A calculation method for the recurrence period of extreme precipitation with diachronic coordination

Abstract

The present invention relates to a method for calculating the recurrence period of extreme precipitation with duration coordination, belonging to the technical field of hydrometeorology. The method specifically includes: S1: Establishing sample sequences of extreme precipitation with different durations; S2: Optimizing probability models for precipitation sequences with each duration and calculating precipitation amounts for different recurrence periods; S3: Fitting the variation of precipitation amount with duration under a specific recurrence period to obtain a duration adjustment coefficient; S4: Establishing the relationship between the duration adjustment coefficient and the recurrence period to obtain a recurrence period adjustment coefficient; S5: Substituting the recurrence period adjustment coefficient into the duration adjustment coefficient to obtain a comprehensive calculation formula for precipitation amounts at any duration and any recurrence period. The present invention can effectively reduce the uncertainty of calculation results for a single duration, obtain a comprehensive calculation formula for the recurrence period of extreme precipitation with different durations with high precision, and provide technical support for efficiently and conveniently carrying out rainstorm-related operations and services.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrometeorology, and relates to business applications such as rainstorm monitoring and assessment, risk zoning, etc., and technical service fields such as flood control and drainage planning, design, management, and scheduling. Specifically, it relates to a method for calculating the return period of extreme precipitation with duration coordination. Background Art

[0002] The calculation of the return period of extreme precipitation with different durations is often applied to the analysis of the risk of rainstorm disasters, precipitation monitoring and assessment business services, and the design of drainage and flood control projects. It mainly involves the establishment of an extreme precipitation sample sequence for a certain duration, the fitting and optimization of different types of extreme probability distribution functions, and the calculation of the return period using the optimal line type. The calculation results of the return period for a single duration usually have high accuracy within the sample length. The calculation results of the high return period beyond the sample length are extrapolated by statistical methods, resulting in large uncertainties. When conducting joint analysis of multiple durations, there will be a phenomenon that the precipitation with a short duration and a high return period is greater than the precipitation with a corresponding return period of a long duration, which violates objective facts. In the current general survey of rainstorm disaster risks, it is required to calculate the precipitation values with different return periods at the hourly scale and daily scale. There are often situations where the 3-hour precipitation with a hundred-year return period is greater than the 6-hour or 12-hour precipitation, which has caused much controversy and discussion. This situation is caused by the existence of large outliers in the extreme sequence and the different abilities of different extreme probability models to describe large outliers. If the same model, such as the commonly used extreme value type I (Gumbel) distribution, is selected for all extreme precipitation sequences with different durations, the above anomalies can be better avoided, but the fitting accuracy of the extreme value sequence will be reduced, and the calculation results of high return period precipitation are usually on the small side, posing a certain hidden danger to design safety. How to balance the fitting accuracy of a single duration and the precipitation coordination of multiple durations is a key problem that urgently needs to be solved in current rainstorm-related operations and services. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method for calculating the return period of extreme precipitation with duration coordination. This method can effectively reduce the uncertainty of the calculation results for a single duration, obtain a comprehensive calculation formula for the return period of extreme precipitation with different durations with high accuracy, and provide technical support for rainstorm-related operations and services. In addition, by dividing the precipitation intensity according to the interval where the return period is located, targeted services can also be carried out in combination with the design requirements of local flood control and drainage departments for the return period of precipitation, improving the accuracy and technical content of forecasting and early warning.

[0004] To achieve the above purpose, the present invention provides the following technical solutions:

[0005] A method for calculating the recurrence period of extreme precipitation with duration coordination. Under the condition of satisfying the objective fact that the precipitation of a specific recurrence period increases with the increase of duration, the calculation results of the recurrence period for a single duration are constrained and adjusted to reduce the uncertainty of the extrapolation results, and a comprehensive calculation formula for the recurrence period of extreme precipitation with duration coordination is obtained, so as to efficiently and conveniently carry out rainstorm-related business applications and services, and provide more accurate calculation results for rainstorm disaster risk zoning, drainage and flood control engineering design, etc. The method specifically includes the following steps:

[0006] S1: Establish extreme precipitation sample sequences with different durations;

[0007] S2: Optimize the probability model for the precipitation sequence by duration, and calculate the precipitation amounts for different recurrence periods;

[0008] S3: Fit the variation of precipitation amount with duration under a specific recurrence period to obtain a duration adjustment coefficient;

[0009] S4: Establish the relationship between the duration adjustment coefficient and the recurrence period to obtain a recurrence period adjustment coefficient;

[0010] S5: Substitute the recurrence period adjustment coefficient into the duration adjustment coefficient to obtain a comprehensive calculation formula for the precipitation amount at any duration and any recurrence period.

[0011] Furthermore, in step S1, establishing extreme precipitation sample sequences with different durations specifically includes: Based on the hourly or minute precipitation data of meteorological stations, sliding statistics of the maximum 1 or multiple precipitation events in 1 - 24 hours (h) over the years are used as extreme value samples.

[0012] Furthermore, step S2 specifically includes: Using a variety of generally applicable extreme value probability models for fitting and optimization, and calculating the precipitation amount R for different recurrence periods.

[0013] Furthermore, in step S2, a variety of generally applicable extreme value probability models mainly include the generalized Pareto distribution, generalized extreme value distribution, generalized logistic distribution, lognormal distribution, Weibull distribution, Pearson - type III distribution, Gumbel distribution, exponential distribution, etc. The optimal line type can be selected to calculate the recurrence period, and the selected probability model needs to meet the statistical significance requirements. Generally, it passes the Kolmogorov - Smirnov goodness - of - fit test (K - S test) or chi - square (χ 2 ) test with a significance level of 0.05, or the root mean square error (RMSE) and relative root mean square error (RRMSE) between the fitted value and the observed value meet the accuracy requirements.

[0014] Furthermore, in step S3, obtaining the duration adjustment coefficient specifically includes: For the variation of precipitation at each duration under the same recurrence period, establish the relationship between the precipitation amount R and the duration t under a specific recurrence period T i : R(t|T i ) = A iln(t) + B i or R(t|T i ) = A i t Bi , ensure that the precipitation amount at a specific recurrence period increases with the increase of the duration, and obtain the duration adjustment coefficients A i and B i .

[0015] Furthermore, in step S3, the recurrence period T is determined according to the annual average sample number λ. From the event occurrence probability P = 1 / (λT) ≤ 1, it can be seen that T ≥ 1 / λ. Generally, the equal sign is not taken (extreme events cannot occur 100%); the recurrence period T of the annual maximum sampling is generally taken as 2 years, 3 years, 5 years, 10 years, 20 years, 30 years, 50 years, 100 years, and the recurrence period of the annual multiple method is additionally increased by 2 / λ to 1 year.

[0016] In step S3, the duration adjustment coefficients A i and B i under a specific recurrence period T i are the fitting parameters of the logarithmic or power exponential function. The function type is selected according to the fitting effect, that is: select the function with a larger sum of determination coefficients at different recurrence periods, and it is necessary to satisfy the determination coefficient R i 2 ≥ 0.9. Discard A i and B i under the recurrence period that does not meet the conditions; when the remaining number of A i and B i is small (less than 5), use A i ≤ the number of sample years i and B i for calculation.

[0017] Furthermore, in step S4, obtain the recurrence period adjustment coefficient, specifically including: establish the relationship between the duration adjustment coefficients A i and B i and the recurrence period T i : A(T) = aln(T) + b or A(T) = aT b , B(T) = cln(T) + d or B(T) = cT d , select the fitting formula with a larger determination coefficient R A 2 and R B 2 (not less than 0.9) as the recurrence period adjustment coefficients A i and B i of A(T|a, b), B(T|c, d); where a, b, c, d are fitting coefficients.

[0018] Further, step S5 specifically includes: according to the fitting coefficients a, b, c, d and the adopted logarithmic formula or power exponential formula, the precipitation R for any recurrence period T and any duration t can be calculated, and the comprehensive calculation formula for the recurrence period precipitation is obtained: R(T, t|a, b, c, d) = A(T|a, b)ln(t) + B(T|c, d) or R(T, t|a, b, c, d) = A(T|a, b)t B(T|c,d) .

[0019] In step S5, based on the comprehensive calculation formula for precipitation with different durations and recurrence periods of the fitting coefficients a, b, c, d, the relative root mean square error RRMSE between the calculation result and the calculation result of the optimal probability model with a recurrence period not exceeding the number of sample years in step S2 satisfies RRMSE ≤ 5%.

[0020] The beneficial effects of the present invention are as follows:

[0021] (1) On the premise of ensuring high-precision calculation results, the present invention can effectively avoid the situation where short-duration precipitation is greater than long-duration precipitation in the calculation results of high recurrence periods beyond the sample length, which is more in line with objective laws;

[0022] (2) The present invention can simply and quickly calculate the precipitation for any recurrence period and any duration, and can be applied in services such as rainstorm monitoring and assessment, risk zoning, etc., and at the same time provides a theoretical support for flood control and drainage planning, design, management, and scheduling.

[0023] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent description, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0025] Figure 1 is the flow chart of the calculation method for the recurrence period of extreme precipitation of the present invention;

[0026] Figure 2 is the schematic diagram of the calculation results of the recurrence period of extreme precipitation with different durations in the embodiment;

[0027] Figure 3 is the adjustment coefficient A for the duration of a single recurrence period in the embodiment i , B i schematic diagram of the calculation results;

[0028] Figure 4Relationship diagram between the duration adjustment coefficient and the recurrence period in the embodiment;

[0029] Figure 5 Schematic diagram for comparing the calculation results of single-duration recurrence period and comprehensive formula calculation in the embodiment. Specific implementation manners

[0030] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0031] Please refer to Figures 1 to 5 , Figure 1 shown is a method for calculating the recurrence period of extreme precipitation with duration coordination, which specifically includes the following steps:

[0032] Step S1, establish an extreme value sample sequence. The extreme value sample sequence can be established by using the annual maximum sampling or annual multiple sample sampling method according to the actual number of years of the data. In this embodiment, the hourly precipitation data of a national meteorological station from 1991 to 2021 is used to establish an annual maximum precipitation sequence of 1 to 24 hours (h) based on annual maximum sampling, and the sample length is 31 years.

[0033] Step S2, use a variety of suitable extreme value probability models for fitting and optimization, and calculate the extreme precipitation amounts for different recurrence periods (2 years, 3 years, 5 years, 10 years, 20 years, 30 years, 50 years, 100 years) of each duration. In this embodiment, 6 probability models such as the generalized extreme value distribution, lognormal distribution, Weibull distribution, Pearson type III distribution, Gumbel distribution, and exponential distribution are used to fit the extreme precipitation sequences of different durations respectively. The probability model with the smallest comprehensive error is selected as the optimal line type to calculate the recurrence period precipitation, and a statistical significance test is performed on it. The following table shows the optimal line type and error distribution of each duration.

[0034] Table 1 Optimization of probability models and error distribution of extreme precipitation sequences of different durations

[0035]

[0036] In Table 1, the critical threshold of the K-S test with a sample size of 31 and a significance level of 0.05 is 0.24; chi-square (χ 2) The degree of freedom for the test is k - l - 1. Here, k represents the number of groups, generally taking values from 2.5lg n to 5lg n. In this embodiment, the integer part of 5lg n is taken, and it is divided into 7 groups (k = 7). l represents the number of estimated parameters in the theoretical function (l = 3). The critical value of the chi-square test with a degree of freedom of 3 and a significance level of 0.05 is 7.8. The root mean square error (RMSE) and relative root mean square error (RRMSE) are calculated based on the fitting of precipitation by the theoretical function and actual observations.

[0037] The precipitation for each duration in Table 1 has passed the K - S test with a significance level of 0.05. Most durations have passed the chi-square test with a significance level of 0.05, and the maximum RMSE and RRMSE do not exceed 1.8 mm / h and 7.1% respectively, indicating a high fitting accuracy.

[0038] The precipitation with different return periods for each duration obtained by the optimal line type fitting is shown specifically in Figure 2 . The precipitation with a return period of 100 years (a) within 14 - 17 hours (h) is greater than that of longer durations, which is contrary to the objective facts.

[0039] Step S3: Establish the relationship between the precipitation with a single return period and the precipitation duration to obtain the duration adjustment coefficients A i and B i , as shown specifically in Figure 3 . The change of precipitation with duration for each return period is fitted using logarithms and power exponents. In this embodiment, the determination coefficient of the logarithmic fitting result is higher than that of the power exponent fitting for each return period, and all determination coefficients of the logarithmic fitting are ≥ 0.9, meeting the accuracy requirements.

[0040] Step S4: Take the logarithmic fitting parameters A i and B i with better fitting effects as the duration adjustment coefficients, and establish the relationship between the duration adjustment coefficients and the return period. Similarly, use the logarithmic distribution and power exponent distribution, and select the fitting function with a larger determination coefficient as the final result, as shown specifically in Figure 4 . Coefficient A i is more in line with the power exponent distribution, and its fitting parameters are (a, b). Coefficient B i is more in line with the logarithmic distribution, and its fitting parameters are (c, d). The determination coefficients R A 2 and R B 2 are both ≥ 0.99, indicating an extremely high fitting accuracy.

[0041] Step S5. Based on the fitting coefficients (a, b, c, d) and their corresponding fitting functions, the precipitation R for any return period T and any duration t can be calculated, and the comprehensive calculation formula for return period precipitation is obtained: R(T, t|a, b, c, d) = A(T|a, b)ln(t) + B(T|c, d) or R(T, t|a, b, c, d) = A(T|a, b)t B(T|c,d) , the comprehensive calculation formula of this embodiment is as follows:

[0042] R(T, t|a, b, c, d) = aT b ln(t) + cln(T) + d

[0043] In the formula: a = 15.575, b = 0.245, c = 11.005, d = 20.352;

[0044] At return periods lower than the sample length, that is, when the return period is 2 - 30 years (a), the relative root mean square error RRMSE between the comprehensive formula and the single - duration optimal line - type fitting result is 3.1%, indicating a high fitting accuracy. See specifically Figure 5 .

[0045] According to the prepared comprehensive formula, the magnitude of the rainfall R with any duration t and any return period T in the area where the meteorological station is located can be calculated simply and quickly. Combining the selected urban scale and the requirements for the design return period of local waterlogging prevention, the grade thresholds of different precipitation intensities can be divided. By forecasting the magnitude of precipitation, the corresponding warning levels can be issued, or the intensity of rainstorms with different durations can be quantitatively evaluated based on the actual precipitation, greatly improving the work efficiency and technical level of precipitation monitoring and evaluation operations. The comprehensive formula can also effectively connect the intensities of short - duration and long - duration precipitation, and has certain reference value for flood control and drainage planning, design, management, and scheduling, etc.

[0046] The present invention uses a duration adjustment coefficient and a return - period adjustment coefficient to derive a method for calculating the return period of extreme precipitation with duration coordination, and obtains a comprehensive calculation formula for return - period precipitation. It not only makes up for the limitations of the calculation results of single - duration return - period precipitation, avoids the situation where the calculation result of short - duration is greater than that of long - duration due to the uncertainty of high - return - period precipitation during extrapolation, but also has the advantages of simple and rapid calculation and convenient application of the results.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating the recurrence period of extreme precipitation with diachronic coordination, characterized in that The method specifically includes the following steps: S1: Establish sample sequences of extreme precipitation with different durations; S2: Optimize the probability model for the precipitation sequence of each duration, and calculate the precipitation amounts for different return periods; S3: Fit the variation of precipitation with duration for a specific return period to obtain the duration adjustment coefficient, specifically including: for the variation of precipitation with different durations under the same return period, establish a specific return period T i precipitation R and duration t relationship: R ( t | T i ) = A i ln( t ) + B i or R ( t | T i ) = A i t Bi , and obtain the duration adjustment coefficients A i 、 B i ; S4: Establish the relationship between the duration adjustment coefficient and the recurrence period to obtain the recurrence period adjustment coefficient, specifically including: establishing the duration adjustment coefficient A i 、 B i and the recurrence period T i relationship: A ( T ) = a ln( T ) + b or A ( T ) = aT b , B ( T ) = c ln( T ) + d or B ( T ) = cT d , select the fitting formula with a larger coefficient of determination R A 2 、 R B 2 as the duration adjustment coefficient A i 、 B i recurrence period adjustment coefficient A ( T | a, b )、 B ( T | c, d );Among them, a 、 b 、 c 、 d are fitting coefficients; S5: Substitute the recurrence period adjustment coefficient into the duration adjustment coefficient to obtain the comprehensive calculation formula for precipitation at any duration and any recurrence period, specifically including: According to the fitting coefficients a , b , c , d and the logarithmic formula or power exponent formula adopted, calculate the precipitation T at any recurrence period t and any duration R to obtain the comprehensive calculation formula for recurrence period precipitation: R ( T , t | a, b, c, d ) = A ( T | a, b ) ln( t ) + B ( T | c, d ) or R ( T , t | a, b, c, d ) = A ( T | a, b ) t B(T | c, d) ; The relative root mean square error between the comprehensive calculation formula and the optimal probability model fitting result T i ≤ the sample years is not greater than 5%.

2. The method for calculating the recurrence period of extreme precipitation according to claim 1, wherein In step S1, to establish sample sequences of extreme precipitation with different durations, it specifically includes: Based on the hourly or minute precipitation data of meteorological stations, sliding statistics are carried out on the annual maximum one or multiple precipitations of 1 to 24 hours in each year as extreme value samples.

3. The method for calculating the return period of extreme precipitation according to claim 1, characterized in that, Step S2 specifically includes: fitting and optimizing by using a variety of generally applicable extreme value probability models, and calculating precipitation with different recurrence periods. R The selected probability model needs to meet the statistical significance requirement, or the absolute root mean square error and the relative root mean square error meet the accuracy requirement.

4. The method for calculating the recurrence period of extreme precipitation according to claim 1, characterized in that In step S3, the duration adjustment coefficient under a specific return period is A i , B i , the coefficient of determination must be satisfied R i 2 ≥0.9, for the case where the return period does not meet the conditions A i , B i to be discarded; when the remaining A i , B i When the number is small, use T i ≤ Sample years A i , B i Perform calculations.

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