CN106202788A - A kind of tide flood combined probability analysis method based on Copula function and application thereof - Google Patents

Abstract

The invention relates to a tidal flood joint probability analysis method based on Copula function and its application. The purpose of the tidal flood analysis method is to provide the basis for flood control construction of tidal river sections. The joint probability distribution function of "rainfall" can reflect the function of the characteristic quantities that affect the flow and regulation and storage capacity of flood facilities, and provide a reliable basis for flood control construction.

Description

A Copula Function Based Tidal and Flood Joint Probability Analysis Method and Its Application

technical field

The invention relates to the field of joint probability analysis, in particular to a tidal flood joint probability analysis method based on Copula function and its application.

Background technique

The section at the estuary of the river channel is called the tidal section, and the so-called tidal section refers to the section where the downstream outlet of the section is supported by the tide, and the flow and water level are affected by the tide. The upper reaches of the basin are greatly affected by the rainfall in the basin, and the lower reaches not only bear and discharge the upstream flood into the river, but also are affected by the support of the tide level. As a result, the flood disasters suffered by the basin are not only related to the internal rainstorm, but also related to the tide level encountered during the rainstorm. closely related. Therefore, in order to reasonably analyze the flood risk of the watershed and understand the probability risk rule of rainstorm and tide level encounter in the watershed, it is very important to study the encounter combination of rainstorm and tide level in the watershed.

The movement of the river in the tidal reach is complicated and there are many disturbance factors, but it is mainly affected by the upstream flood and the downstream tidal level. In order to simplify the analysis, the probabilistic risk analysis of encounters is mainly based on the joint distribution of rainstorm and flood level in the basin, but they are only related to a certain extent, and the correlation is not very strong. The joint distribution cannot be obtained simply by multiplying the marginal distributions. This requires a more complete theory to analyze and study. Copula theory has the advantage of flexibility in constructing the joint distribution of multivariable encounter events, which provides great convenience for the study of flood risk in tidal reaches and expands new research methods.

Current methods for joint probabilistic analysis of tide levels and floods have limitations. First of all, the current analysis method only analyzes the upstream water level and downstream tidal level, without considering factors such as rainfall duration, and the relationship between tidal and flood encounters cannot be completely analyzed only through the two-dimensional Copula function; secondly, the current analysis method often It is to first select the marginal distribution function with better simulation, and perform joint probability analysis through the marginal distribution with better performance of the two series, but the fact that the marginal distribution performs well does not necessarily determine the optimality of the joint distribution.

Contents of the invention

The present invention designs a tidal-flood joint probability analysis method based on Copula function and its application. The technical problem it solves is the lack of comprehensive consideration of sub-rainfall and rainfall peaks that characterize rainfall characteristics in tidal-flood combination analysis. At the same time The method of selecting the marginal distribution has limitations, often a good marginal distribution may not be able to obtain an accurate joint distribution. In order to solve the above-mentioned technical problems, the present invention adopts the following scheme:

A method for tidal flood joint probability analysis based on Copula function, comprising the following steps:

Step 1. Select the representative tide level station and rainfall gauge station in the analyzed river section. The representative tide station should be located at the estuary of the river section and obtain its tide level series data; the representative rainfall gauge station should be located in the downstream basin of the analyzed river section and obtain its rainfall data;

Step 2. Perform consistency correction on the tide level series data obtained in step 1;

Step 3. For each representative rainfall station selected in step 1, the continuous rainfall time series is divided into rainfall events by using the rainfall intensity method, and the rainfall data is divided, and the rainfall time series is divided into different rainfall events, and then the statistics The two characteristic variables that characterize the rainfall pattern are "secondary rainfall" and "rainfall peak";

Step 4. Use the annual maximum value method to sample the "secondary rainfall" and "peak rainfall" obtained in step 3: according to different regional characteristics, take the design duration of 720min (ie 12h) or 360min (ie 6h) or N min as an example, N is a natural number, sampling the largest "sub-rainfall" numerical samples and "rainfall peak" numerical samples in each year;

Step 5. Based on the maximum "secondary rainfall" numerical sample and "rainfall peak" numerical sample in step 4, use the Thiessen polygon method to calculate the two characteristic variables of the watershed area "secondary rainfall" and "rainfall peak";

Step 6. For the secondary rainfall, rainfall peak and tide level series, calculate the marginal probability distribution of each series respectively, and select a variety of distribution line types in the hydrological frequency analysis for the "tide level", "rainfall peak" and "secondary rainfall Quantity" for curve fitting;

Step 7. Three goodness-of-fit testing methods, the probability point data correlation coefficient test method (PPCC), the approximate optimal sum of squares criterion (RMSE) and the approximate absolute value criterion (MAE), are used to determine the best-of-fit test method for each variable data series. Two edge distribution line types with the best combination effect;

Step 8, using the widely used Frank Copula and AMH Copula functions in the Archimedes-type Copula family to construct the joint probability distribution of rainfall characteristic variables;

Step 9. Select the AIC Information Criterion (AIC) and the Least Sum of Squares (OLS) method to evaluate the goodness-of-fit of the Copula function, and select the most suitable joint probability distribution.

Further, the order of Step 2 and Step 3 can be replaced without affecting the evaluation result in Step 9.

Further, the various distribution line types in the hydrological frequency analysis in step 6 are: P-Ⅲ type distribution curve (P3), log-normal distribution curve (LN2) and generalized extreme value distribution curve (GEV).

Further, in step 8, since each variable data series is simulated by using two types of linearity, 8 calculations are required for each Copula function.

An application for restoring tidal level data using the above correction method is characterized in that: the influence of the changing environment on the data is eliminated through the correction, the consistency of the tidal level data is restored, and the reliability of the hydrological frequency analysis using the tidal level data is ensured. The subsequent monthly tide level data provide a reliable basis for urban flood control.

The present invention can be applied to the flood forecasting of tidal river sections. The tidal river sections refer to river estuary sections of rivers. The water levels of these river sections are not only affected by upstream incoming water, but also by downstream tidal levels. The invention can provide effective reference information for flood forecasting in tidal river sections. Specifically, based on the premise of determining the peak rainfall, the probability of simultaneous occurrence of the rainfall greater than a certain value and the tide level greater than a certain tide level is calculated, or under the premise that the rainfall is determined, the rainfall peak is greater than a certain value and the tide level is greater than The probability of a certain tide level occurring at the same time provides a basis for the construction of flood control projects and flood forecasting.

The tidal flood joint probability analysis method based on Copula function has the following beneficial effects:

(1) The purpose of the tidal flood analysis method of the present invention is to provide the basis for flood control construction of tidal river sections. By establishing the joint probability distribution function of "tide level", "rainfall peak value" and "secondary rainfall", it can reflect the influence of flood facilities The function of the characteristic quantity of overcurrent and regulation and storage capacity provides a reliable basis for flood control construction.

(2) The present invention not only establishes a three-dimensional Copula function for evaluating better marginal distributions, but selects two better distribution line types in marginal distributions, and establishes multiple joint probability distributions through different combinations, and then optimizes the best performance The construction method can avoid the disadvantage that the optimal marginal distribution cannot obtain a good joint distribution.

detailed description

Below in conjunction with embodiment, the present invention will be further described:

Step 1. Select and analyze the representative tide level station and rainfall station of the river section. The tide station should be located at the estuary of the river section and the tide level data is complete; according to the size of the downstream basin, select the representative water and rainfall station in the river basin. The length of the rainfall series of different rainfall stations should be basically the same;

Step 2. Carry out consistency correction to the tide level data;

Step 3. For each selected rainfall station, use the rainfall intensity method to divide the continuous rainfall time series into rainfall events. For example, according to the standard of "rainfall intensity is less than 0.1mm/h, and the duration exceeds 10h", the rainfall data Segmentation, which divides the rainfall time series into different rainfall events, and then counts the two characteristic variables of "secondary rainfall" and "rainfall peak";

Step 4, use the annual maximum value method for sampling. According to the characteristics of different regions, take the design time of 720min (ie 12h) or 360min (ie 6h) as an example to sample samples;

Step 5, using the Thiessen polygon method to calculate the two characteristic variables of the watershed surface "secondary rainfall" and "rainfall peak";

Step 6. For the sub-rainfall, rainfall peak and tide level series, calculate the marginal probability distribution of each series respectively, and select three distribution line types commonly used in hydrological frequency analysis (P-Ⅲ distribution curve (P3), logarithmic The normal distribution curve (LN2) and the generalized extreme value distribution curve (GEV)) were used for curve fitting of "tide level", "rainfall peak" and "secondary rainfall" respectively;

Step 7. Using three goodness-of-fit test methods, Probabilistic Point Data Correlation Coefficient Test (PPCC), Approximate Sum of Squares (RMSE) and Approximate Absolute Value (MAE) methods, to determine the best-of-fit test method that is closely related to each variable data series. The two edge distribution line types with the best combination effect;

The hypothesis optimization test is as follows:

Probability point data correlation coefficient test method (PPCC), fitted optimal sum of squares criterion method (RMSE) and fitted absolute value criterion method (MAE) will have a value for each fitting test, and comprehensive analysis will select The two fitting methods that best fit a project.

For the tide level item in the above example, the larger the PPCC test value, the better, and the smaller the RMSE and MAE, the better. Therefore, LN2 and GEV are selected as fitting methods. It can be seen that when there are more maximum and minimum test values in the distribution line type, it will be selected; otherwise, it will be discarded.

In the above table, "rainfall peak" and "secondary rainfall" are omitted because the inspection method is exactly the same as that of "tide level". In short, all blanks need to be checked, and they are checked by three inspection methods: PPCC, RMSE, and MAE. The principle is the same. The larger the PPCC inspection value, the better, and the smaller the RMSE and MAE, the better.

Step 8. Use the widely used Frank Copula and AMH Copula functions in the Archimedes-type Copula family to construct the joint distribution of rainfall characteristic variables. Since each series uses two types of linear simulations, each Copula function Need to calculate 8 times;

For each item below, we use A and B to represent the two fitting methods selected

The above is the combination of Copula joint distribution calculation, and the optimal joint distribution combination is selected through AIC and OLS tests.

Step 9: Select AIC information criterion method (AIC) and deviation sum of squares least (OLS) criterion method to evaluate the goodness of fit of the Copula function.

The present invention has been exemplarily described above in conjunction with the embodiments. Obviously, the realization of the present invention is not limited by the above-mentioned mode, as long as various improvements of the method concept and technical solutions of the present invention are adopted, or the present invention is implemented without improvement. The ideas and technical schemes directly applied to other occasions are within the protection scope of the present invention.

Claims (5)

1. a tide flood combined probability analysis method based on Copula function, comprises the following steps:

Tidal level station that step 1, Analysis on Selecting section are representative and precipitation station, representational tidal level station should be at section and enters sea At Kou and obtain its tidal level series materials；Representational precipitation station is positioned to be analyzed the basin, downstream of section and obtains its rainfall money Material, chooses the precipitation station of respective amount according to the downstream drainage area size analyzing section；

Step 2, step 1 gained tidal level series materials is carried out consistent correction；

Step 3, each representational precipitation station selected by step 1, use rainfall intensity method, by continuous print rain time Sequences segmentation becomes catchment, carries out rainfall data segmentation, and precipitation time series is divided into different rainfall plays, Jin Ertong Meter " single storm " and " rainfall peak value " two characterizes the characteristic variable of rainfall pattern；

Step 3 gained " single storm " and " rainfall peak value " are sampled by step 4, employing annual maximum design flood: according to not same district Characteristic of field, as a example by design lasts 720min (i.e. 12h) or 360min (i.e. 6h) or Nmin, N is natural number, samples in each year Maximum " single storm " numerical value sample and " rainfall peak value " numerical value sample；

Step 5, for maximum " single storm " the numerical value sample in step 4 and " rainfall peak value " numerical value sample, use Tyson many Limit shape method calculates face, basin " single storm " and " rainfall peak value " two characteristic variables；

Step 6, for single storm, rainfall peak value and tidal level series, calculate the marginal probability distribution of each series respectively, choose Multiple distribution linetype in hydrologic(al) frequency analysis carries out curve plan to " tidal level ", " rainfall peak value " and " single storm " respectively Close；

Step 7, use Probability Point according to related-coefficient test method (PPCC), intend excellent sum-of-squares criterion method (RMSE) and plan excellent absolute value Three kinds of goodness-of-fit test methods of Criterion Method (MAE) determine that the two kind edges best with each variable data series fit effect divide Cloth line style；

Step 8, employing archimedes type Copula family apply wide Frank Copula and AMH Copula function Build the joint probability distribution of characteristics of rainfall variable respectively；

Step 9, selection AIC information criterion method (AIC) and sum of deviation square minimum criteria method (OLS) matching to Copula function Goodness is evaluated, and chooses optimal joint probability distribution.

Tide flood combined probability analysis method based on Copula function the most according to claim 1, it is characterised in that: step 2 Can replace with the order of step 3, not affect the evaluation result in step 9.

Tide flood combined probability analysis method based on Copula function the most according to claim 1 or claim 2, it is characterised in that: step Multiple distribution linetype in hydrologic(al) frequency analysis in rapid 6 is respectively as follows: P-III type distribution curve (P3), logarithm normal distribution song Line (LN2) and generalized extreme value distribution curve (GEV).

4. according to tide flood combined probability analysis method based on Copula function described in claim 1,2 or 3, it is characterised in that: Due to the two kinds of linear simulations of each variable data series in step 8, so needing for each Copula function Calculate 8 times.

5. in any of the one of claim 1-4 based on Copula function tide flood combined probability analysis method should With, it is characterised in that: on the premise of determining rainfall peak value, calculate single storm and be more than more than some numerical value and tidal level The simultaneous probability of some tidal level, or on the premise of single storm determines, rainfall peak value is big more than a certain numerical value and tidal level In the simultaneous probability of a certain tidal level, construction and flood forecasting for flood control works provide foundation.