CN115330152A - Waterlogging risk calculation method under combined action of storm surge and rainstorm - Google Patents
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Abstract
The invention discloses a waterlogging risk calculation method under the combined action of storm surge and rainstorm, which comprises the following steps: collecting the maximum daily rainfall data before and after the occurrence of historical storm surge and storm surge; step two, performing rank correlation analysis on a combined sequence consisting of storm surge water and maximum daily rainfall to judge whether the storm surge water and the maximum daily rainfall are obviously correlated; step three, if the correlation is not obvious, the calculation is finished; if the correlation is obvious, respectively substituting the storm surge water increasing sequence and the maximum daily rainfall sequence into generalized extreme value distribution to respectively obtain corresponding distribution functions; step four, substituting a combined sequence consisting of the two distribution functions into an Archimedes cluster Copula function, applying AIC value test, and judging an optimal fitting function, namely a joint distribution function; and step five, calculating a joint recurrence period according to a joint distribution function, and determining the joint waterlogging risk according to the ratio of the maximum daily rainfall under the action of storm surge to the maximum daily rainfall during independent rainfall. The method is simple and practical.
Description
Technical Field
The invention relates to the technical field of natural disaster risk assessment, in particular to a waterlogging risk calculation method under the combined action of storm surge and rainstorm.
Background
Coastal delta areas are usually low in land and developed in industry, are influenced by various factors such as storm surge, rainfall, waves, runoff, tides and the like, and are one of areas with frequent flood disasters. However, the existing standard for flood control (SL 723-2016) often only focuses on the effects of rainstorms, and in fact, in estuary delta regions, flood disasters are often combined by storm surge and rainstorms. On one hand, storm surge can hinder flood peak from discharging through the effect of water damming, so that the water level is lifted, and the waterlogging degree is increased; on the other hand, the typhoon process causing storm surge is often accompanied with strong rainfall, and urban waterlogging is easily formed. In recent years, a large number of scholars combine two or more disaster-causing factors by using basin mathematical models or observation data, but research on flood risks in delta areas under the combined action of storm surge and rainstorm is still less. In addition, the construction of the mathematical model consumes a lot of time and is inefficient. Therefore, the method for conveniently and rapidly calculating the waterlogging risk under the combined action of storm surge and rainstorm is designed, and has important significance for flood control and waterlogging drainage in the estuary delta region.
Disclosure of Invention
It is an object of the present invention to address at least the above problems and to provide at least the advantages described hereinafter.
The invention provides a waterlogging risk calculation method under the combined action of storm surge and rainstorm, which is used for estimating the composite waterlogging occurrence probability of a estuary area, improving the calculation efficiency and providing reference for flood control and waterlogging drainage management and design of the estuary area.
The invention provides a waterlogging risk calculation method under the combined action of storm surge and rainstorm, which comprises the following steps:
collecting historical storm surge data of a waterlogging risk prediction area and maximum daily rainfall data before and after occurrence of the storm surge;
step two, performing rank correlation analysis on a combined sequence consisting of storm surge water and maximum daily rainfall, and judging whether the storm surge water and the maximum daily rainfall are obviously correlated;
step three, if the correlation is not obvious, the calculation is finished; if the correlation is obvious, respectively substituting the storm surge water increasing sequence and the maximum daily rainfall sequence which are obviously correlated into generalized extreme value distribution for frequency analysis to respectively obtain corresponding distribution functions U and V;
substituting a combined sequence consisting of the two distribution functions into an Archimedes cluster Copula function, applying AIC value test, and judging an optimal fitting function, namely a joint distribution function;
step five, calculating a joint recurrence period according to a joint distribution function, and calculating a maximum daily rainfall P under the action of storm surge T ' associated with the maximum daily rainfall P during rainfall alone T The combined waterlogging risk is determined.
Preferably, in the method for calculating the waterlogging risk under the combined action of the storm surge and the rainstorm, in the second step, rank correlation analysis is carried out on a combined sequence consisting of the storm surge water and the maximum rainfall based on a Spearman correlation coefficient r;
wherein,
n is the sample length; r i And K i The rank of the storm surge water increasing sequence and the rank of the maximum daily rainfall sequence are respectively.
Preferably, in the method for calculating the waterlogging risk under the combined action of storm surge and rainstorm, in step three, the distribution function U corresponding to the storm surge water-increasing sequence is
The distribution function V corresponding to the maximum daily rainfall sequence is
Wherein, mu, sigma and zeta are position parameter, shape parameter and scale parameter respectively, S is storm surge water-increasing variable, and P is maximum rainfall variable.
Preferably, in the method for calculating the water logging risk under the combined action of storm surge and rainstorm, the values of μ, σ and ζ are determined by a maximum likelihood estimation method, that is:
respectively substituting the storm surge water-increasing sequence and the maximum daily rainfall sequence into the density functions u (S, mu, sigma, zeta) and v (P, mu, sigma, zeta) of the generalized extremum distribution to obtain corresponding likelihood functions L and K,
and then calculating partial derivatives of the mu, the sigma and the zeta in the likelihood functions L and K, and when the derivative is 0, solving the mu, the sigma and the zeta.
Preferably, in the method for calculating the waterlogging risk under the joint action of storm surge and rainstorm, in step four, the function Copula of the archimedes cluster is as follows: gumbel-Houggaard function, clayton function and Frank function, and the analytical formula corresponding to each function is as follows:
Gumbel-Houggaard：C(u,v)＝exp{-[(-lnu) θ +(-lnv) θ ] 1/θ }θ∈[1,∞)
Clayton:C(u,v)＝(u -θ +v -θ -1) -1/θ θ∈(0,∞)
preferably, in the method for calculating the waterlogging risk under the combined action of storm surge and rainstorm, the value of θ is determined by a maximum likelihood estimation method.
Preferably, in the method for calculating the waterlogging risk under the combined action of storm surge and rainstorm, in step four, AIC =2b-2ln (M);
wherein, b is the number of model parameters, M is a maximum likelihood function value, and the smaller the AIC value is, the better the model fitting degree is.
Preferably, in the method for calculating the waterlogging risk under the combined action of storm surge and rainstorm, in step five, according to the occurrence characteristics of waterlogging, when one variable exceeds a preset value or two variables exceed the preset value simultaneously, that is, when an "or" event occurs, the waterlogging event is defined as a waterlogging event, and the joint recurrence period T is as follows:
then, under the condition that the storm surge S = S' occurs once at T x years, the joint recurrence period T when the waterlogging event occurs is as follows:
wherein P' is a preset rainfall value when storm surge and rainfall occur together; s' is a storm surge preset value when storm surge and rainfall occur together,
preferably, in the method for calculating the waterlogging risk under the combined action of storm surge and rainstorm, the waterlogging risk ratio is combined
The greater the HR, the greater the combined risk of waterlogging.
Preferably, in the method for calculating the waterlogging risk under the combined action of the storm surge and the rainstorm, in the step one, the time range of the historical storm surge data and the daily rainfall data before and after the storm surge is not less than 30 years.
The invention at least comprises the following beneficial effects:
1. the calculation method is simple and easy to realize. After actual measurement data are preprocessed, a Copula function formula is adopted to solve a joint recurrence period, and flood risks are estimated. The method is simple and easy to implement, and overcomes the complex calculation steps of constructing grids by a mathematical model, calibrating parameters, verifying results and the like.
2. And a reference is provided for flood control and drainage management work. According to the method, the contour map of the joint recurrence period (as shown in figure 6) is drawn according to historical storm surge and rainfall data, and when a secondary storm surge occurs in a certain place and is accompanied by strong rainfall, the size of the joint recurrence period can be directly inquired according to the figure 6, so that the waterlogging level can be rapidly judged.
3. Providing basis for the design of the coastal buildings. The method solves the joint waterlogging risk ratio and provides a reference coefficient for waterlogging design of the coastal buildings such as seawalls and wharfs under the combined action of storm surge and rainfall.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
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FIG. 1 is a flow chart of a method for calculating the risk of waterlogging under the combined action of storm surge and rainstorm according to the present invention;
FIG. 2 is a scatter diagram of the storm surge water increase S and the corresponding maximum daily rainfall P in the present invention;
FIG. 3 is a diagram of the frequency analysis of storm surge water increase sequence in the present invention;
FIG. 4 is a frequency analysis chart of a maximum daily rainfall sequence in the present invention;
FIG. 5 is a combined probability distribution of storm surge and rainfall in the present invention;
FIG. 6 is a contour map of the joint recurrence period under the combined action of storm surge and rainfall;
wherein, the cumulative probability of the cumulative distribution of the S data of the water increase of the storm surge, the cumulative distribution of the Pdata of the maximum daily rainfall and the CDF cumulative distribution function are shown as the joint recurrence period of 5 years, 10 years, 20 years, 50 years and 100 years in the mark 5, 10, 20, 50 and 100 in the figure 6.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
It will be understood that terms such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.
It is to be noted that the experimental methods described in the following embodiments are all conventional methods unless otherwise specified, and the reagents and materials, if not otherwise specified, are commercially available; in the description of the present invention, it should be noted that unless otherwise explicitly stated or limited, the terms "mounted," "connected" and "disposed" are to be construed broadly and can be, for example, fixedly connected, disposed, detachably connected, disposed or integrally connected and disposed. The specific meanings of the above terms in the present invention can be understood in a specific case to those of ordinary skill in the art. The terms "transverse," "longitudinal," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in an orientation or positional relationship indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the device or element so referred to must have a particular orientation, be constructed in a particular orientation, and be constructed in operation, and are not to be construed as limiting the invention.
As shown in fig. 1, the present application provides a method for calculating the waterlogging risk under the combined action of storm surge and rainstorm, which comprises the following steps:
step one, collecting historical storm surge data with the time span of the waterlogging risk prediction area not less than 30 years and maximum daily rainfall data within delta days before and after the storm surge occurs to obtain a storm surge water-increasing sequence (S) i ) And maximum daily rainfall sequence (P) i ) I is an integer greater than 0;
step two, pair combination sequence (S) i ，P i ) Performing rank correlation analysis to determine whether the two are significantMaking a correlation;
specifically, the pair of combined sequences (S) is based on the Spearman correlation coefficient r i ，P i ) Performing rank correlation analysis;
wherein,
n is the sample length, i.e. storm surge water sequence (S) i ) Or maximum daily rainfall sequence (P) i ) Length of (d);
R i and K i Respectively a storm surge water-increasing sequence (S) i ) And maximum daily rainfall sequence (P) i ) The order of (1) is that after the collected historical storm surge data and the maximum day rainfall data in delta days before and after the storm surge are arranged from big to small, S i And P i The number of ranks in the corresponding sorted data;
when the significance judges the parameter
(the lower critical value of 95% significance is 1.97 by table lookup), the sequences are combined (S) i ，P i ) Significant correlation, otherwise insignificant correlation;
step three, if the correlation is not obvious, the calculation is finished;
if significant correlation is found, for hydrologic annual extreme elements, generalized extreme distribution (GEV) can satisfy the fitting of most sequences, and the significant correlated storm surge water-increasing sequences (S) i ) And maximum daily rainfall sequence (P) i ) Respectively substituting the generalized extreme value distribution functions into the generalized extreme value distribution functions to carry out frequency analysis, and respectively obtaining corresponding distribution functions U and V;
wherein,
u is
V is
Mu, sigma and zeta are position, shape and size parameters, respectively, S is storm surge water-increasing variable, P is maximum rainfall variable, S is maximum rainfall i Is the specific value of the variable S;
moreover, the values of μ, σ, and ζ can be determined by a maximum likelihood estimation method, specifically:
adding water sequence to storm surge respectively (S) i ) And maximum daily rainfall sequence (P) i ) Substituting into the density functions u (S, mu, sigma, zeta) and v (P, mu, sigma, zeta) of the generalized extremum distribution to obtain corresponding likelihood functions L and K,
the derivatives of μ, σ, ζ in the likelihood functions L and K are then evaluated, when the derivative is 0, i.e.
μ, σ, ζ can be solved.
Step four, substituting the combined sequence (U, V) into an Archimedes cluster Copula function, applying AIC value test, and judging an optimal fitting function, namely a joint distribution function C (U, V);
the method specifically comprises the following steps: and (3) respectively substituting the combined sequences (U, V) into analytical formulas of a Gumbel-Houggaard function, a Clayton function and a Frank function to obtain the analytical formulas respectively as follows:
Gumbel-Houggaard：C(u,v)＝exp{-[(-lnu) θ +(-lnv) θ ] 1/θ }θ∈[1,∞) (9)
Clayton:C(u,v)＝(u -θ +v -θ -1) -1/θ θ∈(0,∞) (10)
determining a theta value by a maximum likelihood estimation method (the third step is specifically referred to by the maximum likelihood estimation method);
and then by the formula AIC =2b-2ln (M) (12)
Calculating the corresponding AIC value of each function;
wherein b is the number of model parameters, and b =1 for the Copula function of the Archimedes cluster; m is a maximum likelihood function value corresponding to a Gumbel-Houggaard function or a Clayton function or a Frank function; the smaller the AIC value, the better the model fit.
Step five, calculating a joint reappearance period according to a joint distribution function C (u, v), and calculating the maximum daily rainfall amount P under the combined action of storm surge and rainfall T ' associated with the maximum daily rainfall P during rainfall alone T Determining the combined waterlogging risk;
the method specifically comprises the following steps: according to the occurrence characteristics of waterlogging, when one variable exceeds a preset value or two variables exceed the preset values at the same time, namely the occurrence time of an OR event is defined as a waterlogging event, and the joint reproduction period T is as follows:
then, under the condition that the storm surge S = S' occurs once in T x years, the joint recurrence period T when the waterlogging event occurs is as follows:
wherein T is independent windThe resurgence period of S occurring during the storm,
p' is a preset rainfall value when storm surge and rainfall occur together; s' is a storm surge preset value when storm surge and rainfall occur together; s and P in this step are not limited to only the single storm surge and single rainfall mentioned in this application,
then, the joint waterlogging risk ratio
The greater the HR, the greater the combined risk of waterlogging.
The method for calculating the waterlogging risk under the combined action of storm surge and rainstorm provided by the invention provides the following embodiments:
taking storm surge and rainfall for logging in hong Kong from 1968 to 2018 as an example, the waterlogging risk under the combined distribution of the storm surge and the storm is analyzed.
Step one, acquiring storm surge water increment S and time t from a hong Kong astronomical phenomena website, finding out the maximum daily rainfall P within t-1 day to t +1 day, and correspondingly drawing an S-P scatter diagram (figure 2), wherein part of S and the value of the corresponding P are shown in a table 1;
TABLE 1 data sheet of partial storm surge water increasing S and corresponding maximum daily rainfall P
Step two, combining the sequence (S) i ，P i ) Substituting into Spearman rank correlation formula (1) (2) to obtain correlation coefficient r =0.22, and determining significance parameter
The combined sequence is proved to meet the requirement of significance correlation;
step three, adding water sequence (S) of storm surge which is obviously related i ) And maximum daily rainfall sequence (P) i ) Respectively substituting into the generalized extreme value distribution function to perform frequency analysis, respectively obtaining corresponding distribution functions U and V through the calculation of formulas (3) to (8), drawing a frequency analysis graph as shown in FIG. 3 and FIG. 4,
u is
V is
Step four, substituting the combined sequences (U, V) into Gumbel-Houggaard function, clayton function and Frank function respectively to obtain corresponding analytical expressions (9), (10) and (11), determining a value theta through a maximum likelihood estimation method, and calculating AIC values of the function models through a formula (12) to be-13.7, -4 and-13.5 in sequence, wherein the AIC value of the Gumbel-Houggaard function model is the minimum, namely the analytical expression corresponding to the Gumbel-Houggaard function is an optimal fitting function, the value theta =1.1772 corresponding to the function, and obtaining the function image as shown in FIG. 5;
step five, drawing isolines of the joint recurrence period at 5 years, 10 years, 20 years, 50 years and 100 years according to the formula (14) and the graph 5 to obtain a graph 6, and calculating the joint waterlogging risk ratio HR according to the formulas (14) and (15). For example, under the condition of 50 year storm surge on coast, firstly according to FIG. 3 or formula (3) and formula
The water increase of the storm surge is 1.19m after the corresponding storm surge is obtained in 50 years by reverse deduction, and then the maximum daily rainfall P corresponding to different combined reappearance periods is inquired/calculated according to the figure 6 or the formula (14) when the storm surge increases the water S =1.19m T ', get:
the combined reproduction period is 5 years, the mostThe rainfall in the sun is P' 5 ＝89mm；
When the combined reproduction period is 10 years, the maximum daily rainfall is P' 10 ＝163mm；
When the combined reproduction period is 20 years, the maximum daily rainfall is P' 20 ＝313mm；
Look up figure 4 or formula (4) and formula
Obtaining the maximum daily rainfall P corresponding to different joint reproduction periods T Namely: the maximum daily rainfall P corresponding to the 5-year, 10-year and 20-year recurrence periods 5 ＝84mm,P 10 ＝148mm,P 20 ＝246mm。
Calculating according to the formula (15), when a storm tide occurs in 50 years, combining the waterlogging risk ratios HR in different reproduction periods:
from the above calculation results, when considering the influence of storm surge in 50 years, the rainstorm (maximum daily rainfall) in different reproduction periods is enlarged by about 1.1 to 1.3 times, and thus, the corresponding risk of waterlogging is also increased. The numerical value has important referential significance for flood control and drainage management of coastal cities.
The number of apparatuses and the scale of the process described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the present invention will be apparent to those skilled in the art.
While embodiments of the invention have been described above, it is not intended to be limited to the details shown, described and illustrated herein, but is to be accorded the widest scope consistent with the principles and novel features herein disclosed, and to such extent that such modifications are readily available to those skilled in the art, and it is not intended to be limited to the details shown and described herein without departing from the general concept as defined by the appended claims and their equivalents.
Claims (10)
1. The method for calculating the waterlogging risk under the combined action of storm surge and rainstorm is characterized by comprising the following steps of:
collecting historical storm surge data of a waterlogging risk prediction area and maximum daily rainfall data before and after occurrence of the storm surge;
step two, performing rank correlation analysis on a combined sequence consisting of storm surge water and maximum daily rainfall, and judging whether the storm surge water and the maximum daily rainfall are obviously correlated;
step three, if the correlation is not obvious, the calculation is finished; if the correlation is obvious, respectively substituting the storm surge water increasing sequence and the maximum daily rainfall sequence which are obviously correlated into generalized extreme value distribution for frequency analysis to respectively obtain corresponding distribution functions U and V;
substituting a combined sequence consisting of the two distribution functions into an Archimedes cluster Copula function, and applying AIC value inspection to judge an optimal fitting function, namely a joint distribution function;
step five, calculating a joint recurrence period according to a joint distribution function, and calculating the maximum daily rainfall P under the action of storm surge T ' associated with the maximum daily rainfall P during rainfall alone T Determining the combined waterlogging risk.
2. The method for calculating the risk of waterlogging under the combined action of storm surge and rainstorm according to claim 1, wherein in step two, rank correlation analysis is performed on a combined sequence consisting of storm surge and maximum daily rainfall based on Spearman correlation coefficient r;
wherein,
n is the sample length; r i And K i The rank of the storm surge water increasing sequence and the rank of the maximum daily rainfall sequence are respectively.
3. The method for calculating the risk of waterlogging caused by combination of storm surge and rainstorm according to claim 1, wherein in step three, the distribution function U corresponding to the storm surge water increase sequence is
The distribution function V corresponding to the maximum daily rainfall sequence is
Wherein, mu, sigma and zeta are position parameter, shape parameter and scale parameter respectively, S is storm surge and water increase variable, and P is maximum daily rainfall variable.
4. The method for calculating the risk of waterlogging under combined storm surge and rainstorm conditions according to claim 3, wherein the values of μ, σ, ζ are determined by maximum likelihood estimation, i.e.:
respectively substituting the storm surge water adding sequence and the maximum daily rainfall sequence into the density functions u (S, mu, sigma, zeta) and v (P, mu, sigma, zeta) of the generalized extremum distribution to obtain corresponding likelihood functions L and K,
and then, calculating the derivatives of mu, sigma and zeta in the likelihood functions L and K, and when the derivative is 0, calculating the derivatives of mu, sigma and zeta.
5. The method for calculating the risk of waterlogging under the combined action of storm surge and rainstorm according to claim 1, wherein in step four, the function Copula of the archimedes cluster is: gumbel-Houggaard function, clayton function and Frank function, and the analytical formula corresponding to each function is as follows:
Gumbel-Houggaard：C(u,v)＝exp{-[(-lnu) θ +(-lnv) θ ] 1/θ }θ∈[1,∞)
Clayton:C(u,v)＝(u -θ +v -θ -1) -1/θ θ∈(0,∞)
Frank:
6. the method of calculating the risk of waterlogging under the combined effect of a storm surge and a storm according to claim 5, wherein the value of θ is determined by maximum likelihood estimation.
7. The method for calculating the risk of waterlogging under combined action of storm surge and rainstorm according to claim 6, wherein in step four, AIC =2b-2ln (M);
wherein, b is the number of model parameters, M is a maximum likelihood function value, and the smaller the AIC value is, the better the fitting degree of the model is.
8. The method for calculating the risk of waterlogging under combined action of storm surge and rainstorm according to claim 1, wherein in step five, when one variable or both variables exceed a predetermined value according to the occurrence characteristics of waterlogging, that is, when an "or" event occurs, a waterlogging event is defined, and the joint recurrence period T thereof is:
then, under the condition that the storm surge S = S' occurs once in T x years, the joint recurrence period T when the waterlogging event occurs is as follows:
wherein P' is a preset rainfall value when storm surge and rainfall occur together; s' is a storm surge preset value when storm surge and rainfall occur together,
9. the method of claim 8, wherein the waterlogging risk is calculated by combining storm surge and rainstorm, wherein the waterlogging risk ratio is combined
The greater the HR, the greater the combined risk of waterlogging.
10. The method for calculating the waterlogging risk under the combined action of a storm surge and a storm according to claim 1, wherein in the first step, the time range of the historical storm surge data and the daily rainfall data before and after the storm surge is not less than 30 years.
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| CN112163349A (en) * | 2020-10-29 | 2021-01-01 | 武汉大学 | Method for determining drainage planning standard of drainage area and application thereof |
| CN114722744A (en) * | 2022-06-08 | 2022-07-08 | 水利部交通运输部国家能源局南京水利科学研究院 | Evaluation method and system for rainstorm and tide level coordination of plain basin design |
| CN114756817A (en) * | 2022-02-22 | 2022-07-15 | 南方科技大学 | Copula function-based combined probability analysis method for composite flood disasters |
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| CN112163349A (en) * | 2020-10-29 | 2021-01-01 | 武汉大学 | Method for determining drainage planning standard of drainage area and application thereof |
| CN114756817A (en) * | 2022-02-22 | 2022-07-15 | 南方科技大学 | Copula function-based combined probability analysis method for composite flood disasters |
| CN114722744A (en) * | 2022-06-08 | 2022-07-08 | 水利部交通运输部国家能源局南京水利科学研究院 | Evaluation method and system for rainstorm and tide level coordination of plain basin design |
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| CN117408511A (en) * | 2023-10-16 | 2024-01-16 | 中国地质大学（武汉） | Attribution method, medium and equipment for typhoon-induced extremely-heavy storm event occurrence probability |
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