的发生频次,建立台风发生频次的Poisson分布;S1. Count the frequency of typhoons in the research area within a certain period of time, and establish the Poisson distribution of typhoon frequency;
S2.统计所研究区域内的河口情况,建立每个河口由台风引起的最大增水的最佳一维边缘分布;S2. Statistics of the estuaries in the research area, and establish the best one-dimensional marginal distribution of the maximum water increase caused by typhoons in each estuary;
S3.建立每个河口由台风引起的最大增水复合台风发生频次的一维Poisson复合极值分布;S3. Establish the one-dimensional Poisson composite extreme value distribution of the frequency of occurrence of the maximum water-increasing composite typhoon caused by the typhoon in each estuary;
S4.建立所研究区域内所有河口由台风引起的最大增水复合台风发生频次的多维Poisson 复合极值分布;S4. Establish the multi-dimensional Poisson composite extreme value distribution of the frequency of the maximum water-increasing composite typhoon caused by typhoons in all estuaries in the study area;
S5.获得多河口风暴潮增水联合重现期。S5. Obtain the joint return period of storm surge flooding in multiple estuaries.
进一步地,所述步骤S2具体包括:Further, the step S2 specifically includes:
S21.统计所研究区域内的河口的数量;S21. Statistics on the number of estuaries within the study area;
S22.收集每个河口由台风引起的最大增水的数据;S22. Collect the data of the maximum water increase caused by the typhoon in each estuary;
S23.选择合适的分布线型对每个河口由台风引起的最大增水数据进行拟合;S23. Select the appropriate distribution line type to fit the maximum water increase data caused by the typhoon in each estuary;
S24.确定每个河口由台风引起的最大增水的最佳一维边缘分布。S24. Determine the optimal one-dimensional marginal distribution of maximum typhoon-induced flooding for each estuary.
进一步地,所述步骤S23中,所述分布线性包括Pearson-III型分布、Weibull分布、广义极值分布和对数正态分布。Further, in the step S23, the linear distribution includes Pearson-III type distribution, Weibull distribution, generalized extreme value distribution and lognormal distribution.
进一步地,所述步骤S24中,通过K-S检验、观测值、估计值的离差平方和及AIC信息准则来确定每个河口由台风引起的最大增水的最佳一维边缘分布。Further, in the step S24, the optimal one-dimensional marginal distribution of the maximum water increase caused by the typhoon for each estuary is determined through the K-S test, the sum of squared deviations of the observed values and estimated values, and the AIC information criterion.
进一步地,所述步骤S4具体包括:Further, the step S4 specifically includes:
S41.采用合适的Copula函数建立所有河口由台风引起的最大增水复合台风发生频次的多维Poisson复合极值分布;S41. Adopt suitable Copula function to establish the multidimensional Poisson composite extremum distribution of the maximum water-increasing composite typhoon occurrence frequency of all estuaries caused by typhoons;
S42.确定所有河口由台风引起的最大增水复合台风发生频次的最佳多维Poisson复合极值分布。S42. Determine the optimal multi-dimensional Poisson composite extreme value distribution of the typhoon-induced maximum flooding composite typhoon frequency in all estuaries.
进一步地,所述步骤S41中,所述Copula函数包括正态Copula、Frank Copula、Clayton Copula和Gumbel-Hougaard(G-H)Copula。Further, in the step S41, the Copula function includes Normal Copula, Frank Copula, Clayton Copula and Gumbel-Hougaard (G-H) Copula.
进一步地,所述步骤S34中,通过K-S检验及AIC信息准则来确定所有河口由台风引起的最大增水复合台风发生频次的最佳多维Poisson复合极值分布。Further, in the step S34, the optimal multi-dimensional Poisson composite extreme value distribution of the frequency of occurrence of the maximum water-increasing composite typhoon in all estuaries caused by typhoon is determined by K-S test and AIC information criterion.
本发明提出了一种更符合风暴潮影响下区域多河口成灾程度的联合概率模型,对进行多个河口联合成灾风险分析具有重要意义。同时对于同一场台风,其影响区域内的不同河口的风暴增水程度不同。同一影响区域内河口的风暴增水具有一定的相关性,通过对同一台风影响区域不同河口的风暴增水联合概率计算,特别是风暴增水的同步性研究,可以确定固定重现期下受同一台风影响各个河口的风暴增水,对于该地区的工程防护具有重要意义,可以对区域防灾减灾有的放矢,台风增水高的河口区域加强工程防护,不必所有河口地区防灾物资平均分配,实现精准防控,为科学的防灾减灾提供科学决策。The present invention proposes a joint probability model that is more in line with the disaster degree of multiple estuaries in a region under the influence of storm surges, which is of great significance for the joint disaster risk analysis of multiple estuaries. At the same time, for the same typhoon, different estuaries in the affected area have different storm flooding degrees. The storm surge in estuaries in the same affected area has a certain correlation. Through the calculation of the joint probability of storm surge in different estuaries in the same typhoon affected area, especially the synchronous study of storm surge, it can be determined that the same typhoon is affected by the same typhoon in the return period. The typhoon affects the storm water increase of each estuary, which is of great significance to the engineering protection of this area. It can be targeted for regional disaster prevention and mitigation. The estuary area with high typhoon water increase will strengthen engineering protection, and it is not necessary to distribute disaster prevention materials equally in all estuary areas to achieve accurate Prevention and control, providing scientific decision-making for scientific disaster prevention and mitigation.
附图说明Description of drawings
图1为台风发生频次的Poisson分布拟合;Figure 1 is the Poisson distribution fitting of typhoon frequency;
图2为南崁溪、磺溪与兰阳溪的河口的台风增水序列(1980-2004年);Figure 2 shows the typhoon flooding sequence (1980-2004) at the estuaries of Nankan Creek, Suoxi Creek and Lanyang Creek;
图3为三条溪流河口处的台风增水序列的散点图;Figure 3 is a scatter diagram of the typhoon water increase sequence at the mouth of the three streams;
其中,(a)为南坎溪的散点图;(b)为磺溪的散点图;(c)为兰阳溪的散点图;Among them, (a) is the scatter diagram of Nankan River; (b) is the scatter diagram of Sulfur River; (c) is the scatter diagram of Lanyang River;
图4为南坎溪河口处的台风增水各种分布概率密度与累积分布拟合;Figure 4 shows the fitting of various distribution probability densities and cumulative distributions of typhoon water increase at the mouth of the Nankan River;
其中,(a)为Pearson-III拟合结果;(b)为Weibull拟合结果;(c)为GEV拟合结果;(d) 为Lognormal拟合结果;Among them, (a) is the fitting result of Pearson-III; (b) is the fitting result of Weibull; (c) is the fitting result of GEV; (d) is the fitting result of Lognormal;
图5为磺溪河口处的台风增水各种分布概率密度与累积分布拟合;Figure 5 is the fitting of various distribution probability densities and cumulative distributions of typhoon water increase at the mouth of the Sulfur Creek River;
其中,(a)为Pearson-III拟合结果;(b)为Weibull拟合结果;(c)为GEV拟合结果;(d) 为Lognormal拟合结果;Among them, (a) is the fitting result of Pearson-III; (b) is the fitting result of Weibull; (c) is the fitting result of GEV; (d) is the fitting result of Lognormal;
图6为兰阳溪河口处的台风增水各种分布概率密度与累积分布拟合;Figure 6 shows the fitting of various distribution probability densities and cumulative distributions of typhoon water increase at the mouth of Lanyangxi River;
其中,(a)为Pearson-III拟合结果;(b)为Weibull拟合结果;(c)为GEV拟合结果;(d)为Lognormal拟合结果;Among them, (a) is the fitting result of Pearson-III; (b) is the fitting result of Weibull; (c) is the fitting result of GEV; (d) is the fitting result of Lognormal;
图7为三河口台风增水的联合重现期等值面;Figure 7 is the isosurface of the joint return period of typhoon flooding in Sanhekou;
图8为三河口台风增水50年一遇联合分布联合概率;Figure 8 shows the combined probability of the joint distribution of the Sanhekou typhoon flood increase once in 50 years;
其中,(a)为三河口台风增水2%联合概率曲面;(b)为南崁溪与磺溪的2%联合概率侧视图;(c)为南崁溪与兰阳溪的2%联合概率侧视图;(d)为磺溪与兰阳溪的2%联合概率侧视图。Among them, (a) is the 2% joint probability surface of Sanhekou typhoon water increase; (b) is the side view of the 2% joint probability of Nankan Creek and Sulfur Creek; (c) is the 2% joint probability surface of Nankan Creek and Lanyang Creek Probability side view; (d) is the 2% joint probability side view of Sulfur Creek and Lanyang Creek.
具体实施方式Detailed ways
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图和实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅用以解释本发明,并不用于限定本发明。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.
本发明的多个河口风暴潮增水联合重现期的确定方法,包括如下步骤,The method for determining the combined return period of a plurality of estuary storm surge surges of the present invention comprises the following steps,
S1.统计一段时间内,所研究区域内台风的发生频次,建立台风发生频次的Poisson分布;S1. Count the frequency of typhoons in the research area within a certain period of time, and establish the Poisson distribution of typhoon frequency;
现收集一段时间内,一般以年为单位,所研究区域内发生台风的数量情况,建立台风发生频次的Poisson分布。Now collect the number of typhoons in the study area within a period of time, generally in units of years, and establish the Poisson distribution of typhoon frequency.
S2.统计所研究区域内的河口情况,建立每个河口由台风引起的最大增水的最佳一维边缘分布;所述步骤S2具体包括:S2. Statistics on the estuary situation in the research area, establish the best one-dimensional edge distribution of the maximum water increase caused by the typhoon in each estuary; the step S2 specifically includes:
S21.统计所研究区域内的河口的数量;S21. Statistics on the number of estuaries within the study area;
S22.收集每个河口由台风引起的最大增水的数据;S22. Collect the data of the maximum water increase caused by the typhoon in each estuary;
S23.选择合适的分布线型对每个河口由台风引起的最大增水数据进行拟合;所述分布线性包括Pearson-III型分布、Weibull分布、广义极值分布和对数正态分布。S23. Choose an appropriate distribution line type to fit the maximum water increase data caused by the typhoon in each estuary; the distribution line includes Pearson-III type distribution, Weibull distribution, generalized extreme value distribution and logarithmic normal distribution.
S24.确定每个河口由台风引起的最大增水的最佳一维边缘分布;通过K-S检验、观测值、估计值的离差平方和及AIC信息准则来确定最佳一维边缘分布。S24. Determine the best one-dimensional marginal distribution of the maximum water increase caused by the typhoon in each estuary; determine the best one-dimensional marginal distribution through the K-S test, the sum of squared deviations of observed values and estimated values, and the AIC information criterion.
S3.建立每个河口由台风引起的最大增水复合台风发生频次的一维Poisson复合极值分布;S3. Establish the one-dimensional Poisson composite extreme value distribution of the frequency of occurrence of the maximum water-increasing composite typhoon caused by the typhoon in each estuary;
若某地区每年发生的台风n为一个离散型随机变量,而每次台风过程中的极值波高设为ξ,无台风年份的极值波高设为η。假设ξ为连续型随机向量,其概率分布函数为G(x)。设ξi为ξ的第i次观测值,n为与ξ独立的取值非负整数的随机变量,其分布函数记为:If the annual typhoon n in a certain area is a discrete random variable, and the extreme wave height in each typhoon process is set to ξ, and the extreme wave height in a typhoon-free year is set to η. Suppose ξ is a continuous random vector, and its probability distribution function is G(x). Let ξi be the i-th observation value of ξ, n is a random variable with non-negative integer value independent of ξ, and its distribution function is recorded as:
假定随机向量:Assume random vectors:
则称F0(x)为一维复合极值分布:Then F0(x) is called a one-dimensional composite extreme value distribution:
假设λ表示每年台风出现的平均次数,若台风过程出现频次n符合Poisson分布:Assuming that λ represents the average number of typhoon occurrences per year, if the frequency n of the typhoon process conforms to the Poisson distribution:
由式(3)可以得到:From formula (3) we can get:
式中,G(x)若为Pearson-III型分布、Weibull分布、广义极值(GEV)分布或对数正态 (lognormal)分布,代入式(5),即可得到Poisson-Pearson III分布、Poisson-Weibull分布、Poisson-GEV分布或Poisson-lognormal分布模型。In the formula, if G(x) is Pearson-III type distribution, Weibull distribution, generalized extreme value (GEV) distribution or lognormal (lognormal) distribution, it can be substituted into formula (5) to get Poisson-Pearson III distribution, Poisson-Weibull distribution, Poisson-GEV distribution, or Poisson-lognormal distribution model.
S4.建立所研究区域内所有河口由台风引起的最大增水复合台风发生频次的多维Poisson 复合极值分布;S4. Establish the multi-dimensional Poisson composite extreme value distribution of the frequency of the maximum water-increasing composite typhoon caused by typhoons in all estuaries in the study area;
S41.采用合适的Copula函数建立所有河口由台风引起的最大增水复合台风发生频次的多维Poisson复合极值分布;S41. Adopt suitable Copula function to establish the multidimensional Poisson composite extremum distribution of the maximum water-increasing composite typhoon occurrence frequency of all estuaries caused by typhoons;
推到过程为:The push process is:
假设每次台风过程中的N个海洋环境随机变量为(ξ1,ξ2,···,ξN),无台风年份中的极值海洋环境随机变量为(ζ1,ζ2,···,ζN)。以G(x1,x2,···,xN)和g(x1,x2,···,xN)分别表示随机变量(ξ1, ξ2,···,ξN)的联合分布函数和联合概率密度函数,Q(x1,x2,···,xN)表示随机变量(ζ1,ζ2,···,ζN)的联合分布函数。以(ξ1i,ξ2i,ξ3i,···,ξNi,)分别为N个随机变量的第i次观测值,再以n表示与ξ独立的取值非负整数的随机变量,其概率分布函数记为式(1)。现定义一个随机变量(X1,X2,···, XN):Assume that the N marine environment random variables in each typhoon process are (ξ 1 , ξ 2 ,...,ξ N ), and the extreme marine environment random variables in typhoon-free years are (ζ 1 , ζ 2 ,... ·,ζ N ). Let G(x 1 ,x 2 ,···,x N ) and g(x 1 ,x 2 ,···,x N ) denote random variables (ξ 1 , ξ 2 ,···,ξ N ) The joint distribution function and joint probability density function of , Q(x 1 ,x 2 ,···,x N ) represents the joint distribution function of random variables (ζ 1 ,ζ 2 ,···,ζ N ). Let (ξ 1i , ξ 2i , ξ 3i ,···,ξ Ni ,) be the i-th observation value of N random variables respectively, and then let n denote a random variable independent of ξ with a non-negative integer value, where The probability distribution function is recorded as formula (1). Now define a random variable (X 1 ,X 2 ,..., X N ):
则(X1,X2,···,XN)的联合分布函数为:Then the joint distribution function of (X 1 ,X 2 ,···,X N ) is:
式中,多维随机变量(X1,X2,···,XN)的联合分布函数和概率密度函数分别为G(x1,x2,···,xN) 和g(x1,x2,···,xN);GX1(u1)为G(x1,x2,···,xN)边缘分布函数,即In the formula, the joint distribution function and probability density function of the multidimensional random variable (X 1 ,X 2 ,···,X N ) are G(x 1 ,x 2 ,···,x N ) and g(x 1 ,x 2 ,···,x N ); G X1 (u 1 ) is the marginal distribution function of G(x 1 ,x 2 ,···,x N ), namely
GX1(u1)=G(u1,+∞,…,+∞) (8)G X1 (u 1 )=G(u 1 ,+∞,…,+∞) (8)
假设每年台风发生频次n服从Poisson分布(式(4)),式(7)即可化为:Assuming that the annual typhoon frequency n obeys the Poisson distribution (Equation (4)), Equation (7) can be transformed into:
式(9)即为随机变量(X1,X2,···,XN)的多维Poisson复合极值分布函数。Equation (9) is the multidimensional Poisson compound extreme value distribution function of random variables (X1, X2,...,XN).
其相应的概率密度函数为:The corresponding probability density function is:
式(10)中的g(x1,x2,,xN)表示不考虑台风发生频次情况下的多维随机变量的原始联合概率密度函数,若采用copula函数建立多维随机变量的原始联合分布模型,g(x1,x2,,xN)可按下式表示:g(x 1 ,x 2 ,,x N ) in formula (10) represents the original joint probability density function of the multidimensional random variable without considering the typhoon frequency. If the copula function is used to establish the original joint distribution model of the multidimensional random variable , g(x 1 ,x 2 ,,x N ) can be expressed as follows:
g(x1,x2,…,xN)=c(x1,x2,…,xN)·f(x1)·f(x2)·…·f(xN) (11)g(x 1 ,x 2 ,…,x N )=c(x 1 ,x 2 ,…,x N )·f(x 1 )·f(x 2 )···f(x N ) (11)
式(11)中的c(x1,x2,,xN)为copula函数的概率密度函数,f(xi)表示单变量的概率密度函数。c(x 1 ,x 2 ,,x N ) in formula (11) is the probability density function of copula function, and f( xi ) represents the probability density function of univariate.
根据式(9)和式(10)的多维Poisson复合极值分布,可得到二维Poisson复合极值分布和三维Poisson复合极值分布的概率密度函数和概率分布函数见表2。According to the multidimensional Poisson compound extreme value distribution of formula (9) and formula (10), the probability density function and probability distribution function of the two-dimensional Poisson compound extreme value distribution and the three-dimensional Poisson compound extreme value distribution can be obtained, as shown in Table 2.
表2二维和三维Poisson复合极值分布模型Table 2 Two-dimensional and three-dimensional Poisson compound extreme value distribution models
最后带入合适的Copula函数,包括正态Copula、Frank Copula、Clayton Copula和Gumbel-Hougaard(G-H)Copula进行拟合。Finally, bring in the appropriate Copula function, including Normal Copula, Frank Copula, Clayton Copula and Gumbel-Hougaard (G-H) Copula for fitting.
S42.确定所有河口由台风引起的最大增水复合台风发生频次的最佳多维Poisson复合极值分布。通过K-S检验及AIC信息准则来确定所有河口由台风引起的最大增水复合台风发生频次的最佳多维Poisson复合极值分布。S42. Determine the optimal multi-dimensional Poisson composite extreme value distribution of the typhoon-induced maximum flooding composite typhoon frequency in all estuaries. The optimal multidimensional Poisson composite extreme value distribution of the typhoon-induced maximum flooding composite typhoon frequency in all estuaries is determined by the K-S test and the AIC information criterion.
S5.获得多河口风暴潮增水联合重现期。S5. Obtain the joint return period of storm surge flooding in multiple estuaries.
对多个河口的台风增水序列建立了Poisson多维复合概率模型,即可绘制固定重现期的联合概率等值面。同时可得到多个河口不同台风增水下的联合重现期。A Poisson multi-dimensional composite probability model is established for typhoon flooding sequences in multiple estuaries, and a joint probability isosurface with a fixed return period can be drawn. At the same time, the joint return period under different typhoon intensification of multiple estuaries can be obtained.
为了验证本发明方法的可靠性,本发明选取了中国台湾北部区域的相关数据对本发明的方法进行验证。In order to verify the reliability of the method of the present invention, the present invention selects relevant data in the northern region of Taiwan, China to verify the method of the present invention.
一、计算过程1. Calculation process
1、统计一段时间内,所研究区域内台风的发生频次,建立台风发生频次的Poisson分布;1. Count the frequency of typhoons in the research area within a certain period of time, and establish the Poisson distribution of typhoon frequency;
对影响中国台湾北部的1980-2004年的历史台风进行后报。选择计算的台风条件为:台风路径与中国台湾的距离不超过250km。通过统计,中国台湾北部在1980-2004年内共发生36场台风,每年发生的次数统计见表1。选用Poisson分布对台风年频次进行拟合,参数λ的估计值为1.44。 Poisson分布的拟合检验见表2,其拟合结果见图1,拟合效果很好。因此,频次的确定服从参数为1.44的Poisson分布。Hindcast of historical typhoons affecting northern Taiwan, China from 1980 to 2004. The typhoon conditions selected for calculation are: the distance between the typhoon track and Taiwan, China is not more than 250km. According to statistics, 36 typhoons occurred in the northern part of Taiwan from 1980 to 2004, and the statistics of the number of occurrences each year are shown in Table 1. The Poisson distribution is used to fit the annual typhoon frequency, and the estimated value of the parameter λ is 1.44. The fitting test of the Poisson distribution is shown in Table 2, and the fitting results are shown in Figure 1, and the fitting effect is very good. Therefore, the determination of frequency obeys the Poisson distribution with parameter 1.44.
表1 1980-2004年影响三条溪流河口的台风个数统计Table 1 Statistics of typhoons affecting three streams and estuaries from 1980 to 2004
根据表1,台风发生次数的泊松分布检验统计量为χ2=1.8241,小于显著水平0.05时的假设检验临界值说明台风发生次数符合λ=36/25=1.44的泊松分布。According to Table 1, the test statistic of the Poisson distribution of typhoon occurrences is χ2=1.8241, which is less than the critical value of the hypothesis test at the significant level of 0.05 It shows that the number of typhoon occurrences conforms to the Poisson distribution of λ=36/25=1.44.
表2台风发生频次的统计检验Table 2 Statistical test of typhoon frequency
2、统计所研究区域内的河口情况,建立每个河口由台风引起的最大增水的最佳一维边缘分布;建立每个河口由台风引起的最大增水复合台风发生频次的一维Poisson复合极值分布,通过一维Poisson复合极值分布求得重现值。2. Statistics of the estuaries in the research area of the institute, and establish the best one-dimensional edge distribution of the maximum water increase caused by typhoons in each estuary; establish the one-dimensional Poisson composite of the maximum water increase and composite typhoon frequency of each estuary caused by typhoons Extreme value distribution, the recurrence value is obtained through the one-dimensional Poisson compound extreme value distribution.
中国台湾北部共分布有3各河口,分别是南崁溪(Nang-Kang)、磺溪(Huang)与兰阳溪 (Lan-Yang)。后报计算得到南崁溪(Nang-Kang)、磺溪(Huang)与兰阳溪(Lan-Yang) 的河口在1980-2004年的台风增水序列如图2所示。There are three estuaries in the northern part of Taiwan, namely Nankan River (Nang-Kang), Huang River and Lan-Yang River. The typhoon flooding sequence of the estuaries of Nankan River (Nang-Kang), Huang River and Lan-Yang River from 1980 to 2004 is shown in Figure 2.
从36场风暴台风过程中得到的南崁溪、磺溪与兰阳溪三条溪流河口的最大增水的散点图分别见图3。The scatter diagrams of the maximum water increase in the estuaries of Nankan River, Suo River and Lanyang River obtained from 36 storms and typhoons are shown in Figure 3 respectively.
选用Pearson-III型分布、三参数Weibull分布、GEV分布和Log-normal分布分别对三个序列的增水进行拟合。Pearson-III distribution, three-parameter Weibull distribution, GEV distribution and Log-normal distribution were used to fit the water increase of the three sequences respectively.
a.南崁溪河口处极端增水的拟合a. Fitting of extreme water increase at the mouth of Nankanxi River
对南坎溪河口处的台风增水序列进行拟合,参数估计结果如表3。拟合曲线分别如图4。The typhoon water increase sequence at the mouth of the Nankan River was fitted, and the parameter estimation results are shown in Table 3. The fitting curves are shown in Fig. 4 respectively.
表3南坎溪河口处的台风增水分布拟合的参数估计Table 3 Parameter estimation of typhoon water increase distribution fitting at the mouth of Nankanxi River
注:PA、PB与PC分别表示各个分布的位置、尺度和形状参数。Note: PA, PB and PC represent the location, scale and shape parameters of each distribution, respectively.
由于没有考虑台风发生的次数,图3中横坐标所说的重现频率,并非对应重现期的倒数,只是表示在数据中的重现频率。其他类似拟合图的横坐标意义均是如此。Since the number of typhoon occurrences is not considered, the recurrence frequency mentioned on the abscissa in Figure 3 is not the reciprocal of the corresponding return period, but only the recurrence frequency in the data. The meaning of the abscissa of other similar fitting graphs is the same.
同时采用K-S检验、观测值、估计值的离差平方和及AIC信息准则来比较4种分布对极端增水序列的拟合情况。置信度α=0.05条件下,K-S的统计量D^n和离差平方RMSE和AIC的计算结果如表4。拟合结果表明,Pearson-III型分布、三参数Weibull分布、GEV分布和Log-normal分布都通过了统计检验,其中GEV分布拟合最优,Pearson-III型分布次之。利用一维Poisson复合分布,求得重现值如表5。结果表明,Weibull所得重现值最小,Pearson-III 次之。At the same time, the K-S test, the sum of squared deviations of observed values and estimated values, and the AIC information criterion were used to compare the fit of the four distributions to the extreme water increase series. Under the condition of confidence α=0.05, the calculation results of K-S statistic D^n and dispersion square RMSE and AIC are shown in Table 4. The fitting results showed that Pearson-III distribution, three-parameter Weibull distribution, GEV distribution and Log-normal distribution all passed the statistical test, and GEV distribution was the best fit, followed by Pearson-III distribution. Using one-dimensional Poisson composite distribution, the recurring values are obtained as shown in Table 5. The results showed that Weibull obtained the smallest recurring value, followed by Pearson-III.
表4南坎溪河口处的台风增水分布拟合的K-S检验和离差平方和Table 4 The K-S test and the sum of squares of the typhoon water increase distribution fitting at the Nankanxi Estuary
表5南坎溪河口处的台风增水Poisson复合分布计算的重现值(m)Table 5 Recurrence value (m) calculated by Poisson compound distribution of typhoon water increase at the mouth of Nankanxi River
b.磺溪河口处极端增水的拟合b. Fitting of extreme water increase at the mouth of the Sulfur Creek
对磺溪河口处的台风增水序列进行拟合,,拟合曲线分别如图5参数估计结果如表6。拟合结果表明,拟合结果表明,Pearson-III型分布、三参数Weibull分布、GEV分布和Log-normal 分布都通过了统计检验,其中Pearson-III型分布拟合最优,Weibull分布次之。Fit the typhoon flooding sequence at the mouth of the Sulfur Creek River, and the fitting curves are shown in Figure 5. The parameter estimation results are shown in Table 6. The fitting results showed that the Pearson-III distribution, the three-parameter Weibull distribution, the GEV distribution and the Log-normal distribution all passed the statistical test, among which the Pearson-III distribution was the best fit, followed by the Weibull distribution.
表6磺溪河口处的台风增水分布拟合的参数估计Table 6 Parameter estimation of typhoon water increase distribution fitting at the mouth of the Sulfur Creek
注:PA、PB与PC分别表示各个分布的位置、尺度和形状参数。Note: PA, PB and PC represent the location, scale and shape parameters of each distribution, respectively.
同时采用K-S检验、观测值、估计值的离差平方和及AIC信息准则来比较4种分布对极端增水序列的拟合情况。置信度α=0.05条件下,K-S的统计量D^n和离差平方RMSE和AIC的计算结果如表7。结果表明,Pearson-III型分布、三参数Weibull分布、GEV分布和Log-normal 分布都通过了统计检验,其中Pearson-III的拟合最优,Weibull次之。利用一维Poisson复合分布,求得重现值如表8。结果表明,Weibull所得重现值最小,Pearson-III次之。At the same time, the K-S test, the sum of squared deviations of observed values and estimated values, and the AIC information criterion were used to compare the fit of the four distributions to the extreme water increase series. Under the condition of confidence α=0.05, the calculation results of K-S statistic D^n and deviation square RMSE and AIC are shown in Table 7. The results showed that Pearson-III distribution, three-parameter Weibull distribution, GEV distribution and Log-normal distribution all passed the statistical test, among which Pearson-III fit the best, followed by Weibull. Using one-dimensional Poisson composite distribution, the recurring values are obtained as shown in Table 8. The results showed that Weibull obtained the smallest recurring value, followed by Pearson-III.
表7磺溪河口处的台风增水分布拟合的K-S检验和离差平方和Table 7 The K-S test and the sum of squared deviations of typhoon water increase distribution fitting at the mouth of the Sulfur Creek River
表8磺溪河口处的台风增水Poisson复合分布计算的重现值(m)Table 8 Recurrence value (m) calculated by Poisson composite distribution of typhoon water increase at the mouth of the Sulfur Creek River
c.兰阳溪河口处极端增水的拟合c. Fitting of extreme water increase at the mouth of Lanyangxi
对兰阳溪河口处的台风增水序列进行拟合,拟合曲线分别如图6,参数估计结果如表9 拟合结果表明,Pearson-III型分布、三参数Weibull分布、GEV分布和Log-normal分布都通过了统计检验,其中Pearson-III型分布拟合最优,Lognormal分布次之。Fit the typhoon flooding sequence at the mouth of Lanyangxi River, the fitting curves are shown in Figure 6, and the parameter estimation results are shown in Table 9. The fitting results show that Pearson-III distribution, three-parameter Weibull distribution, GEV distribution and Log- The normal distributions all passed the statistical test, among which the Pearson-III type distribution fit the best, followed by the Lognormal distribution.
表9磺溪河口处的台风增水分布拟合的参数估计Table 9 Parameter estimation of typhoon water increase distribution fitting at the mouth of the Sulfur Creek
注:PA、PB与PC分别表示各个分布的位置、尺度和形状参数。Note: PA, PB and PC represent the location, scale and shape parameters of each distribution, respectively.
同时采用K-S检验、观测值、估计值的离差平方和及AIC信息准则来比较4种分布对极端增水序列的拟合情况。置信度α=0.05条件下,K-S的统计量D^n和离差平方RMSE和AIC的计算结果如表10。结果表明,Pearson-III的拟合最优,Log-normal次之。利用一维Poisson 复合分布,求得重现值如表11。结果表明,Weibull所得重现值最小,GEV次之。At the same time, the K-S test, the sum of squared deviations of observed values and estimated values, and the AIC information criterion were used to compare the fit of the four distributions to the extreme water increase series. Under the condition of confidence α=0.05, the calculation results of K-S statistic D^n and dispersion square RMSE and AIC are shown in Table 10. The results show that Pearson-III has the best fit, followed by Log-normal. Using one-dimensional Poisson compound distribution, the recurring values are obtained as shown in Table 11. The results show that the return value obtained by Weibull is the smallest, followed by GEV.
表10磺溪河口处的台风增水分布拟合的K-S检验和离差平方和Table 10 The K-S test and the sum of squared deviations of typhoon water increase distribution fitting at the mouth of the Sulfur Creek
表11磺溪河口处的台风增水Poisson复合分布计算的重现值(m)Table 11 Recurrence value (m) calculated by Poisson composite distribution of typhoon water increase at the mouth of the Sulfur Creek River
3、建立所研究区域内所有河口由台风引起的最大增水复合台风发生频次的多维Poisson 复合极值分布;3. Establish the multi-dimensional Poisson composite extreme value distribution of the frequency of the maximum water-increasing composite typhoon caused by typhoons in all estuaries in the study area;
在构造南坎溪、磺溪和兰阳溪三条溪流河口台风增水的概率相关模型时,边缘分布皆选为Pearson-III分布,而联合概率分布根据Sklar定理,采用4种常用的三元Copula函数: Clayton Copula、Frank Copula和Gumbel-Hougaard(G-H)Copula。利用K-S检验、AIC法对模型的适用性进行评价,选取最优的三维联合概率模型。When constructing the probability correlation models of typhoon water increase in the mouths of the Nankan River, Suoxi River and Lanyang River, the marginal distributions are all selected as the Pearson-III distribution, and the joint probability distribution is based on the Sklar theorem, using four commonly used ternary copulas Functions: Clayton Copula, Frank Copula, and Gumbel-Hougaard (G-H) Copula. The applicability of the model was evaluated by K-S test and AIC method, and the optimal three-dimensional joint probability model was selected.
表12中,三元G-H模型的累积频率离差平方和RMES和AIC值最小,Frank Copula模型次之。因此,基于三元G-H,本文对三河口的台风增水序列建立了Poisson三维P3-P3-P3复合概率分布模型,记作P-GH-TriP3。南崁溪、磺溪和兰阳溪三个河口台风增水的5年一遇、10年一遇、20年一遇、50年一遇、100年一遇和200年一遇的联合概率等值面如图7。为了更加直观地观察不同重现期的概率等值面,图8给出了重现期为50年的三个侧视图,分别表示三个河口联合概率为2%时的两两河口的侧视图,即联合概率等值线。In Table 12, the ternary G-H model has the smallest RMES and AIC values, followed by the Frank Copula model. Therefore, based on the ternary G-H, this paper established a Poisson three-dimensional P3-P3-P3 composite probability distribution model for the typhoon flooding sequence in Sanhekou, denoted as P-GH-TriP3. Combined probability of typhoon increase in 5-year, 10-year, 20-year, 50-year, 100-year, and 200-year typhoons in Nankanxi, Suoxi and Lanyangxi estuaries, etc. The value surface is shown in Figure 7. In order to observe the probability isosurfaces of different return periods more intuitively, Figure 8 shows three side views with a return period of 50 years, respectively representing the side views of two estuaries when the joint probability of the three estuaries is 2%. , which is the joint probability contour.
表12三河口台风增水的三元Copula模型择优Table 12 Optimum selection of three-dimensional Copula model for typhoon water increase in Sanhekou
表13三河口1980-2004年台风增水联合重现期Table 13 Combined return period of typhoon water increase in Sanhekou from 1980 to 2004
表14给定重现期下,各河口增水设计值Table 14 Under the given return period, the water increase design value of each estuary
根据P-GH-TriP3模型,估计三个河口历史台风增水的联合重现期,如表13。由表中可以看出,P-GH-TriP3得出的三河口台风增水组合中,所有36场台风中,只有4场台风造成的三个河口的增水的联合重现期超过10年,其中Herb(1996)是强度最大台风,联合重现期达到66年。其他3场台风依次是Nockten(2004)、Doug(1994)及Brenda(1985),联合重现期分别为18年、16年及12年。同时,获得了固定重现期下三个河口的风暴增水,三个河口的风暴增水具有一定的差异。通过建立台湾地区多个河口风暴潮增水联合概率模型,可以看出,台风在中国台湾北部的西、北、东三面同时成灾的风险不大,即该模型可对多河口地区联合成灾风险进行分析。同时,获得联合重现期下台风过程不同河口的风暴增水,参见表14,增水较高的河口区域加强防护,对于受灾地区不同河口区域防灾减灾物资调配提供了科学依据。According to the P-GH-TriP3 model, the joint return periods of historical typhoon flooding in the three estuaries are estimated, as shown in Table 13. It can be seen from the table that among all the 36 typhoons in the combination of typhoon water increase in the three estuaries obtained by P-GH-TriP3, only 4 typhoons caused the combined return period of the water increase in the three estuaries to exceed 10 years. Among them, Herb (1996) is the strongest typhoon with a joint return period of 66 years. The other three typhoons were Nockten (2004), Doug (1994) and Brenda (1985) in sequence, and the joint return periods were 18 years, 16 years and 12 years respectively. At the same time, the storm surge of the three estuaries under the fixed return period is obtained, and the storm surge of the three estuaries has certain differences. By establishing a joint probability model of storm surge flooding in multiple estuaries in Taiwan, it can be seen that the risk of typhoons causing disasters on the west, north, and east sides of northern Taiwan is not high at the same time, that is, the model can jointly cause disasters in multiple estuaries Risk analysis. At the same time, the storm water increase in different estuaries during the typhoon process in the joint return period was obtained, see Table 14. Strengthening protection in estuary areas with higher water increase provides a scientific basis for the allocation of disaster prevention and mitigation materials in different estuary areas in disaster-stricken areas.
应当理解的是,对本领域普通技术人员来说,可以根据上述说明加以改进或变换,而所有这些改进和变换都应属于本发明所附权利要求的保护范围。It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should belong to the protection scope of the appended claims of the present invention.
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CN117634325A (en) * | 2024-01-26 | 2024-03-01 | 水利部交通运输部国家能源局南京水利科学研究院 | Method and system for identifying extremum event of data-limited estuary area and researching composite flood disasters |
CN117634325B (en) * | 2024-01-26 | 2024-04-02 | 水利部交通运输部国家能源局南京水利科学研究院 | Methods and systems for identification of extreme events and analysis of composite flood disasters in data-limited estuary areas |
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