CN113806959B - Quantitative research method for estuary design high tide level in future situation - Google Patents
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Abstract
The invention discloses a quantitative research method for designing a estuary in future, which comprises the following steps: step S10, processing the modified long-series observation data of the estuary tide level by using a Mann-Kendall method to judge the trend of the estuary tide level; s20, adopting a Markov Chain Monte Carlo algorithm and combining Metropolis-Hastings sampling to construct a random model, and simulating a tide level sequence through the random model; step S30, combining the historical tide level sequence and the simulated tide level sequence to obtain a new tide level sequence, and checking the new tide level sequence; and S40, calculating an initial value according to the new tide level sequence, and performing visual estimation on the adaptive line by using a P-III type curve to finally obtain the designed high tide level. The invention provides a quantitative solution for designing the short plates for the prediction research of the high tide level in the estuary area, has reasonable and reliable calculation result, and has stronger practical value in the aspects of flood prevention and damp prevention work correlation and corresponding engineering design.
Description
Technical Field
The invention relates to the technical field of hydraulic engineering, in particular to a quantitative research method for designing high tide level of estuary in future situations.
Background
The design tide level is important hydrologic data in coast disaster prevention engineering design, and not only directly influences the determination of the elevation of the embankment engineering, but also influences the selection of building types, structural calculation and the like. The coast disaster prevention engineering has different scale, grade and use condition, and the selected design tide level is different. In the past, in the design of some units in China, the highest water level of the embankment engineering is the highest tide level in the past year, and under the condition that the actual measurement data is short in the years, the highest tide level in the past year is determined according to investigation and demonstration. After analysis and comparison of a large number of tide level data, the relevant units in China recommend a method of annual frequency statistics such as P-III to determine the designed tide level.
Extreme high tide levels are key factors affecting the design of high tide levels. The current design of high tide level is very likely to not meet future flood control requirements and can bring great threat to the embankment and the life and property safety of people due to the influence of a plurality of factors such as sea level rising and ground subsidence. The design of estuary high tide level in future situations is focused by researchers, various research results are obtained, and modes such as regression relation between sea level rising and tide level change are proposed. However, most researches only consider the influence caused by factors such as sea level rising, but quantitative analysis is not performed, and particularly quantitative analysis is not performed on the influence of the designed high tide level aiming at the occurrence frequency of the extremely high tide level, so that a plurality of inconveniences are brought to practical application.
For this purpose, the applicant has found, through a beneficial search and study, a solution to the above-mentioned problems, against which the technical solutions to be described below are developed.
Disclosure of Invention
The invention aims at: the quantitative research method for designing the estuary high tide level in the future situation is convenient for practical application.
In order to achieve the above purpose, the present invention may adopt the following technical scheme:
a quantitative research method for designing high tide level of estuary in future situations comprises the following steps:
step S10, processing the modified long-series observation data of the estuary tide level by using a Mann-Kendall method to judge the trend of the estuary tide level;
s20, adopting a Markov Chain Monte Carlo algorithm and combining Metropolis-Hastings sampling to construct a random model, and simulating a tide level sequence through the random model;
step S30, combining the historical tide level sequence and the simulated tide level sequence to obtain a new tide level sequence, and checking the new tide level sequence;
and S40, calculating an initial value according to the new tide level sequence, and performing visual estimation on the adaptive line by using a P-III type curve to finally obtain the designed high tide level.
In a preferred embodiment of the present invention, in step S10, the process of processing the modified long-series of observations of estuary tide level using the Mann-Kendall method includes the steps of:
step S11, defining Mann-Kendall test statistic S:
where sign0 is a sign function. When X is i -X j Less than, equal to, or greater than zero, sign (X i -X j ) Respectively-1, 0 or 1;
in step S12, the statistic formula S is greater than, equal to, and less than zero, where:
z is positive and shows increasing trend, and negative value shows decreasing trend, and when the absolute value of Z is more than or equal to 1.28, 1.64 and 2.32, the confidence degree of 90%, 95% and 99% is respectively passed through the significance test.
In a preferred embodiment of the present invention, in step S20, the random model is constructed by using Markov Chain Monte Carlo algorithm in combination with the Metropolis-Hastings sampling, and the tide level sequence is simulated by the random model, comprising the steps of:
step S21, according to sequence Y i The mean value EX and the mean square error σ of (a) are divided into five states, as shown in the following table:
in step S22, the probability of state transition of the markov chain depends only on the previous state, which is expressed mathematically as:
P(X t+1 ＝x|X t ，X t-1 ，…)＝P(X t+1 ＝x|X t ) (3)
step S23, due to the converging behavior and of the Markov chainThe initial probability distribution is independent and is determined only by the probability transition matrix P. When n is sufficiently large, matrix P n Is an equal vector pi (plateau):
p in general i P ij ≠P j P ji Defining an acceptance rate alpha ij Such that: p (P) i P ij α ij ＝P j P ji α ji
Record Q ij ＝P ij α ij ，Q ji ＝P ji α ji Constructing a new transfer matrix Q which is smoothly distributed as P (x) and obtaining a transfer sequence x 0 ，x 1 ，…x n ，x n+1 … to obtain a sample x of pi (x) n ，x n+1 …。
Step S24, in order to avoid the rejection skip of the MCMC caused by the small acceptance rate, reduce the time spent by the Markov chain traversing all state spaces and speed up the convergence, the invention bases the acceptance rate alpha on the MCMC ij And alpha ji Scaling up to 1 for the larger (Metropolis-Hastings sampling);
taking a new acceptance rate:
in a preferred embodiment of the present invention, in step S30, the combination of the historical tide level sequence and the simulated tide level sequence to obtain a new tide level sequence, and the verification of the new tide level sequence, comprises the steps of:
step S31, accumulated deviation calculation method
Step S32, calculating the adjustment part:
wherein D is Y Is the variance. Accumulating deviation statistical parameters:
the critical values of (2) are shown in the following table if +.>A value greater than a certain threshold level, the sequence does not have consistency at that level.
In a preferred embodiment of the present invention, in step S40, an initial value is calculated according to the new tide level sequence, and a P-III type curve is used to make an eye estimate for the line, and finally a designed high tide level is obtained, which includes the following steps:
step S41, calculating a sample mean value, a variation coefficient and a bias coefficient by using the unbiased estimation according to the new trend sequence as an initial value of an eye estimation adaptive line;
step S42, the parameters are continuously adjusted by using the P-III type curve so that the curve fitting is better:
the P-III curve is a gamma distribution, which is mathematically expressed as:
wherein Γ (α) is a gamma function of α, β, α 0 The parameters are respectively:
in the method, in the process of the invention,C v 、C s for statistical parameters, respectively representing a sample mean value, a variation coefficient and a bias coefficient, adopting unbiased estimation calculation:
step S43, corresponding design high tide level and reproduction period are obtained according to the designated design assurance rate.
Due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. the invention provides a random model based on MCMC and Metropolis-Hastings sampling, which generates a theoretical highest tide level sequence in the future, is convenient for analyzing the sequence and calculates and designs the tide level according to engineering specification requirements.
2. The method carries out consistency, trend and other tests on the randomly generated tide level, screens out sequences which do not accord with hydrologic rules, and retains the results with the same trend and consistency as the original actually measured sequences.
3. The design tide level obtained by the method can be calculated in batches for a plurality of times, the trend of the design tide level can be seen under a large amount of calculation, the artificial interference factors simulated by the future tide level are reduced, and corresponding simulation prediction can be carried out aiming at some safety conditions such as extremely high tide level.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a quantitative research method for estuary design high tide level in future situations of the invention.
FIG. 2 is a diagram of the Wu Song open area of Shanghai city.
Fig. 3 is a revised long series of observations at station Wu Song in Shanghai city.
FIG. 4 is a graph of a P-III curve eye-estimated fit line prior to 1997 at Wu Song station in Shanghai city.
Fig. 5 is a P-III curve eye fit for 2018 at Wu Song station in Shanghai city. .
FIG. 6 is a plot of diffusion coefficient versus mass envelope range for 0.5mg/L for the conserved mass single-direction pure diffusion problem.
Detailed Description
The invention is further described with reference to the following detailed drawings in order to make the technical means, the creation characteristics, the achievement of the purpose and the effect of the implementation of the invention easy to understand.
Referring to fig. 1, a quantitative research method for designing a estuary with a high tide level in future situations is provided, which comprises the following steps:
and S10, processing the modified long-series observation data of the estuary tide level by using a Mann-Kendall method to judge the trend of the estuary tide level.
The Mann-Kendall test is a non-parametric test method recommended by the world meteorological organization and has been widely used, and was originally proposed by Mann and Kendall to analyze trend changes in tidal level time series.
In step S10, the modified long-series observation data of estuary tide level is processed by the Mann-Kendall method, including the steps of:
step S11, defining Mann-Kendall test statistic S:
in the formula, sign () is a sign function. When X is i -X j Less than, equal to, or greater than zero, sign (X i -X j ) Respectively-1, 0 or 1;
in step S12, the statistic formula S is greater than, equal to, and less than zero, where:
z is positive and shows increasing trend, and negative value shows decreasing trend, and when the absolute value of Z is more than or equal to 1.28, 1.64 and 2.32, the confidence degree of 90%, 95% and 99% is respectively passed through the significance test.
And S20, constructing a random model by adopting a Markov Chain Monte Carlo algorithm and combining Metropolis-Hastings sampling, and simulating a tide level sequence through the random model.
The Markov chain Monte Carlo method (Markov Chain Monte Carlo), referred to as MCMC, introduces a Markov (Markov) process into the Monte Carlo simulation to implement a dynamic simulation of the sampling distribution as the simulation progresses.
In step S20, a random model is constructed by adopting Markov Chain Monte Carlo algorithm and combining with Metropolis-Hastings sampling, and the tide level sequence is simulated by the random model, which comprises the following steps:
step S21, according to sequence Y i The mean value EX and the mean square error σ of (a) are divided into five states, as shown in the following table:
in step S22, the probability of state transition of the markov chain depends only on the previous state, which is expressed mathematically as:
P(X t+1 ＝x|X t ，X t-1 ，…)＝P(X t+1 ＝x|X t ) (3)
in step S23, since the behavior of the convergence of the mahalanobis chain is independent of the initial probability distribution, it is determined only by the probability transition matrix P. When n is sufficiently large, matrix P n Is an equal vector pi (plateau):
p in general i P ij ≠P j P ji Defining an acceptance rate alpha ij Such that: p (P) i P ij α ij ＝P j P ji α ji
Record Q ij ＝P ij α ij ，Q ji ＝P ji α ji Constructing a new transfer matrix Q which is smoothly distributed as P (x) and obtaining a transfer sequence x 0 ，x 1 ，…x n ，x n+1 … to obtain a sample x of pi (x) n ，x n+1 …；
Step S24, in order to avoid the rejection skip of the MCMC caused by the small acceptance rate, reduce the time spent by the Markov chain traversing all state spaces and speed up the convergence, the invention bases the acceptance rate alpha on the MCMC ij And alpha ji The scale-up was made to be 1 for the larger (Metropolis-Hastings sampling).
Taking a new acceptance rate:
step S30, combining the historical tide level sequence and the simulated tide level sequence to obtain a new tide level sequence, and checking the new tide level sequence, wherein the checking comprises consistency checking, trend checking and the like.
The sequence generated by the random model does not necessarily have a consistent trend with the original sequence, nor does it necessarily have direct continuity with the original sequence. For this purpose, the new combined sequences need to be analyzed, and sequences that do not correspond to the identity and the same trend are truncated. Trend was still examined by Mann-Kendall test, and consistency was analyzed by cumulative bias.
In step S30, the historical tide level sequence and the simulated tide level sequence are combined to obtain a new tide level sequence, and the new tide level sequence is checked for consistency, trend and the like, including the following steps:
step S31, accumulated deviation calculation method
Step S32, calculating the adjustment part:
wherein D is Y Is the variance. Accumulating deviation statistical parameters:
the critical values of (2) are shown in the following table. If->A value greater than a certain threshold level, the sequence does not have consistency at that level.
And S40, calculating an initial value according to the new tide level sequence, and performing visual estimation on the adaptive line by using a P-III type curve to finally obtain the designed high tide level.
In step S40, an initial value is calculated according to the new tide level sequence, and a P-III type curve is utilized to perform eye estimation to adapt the line, and finally, a designed high tide level is obtained, which comprises the following steps:
step S41, calculating a sample mean value, a variation coefficient and a bias coefficient by using the unbiased estimation according to the new sequence of the new tide level as an initial value of an eye estimation adaptive line;
step S42, the parameters are continuously adjusted by using the P-III type curve so that the curve fitting is better:
the P-III curve is a gamma distribution, which is mathematically expressed as:
wherein Γ (α) is a gamma function of α, β, α 0 The parameters are respectively:
in the method, in the process of the invention,C v 、C s for statistical parameters, respectively representing a sample mean value, a variation coefficient and a bias coefficient, adopting unbiased estimation calculation:
step S43, corresponding design high tide level and reproduction period are obtained according to the designated design assurance rate.
In order to better illustrate the steps of the invention, the invention analyzes and illustrates the research of the influence of the design of the upper sea Wu Song port aiming at the extremely high tide level, and the method specifically comprises the following steps:
given that Wu Song port historically had a maximum tide level of 5.99m during 9711 typhoons, the effect of 5.99m extreme high tide level scenarios at 3 future scales on Wu Song port design high tide levels (thousand years met) was analyzed based on design scenarios where the future 30 year wu port may again occur at extreme high tide level frequencies (0-2 times).
Referring to fig. 1, the quantitative research method for estuary design high tide level in future situations of the invention comprises the following steps:
1. and processing the modified long-series observation data of the estuary tide level by using a Mann-Kendall method to judge the trend of the estuary tide level.
Wu Song stations are shown in FIG. 2 and their modified observed tidal level sequence S1 for years is shown in FIG. 3. The M-K test statistic was-1.997, and the sequence had a decreasing trend through the 95% confidence significance test.
2. A Markov Chain Monte Carlo algorithm is adopted and combined with Metropolis-Hastings sampling to construct a random model, and the tide level sequence is simulated through the random model.
Wu Song has historically occurred at extremely high tide levels of 5.80m or more 3 times during typhoons 8114, 9711 and 0012, respectively. The extremely high tide level occurs once in 40 years on average and does not occur in the last 20 years, and the possibility that the extremely high tide level occurs 0 to 2 times more in the next 30 years exists. The highest tide level historically found at port Wu Song was 5.99m. Accordingly, the design of the future 30 years of Wu-frame can generate 5.99m extremely high tide level frequency (0-2 times) which corresponds to the extremely high tide level situations under 3 future scales respectively, and the extremely high tide level situations are shown in the table 1.
TABLE 1 extremely high tide level design scenario
For the historical scene, testing the trend by using a Mann-Kendall method at a 95% confidence level, wherein the results are respectively-2.203; for the history and current situations, the initial value is calculated by adopting a formula (12), the P-III fitting curve and parameters after visual estimation are shown in fig. 4 and 5, and the high tide level is 6.389m and 6.582m in the thousand years.
According to the sequence S1, calculating a Markov Chain single-step transfer matrix as follows:
single step transfer frequency matrix
From this iteration, a stationary distribution can be calculated, and then a random model can be constructed, and a simulation sequence S2 can be obtained.
3. And combining the historical tide level sequence and the simulated tide level sequence to obtain a new tide level sequence, and checking the new tide level sequence.
The 3 future scenarios listed in table 1 were each examined for s1+s2 sequences, the results of which are shown in table 2.
TABLE 2 results of inspection of each scenario and tidal level design
4. And calculating an initial value according to the new tide level sequence, and performing visual estimation on the line by utilizing a P-III type curve to finally obtain the designed high tide level.
The initial value calculation is shown in table 2, and the last column of table 2 shows that the designed high tide level is calculated in thousands of years by adopting the mode of fixed Cs and Cv ratio (25.0), unbiased estimation, mean value calculation and equal-multiple ratio amplification of variation coefficient.
In order to eliminate errors caused by random simulation and ensure the representativeness of quantitative research, for three future situations, the same method is adopted respectively, 1000 groups of random sequences meeting the consistency, the trend and the Markov under the same confidence level are randomly generated, and the generated design high tide level situation is calculated as shown in figure 6. The average value of the three scene sequences is 6.605m, 6.717m and 6.823m respectively; standard deviations are 0.034m, 0.033m and 0.031m respectively, and can basically be considered that Wu Song extremely high tide level situations of 0 times, 1 time and 2 times occur in the future 30 years, and the Wu Song port 2050 is designed to have high tide levels of about 6.60m, 6.72m and 6.82m in thousands of years. 1000 calculation results of the three scenes are respectively concentrated in a range with smaller error, and therefore, the problem of predicting the design tide level in the Wu Song future scene mode is well solved by adopting the method and the device.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (1)
1. The quantitative research method for designing the estuary with high tide level in future situations is characterized by comprising the following steps of:
step S10, processing the modified long-series observation data of the estuary tide level by using a Mann-Kendall method to judge the trend of the estuary tide level;
s20, adopting a Markov Chain Monte Carlo algorithm and combining Metropolis-Hastings sampling to construct a random model, and simulating a tide level sequence through the random model;
step S30, combining the historical tide level sequence and the simulated tide level sequence to obtain a new tide level sequence, and checking the new tide level sequence;
step S40, calculating an initial value according to the new tide level sequence, and performing visual estimation on the adaptive line by utilizing a P-III type curve to finally obtain a designed high tide level;
in step S10, the method of Mann-Kendall is used to process the modified long-series observation data of estuary tide level, and includes the following steps:
step S11, defining Mann-Kendall test statistic S:
in the formula, sign () is a sign function, when X i -X j Less than, equal to, or greater than zero, sign (X i -X j ) Respectively-1, 0 or 1;
in step S12, the statistic formula S is greater than, equal to, and less than zero, where:
z is positive value to show increasing trend, and negative value to show decreasing trend, and the absolute value of Z is 90%, 95% and 99% of confidence level test is passed when the absolute value of Z is more than or equal to 1.28, 1.64 and 2.32;
in step S20, a random model is constructed by adopting Markov Chain Monte Carlo algorithm and combining with Metropolis-Hastings sampling, and the tide level sequence is simulated by the random model, which comprises the following steps:
step S21, according to sequence Y i The mean value EX and the mean square error σ of (a) are divided into five states, as shown in the following table:
in step S22, the probability of state transition of the markov chain depends only on the previous state, which is expressed mathematically as:
P(X t+1 ＝x|X t ,X t-1 ,···)＝P(X t+1 ＝x|X t ) (3)
step S23, behavior and initial probability distribution due to the convergence of the Markov chainIndependently, determined only by the probability transition matrix P, when n is sufficiently large n Is an equal vector pi (plateau):
p in general i P ij ≠P j P ji Defining an acceptance rate alpha ij Such that: p (P) i P ij α ij ＝P j P ji α ji
Record Q ij ＝P ij α ij ，Q ji ＝P ji α ji Constructing a new transfer matrix Q which is smoothly distributed as P (x) and obtaining a transfer sequence x 0 ，x 1 ，…x n ，x n+1 … to obtain a sample x of pi (x) n ，x n+1 …；
Step S24, in order to avoid the rejection skip of the MCMC caused by the small acceptance rate, reduce the time spent by the Markov chain traversing all state spaces and speed up the convergence, the invention bases the acceptance rate alpha on the MCMC ij And alpha ji Scaling up to 1 for the larger (Metropolis-Hastings sampling);
taking a new acceptance rate:
in step S30, the combination of the historical tide level sequence and the simulated tide level sequence to obtain a new tide level sequence, and the verification of the new tide level sequence includes the following steps:
step S31, accumulated deviation calculation method
Step S32, calculating the adjustment part:
wherein D is Y For variance, accumulating the deviation statistical parameters:
the critical values of (2) are shown in the following table if +.>If the value is greater than a certain critical value level, the sequence does not have consistency at the level;
in step S40, an initial value is calculated according to the new tide level sequence, and a P-III type curve is utilized to perform eye estimation to adapt the line, and finally, a designed high tide level is obtained, which comprises the following steps:
step S41, calculating a sample mean value, a variation coefficient and a bias coefficient by using the unbiased estimation according to the new trend sequence as an initial value of an eye estimation adaptive line;
step S42, the parameters are continuously adjusted by using the P-III type curve so that the curve fitting is better:
the P-III curve is a gamma distribution, which is expressed mathematically as:
wherein Γ (α) is a gamma function of α, β, α 0 The parameters are respectively:
in the method, in the process of the invention,C v 、C s for statistical parameters, respectively representing a sample mean value, a variation coefficient and a bias coefficient, adopting unbiased estimation calculation:
step S43, corresponding design high tide level and reproduction period are obtained according to the designated design assurance rate.
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