An Adaptive Calculation Method for the Recurrence Period of Hydrological Extremes Based on Data Adequacy Judgment

Abstract

This invention discloses an adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment, relating to the fields of hydrological statistics and marine engineering technology. The invention first obtains the annual extreme water level sequence and records the sample size, calculating the upper limit of the reliable return period. If the maximum return period input by the user does not exceed this upper limit, frequency analysis is directly performed using both Pearson Type III and Günber distributions. Parameters are automatically estimated through the method of moments and optimized fitting, and the optimal model is recommended based on the root mean square error. Simultaneously, a Hessian frequency grid is plotted. If the upper limit is exceeded, insufficient data is indicated, and the correlation coefficient and regression equation are calculated using synchronous data from highly correlated reference stations. The design water level of the target station is then extrapolated from the design water level of the reference station. This invention achieves full automation and adaptive judgment in the return period calculation process, avoiding extrapolation distortion caused by insufficient data, and integrates dual-station correlation analysis, significantly improving the efficiency and reliability of design parameter determination.

Description

Technical Field

[0001] This invention relates to the fields of hydrological statistics and marine engineering technology, specifically to an adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment. Background Technology

[0002] The return period is an important indicator used in hydrological, marine, and meteorological engineering to assess the probability of extreme events. It is defined as the average number of years it takes for an event of a certain magnitude to occur over long-term statistics. In coastal engineering, seawall design, flood control planning, and storm surge disaster risk assessment, determining the design water level, design wave height, or design wind speed for a specified return period is a crucial step in ensuring the safety and economic rationality of the project.

[0003] Currently, commonly used methods for calculating return periods mainly include the Pearson Type III (P-III) distribution and the Gumbel distribution. Both belong to the annual extreme value method, which involves performing frequency analysis on historical extreme value sequences, fitting the theoretical distribution curve, and then extrapolating to obtain the design parameters for a multi-year return period. Traditional return period calculation processes usually rely on manual table lookups or specialized statistical software.

[0004] Taking the Pearson Type III distribution as an example, the mean, coefficient of variation (Cv), and skewness coefficient (Cs) of the sample must first be calculated. Then, by referring to the "Table of Modulus Ratio Coefficient Kp Values ​​for Pearson Type III Curves" or the table of deviation coefficients (Φ values), the design value corresponding to the specified frequency can be obtained. The Gumbel distribution also requires consulting the corresponding deviation coefficient table.

[0005] The aforementioned method of table lookup and calculation is not only cumbersome and time-consuming, but also often employs coarse methods such as the method of moments or the three-point method for parameter estimation. This makes the fitting accuracy highly susceptible to subjective judgment, potentially leading to significantly different results from different operators. Furthermore, the fitting process often relies on manual visual adjustments, lacking a unified optimization criterion, resulting in inconsistent outcomes.

[0006] With the development of computer technology, although some software has been able to calculate the recurrence interval, most are still based on fixed models and lack the ability to automatically compare multiple distribution models and recommend the optimal model. For sites lacking long-term data, it is necessary to perform synchronous correlation analysis using neighboring long-sequence sites, but existing tools often do not integrate this function and require separate processing.

[0007] Meanwhile, plotting frequency curves requires specialized plotting software, which hinders engineers from quickly and intuitively assessing the fitting effect. Therefore, developing an integrated return period calculation and analysis system to improve the efficiency and accuracy of design parameter determination is a technical problem that urgently needs to be solved by those skilled in the art.

[0008] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0009] To address the aforementioned technical problems, embodiments of the present invention provide an adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment, thereby solving the problems mentioned in the background art, comprising the following steps: An adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment includes the following steps: S1. Obtain the annual extreme water level sequence data of the target station and record the sample size. .

[0010] S2. Parse the user-input list of recurrence periods. Calculate the upper limit of reliable return period ,Will The calculation result is rounded to an integer, and the maximum recurrence period input by the user is determined. Is it greater than .

[0011] like Then proceed to step S4.

[0012] like If so, the user is prompted that the current data volume is limited, and step S3 is executed.

[0013] S3. Calculate the design water level of the target station using the design water level of a highly correlated reference station.

[0014] S4. Frequency analysis is performed on the current site data sequence using both Pearson Type III distribution and Günbel distribution models.

[0015] S5. The statistical parameters of the two distribution models are automatically estimated by combining the method of moments with the optimization fitting technique.

[0016] S6. Based on one or more recurrence periods input by the user. The system automatically calculates the corresponding water level value.

[0017] S7. Calculate the root mean square error between the empirical frequency points and the theoretical curves of the two models, automatically recommend the optimal model based on the magnitude of the root mean square error, and plot the Hessian frequency grid to display the empirical data and the theoretical curves.

[0018] S8. Output the design water level value of the recommended model.

[0019] Preferably, step S3 specifically includes: S31. Load the synchronous observation data of the target station and the reference station respectively. .

[0020] S32. Calculate the Pearson correlation coefficient. The formula is: .

[0021] And perform a significance test to construct the t-statistic: .

[0022] S33. Select reference sites with a correlation coefficient absolute value higher than 0.8 and significant correlation, and establish a linear regression equation with the reference sites as independent variables and the target sites as dependent variables. ,in: .

[0023] S34. Using reference station data, perform the same frequency analysis steps as steps S4-S7 to obtain the design water level value of the reference station under the target return period. .

[0024] S35, Refer to the design water level value of the station Substitute the values ​​into the regression equation to calculate the design water level for the target site during the corresponding return period. .

[0025] S36. Draw a scatter plot and regression line between the target site and the reference site.

[0026] Preferably, in step S5, for the Pearson type III distribution: Its probability density function is: .

[0027] Where, in the formula , , These are shape, scale, and location parameters, respectively, and the mean values ​​of hydrological parameters. Coefficient of variation and skewness coefficient The relationship is: .

[0028] The method of moments is used to estimate the sample mean. Coefficient of variation and skewness coefficient : .

[0029] .

[0030] .

[0031] Then, taking the minimization of the sum of squared deviations between empirical frequency data and the theoretical curve as the objective function, optimization is performed. Value; the objective function is: .

[0032] in, Let j be the j-th sample value arranged in descending order. For empirical frequency, The deviation coefficient is calculated using the following formula: .

[0033] In the formula It is the inverse function of the incomplete gamma function.

[0034] Preferably, given a return period Corresponding frequency The design water level for Pearson type III distribution is... for: .

[0035] Preferably, in step S5, for the Gumbel distribution: Its probability distribution function is: .

[0036] Where, in the formula For scale parameters, For position parameters; the method of moments is used to estimate the parameters: .

[0037] in, , and for The mean and standard deviation, and The sample mean and standard deviation are calculated as follows: .

[0038] .

[0039] The preferred formula for calculating the return period water level according to the Gumbel distribution is: .

[0040] Preferably, the formula for calculating the root mean square error in step S7 is: .

[0041] And at the same time, the suggested information is displayed: "Data total Year, suggested estimate "Recurrence periods of 1 year or less are considered more reliable," among which... .

[0042] Preferably, when drawing the Hessian frequency grid in step S7, the horizontal axis is converted to the standard normal quantile. ,in The vertical axis represents the inverse function of the standard normal distribution function, and the vertical axis represents the water level value.

[0043] Plot empirical data scatter points and two theoretical frequency curves, Pearson Type III and Günbel Type, on graph paper; the horizontal axis scale is automatically converted to commonly used frequency values.

[0044] The adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment provided in this invention has the following beneficial effects: (1) The present invention has a high degree of automation. By integrating the entire process of data input, parameter estimation, model fitting and result output, there is no need for manual table lookup or program writing. Users only need to input the annual extreme value sequence and the return period list, and the system can automatically complete the calculation and output the design water level value, which significantly reduces the operation threshold and calculation time.

[0045] (2) This invention is highly objective. It uses the method of moments to estimate the statistical parameters of Pearson type III distribution and Gumbel distribution by combining optimization fitting technology. In particular, in Pearson type III distribution, it automatically searches for the optimal skewness coefficient with the objective function of minimizing the sum of squared deviations between empirical frequency data and theoretical curves. This avoids the subjectivity of traditional manual fitting and ensures the objectivity and repeatability of the fitting results.

[0046] (3) This invention provides an intuitive model comparison function, and gives the frequency analysis results of two models, Pearson Type III distribution and Günber distribution, and calculates the root mean square error of the empirical points and theoretical curves of the two models. Based on the magnitude of the root mean square error, the optimal model is automatically recommended to assist engineering technicians in scientifically selecting design parameters.

[0047] (4) The present invention has the ability to adaptively judge data sufficiency. The upper limit of the reliable return period L is calculated based on the sample size of the target site and is equal to 2.5n and rounded. When the maximum return period input by the user exceeds the upper limit, the system actively prompts that the data volume is limited and guides the user to use highly relevant reference sites to calculate the design water level. This avoids the problem of serious distortion of the extrapolation results due to insufficient samples and improves the reliability of engineering design.

[0048] (5) This invention integrates the function of dual-station correlation analysis, and has built-in functions such as Pearson correlation coefficient calculation, significance test, linear regression equation establishment, and calculation of unknown station design water level based on known station design water level. It fills the gap of existing return period calculation software lacking synchronous correlation analysis function, and provides an effective way to calculate design parameters for stations lacking long-term observation data.

[0049] (6) The present invention has good visualization effect, automatically draws Hessen frequency grid paper, converts the horizontal axis to standard normal quantiles, the vertical axis is the water level value, and simultaneously displays empirical data scatter points and two theoretical frequency curves of Pearson type III and Günber type on the grid paper. The horizontal axis scale is automatically converted to commonly used frequency values. The graph supports scaling and saving in multiple formats, which makes it easy for engineering technicians to intuitively judge the fitting effect. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the module composition and data flow of the system of the present invention.

[0051] Figure 2 This is a schematic diagram of the main interface layout of the hydrological extreme value return period calculation system in this invention.

[0052] Figure 3 This is a diagram showing the calculation results of the hydrological extreme value return period calculation system in this invention.

[0053] Figure 4 This invention relates to a graph showing empirical data and theoretical frequency curves on the Hessen frequency grid paper.

[0054] Figure 5 This is a schematic diagram of the dual-station correlation analysis window in this invention.

[0055] Figure 6 This is a schematic diagram of the tide level calculation window designed in this invention.

[0056] Figure 7 This is a scatter plot showing the correlation between the water levels of the target station and the reference station in this invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] Example 1: Specific operation steps of the method of the present invention.

[0059] The hydrological extreme value return period calculation and correlation analysis system provided by this invention includes the following steps: S1. Obtain the annual extreme water level sequence data of the target station and record the sample size. .

[0060] The system supports inputting annual extreme water level data via file selection (.txt / .dat) or manual pasting. Automatically sort the data from largest to smallest. And calculate the number of samples. mean Statistical information such as maximum and minimum values.

[0061] S2. Parse the user-input list of recurrence periods. Calculate the upper limit of reliable return period (Round to the nearest integer) and determine the maximum recurrence period of the user input. Is it greater than .

[0062] like If so, then S4 will be executed directly.

[0063] like If the current data volume is limited, the calculation result may be unreliable. It is recommended to use the design water level of a highly relevant reference site for calculation and execute S3.

[0064] S3. Calculate the design water level of the target station using the design water level of a highly correlated reference station, specifically including: S31. Load the synchronous observation data from the two tide gauge stations (target station and reference station) respectively. ， Required sample size for reference stations And it is synchronized with the target station's data.

[0065] S32. Calculate the Pearson correlation coefficient. And perform a significance test: .

[0066] Construct the t-statistic: .

[0067] Determine the significance of the correlation based on the t-distribution, given a significance level. .

[0068] S33. Select reference sites with a correlation coefficient absolute value higher than 0.8 and significant correlation, and establish a linear regression equation with the reference sites as independent variables and the target sites as dependent variables. ,in: .

[0069] S34. Perform the same frequency analysis steps as S4-S7 below using reference site data, and input the target return period. The design water level of the recommendation model for the reference site is obtained. (The reference site sample is sufficient and can be calculated directly).

[0070] S35, Refer to the design water level value of the station Substitute the values ​​into the regression equation to calculate the design water level for the target station during the corresponding return period. .

[0071] S36. Draw a scatter plot and regression line between the target station and the reference station, and display the regression equation and correlation coefficient; output the estimated design water level of the target station, and do not execute S4-S7 again.

[0072] S4. Frequency analysis is performed on the current site data sequence using both Pearson Type III distribution and Günbel distribution models.

[0073] S5. The statistical parameters of the two distribution models are automatically estimated by combining the method of moments with the optimization fitting technique.

[0074] S51. For the Pearson type III distribution, its probability density function is: .

[0075] In the formula , , These are shape, scale, and location parameters, respectively. In hydrological calculations, the mean is commonly used. Coefficient of variation and skewness coefficient This indicates that their relationship is: .

[0076] In practical applications, the method of moments is first used to estimate the sample mean. and : , .

[0077] .

[0078] Then, taking the minimization of the sum of squared deviations between empirical frequency data and the theoretical curve as the objective function, optimization is performed. Value. The objective function is: .

[0079] in Let j be the j-th sample value arranged in descending order. For empirical frequency, The deviation coefficient is calculated using the following formula: .

[0080] In the formula It is the inverse function of the incomplete gamma function.

[0081] S52, Given a return period (Year), corresponding frequency The design water level of Pearson III type for: .

[0082] S53. For the Gumbel distribution, its probability distribution function is: .

[0083] In the formula For scale parameters, These are the location parameters. The method of moments is used to estimate the parameters: .

[0084] in , and for The mean and standard deviation, and The sample mean and standard deviation are calculated as follows: .

[0085] .

[0086] S54. The formula for calculating the water level during the return period of the Gumbel distribution is: .

[0087] S6. Based on one or more recurrence periods input by the user. The system automatically calculates the corresponding water level value and displays the calculation results of both models in tabular form.

[0088] S7. Calculate the root mean square error (RMSE) of the empirical frequency points and theoretical curves for the two models. Based on the magnitude of the RMSE, automatically recommend the optimal model and suggest the return period, and plot the Hessian frequency grid to display the empirical data and theoretical curves.

[0089] S71. Automatically recommend a better model based on the RMSE value, and highlight the recommendation results and the corresponding RMSE value in the interface.

[0090] Formula for calculating root mean square error: .

[0091] S72, Simultaneously display the suggested information: "Data total..." Year, suggested estimate "Recurrence periods of 1 year or less are considered more reliable," among which... .

[0092] S73. Automatically draws Hessian frequency graph paper, converting the horizontal axis to standard normal quantiles. ,in The graph is the inverse function of the standard normal distribution function, with the vertical axis representing the water level value. It plots empirical data scatter points and two theoretical frequency curves (P-III and Gumbel) on graph paper. The horizontal axis scale is automatically converted to commonly used frequency values ​​(such as 0.01%, 0.1%, 1%, ..., 99.9%). The graph supports scaling and can be saved in PNG, SVG, PDF, and other formats.

[0093] S8, Output the design water level value of the phase recommendation model.

[0094] The system uses Tkinter to build the graphical user interface. The main window includes a data input area, a parameter setting area, a result table area, a recommendation label area, and a function button area. All modules are coordinated and run through the system control center to realize data flow and command distribution. The system is packaged as a standalone executable file (.exe) and can run without a Python environment.

[0095] Example 2: Specific application example of the method of the present invention.

[0096] (I) Experimental Preparation

[0097] First, taking the extreme high tide level data from the Huangpu River tide gauge station over 63 years as an example, the data are as follows (unit: cm): 162, 192, 210, 180, 184, 189, 190, 171, 176, 165, 170, 185, 157, 208, 174, 159, 184, 181, 201, 208, 202, 185, 193, 215, 187, 213, 206, 1 97, 217, 194, 189, 184, 204, 185, 180, 219, 174, 228, 181, 175, 213, 174, 173, 229, 169, 223, 182, 238, 208, 185, 201, 191, 221, 170, 177, 238, 185, 202, 192, 248, 210, 193, 269.

[0098] Enter these data on the system's main interface, and enter "10,30,50,80,100,150" for the recurrence period, then click "Calculate". The system will automatically calculate and display the results as shown in Table 1 below. Figure 2and Figure 3 As shown: Table 1

[0099] The system calculates the RMSE: P-III is 3.916 cm, and Gumbel is 1.672 cm. The Gumbel distribution is recommended as the superior model. The recommended results and reliable calculation years of 157 years or less are displayed at the bottom of the interface, along with a frequency curve. Figure 4 As shown.

[0100] The station data was changed to the 30-year extreme high tide data of Station A, as follows (unit: m): Station A: 2.41, 2.78, 2.65, 2.78, 2.71, 3.02, 2.84, 3.20, 2.96, 3.32, 3.14, 3.42, 3.23, 3.45, 3.26, 3.45, 3.29, 3.42, 3.14, 3.32, 3.02, 3.17, 2.90, 3.17, 2.71, 2.96, 2.68, 2.75, 2.71, 2.59.

[0101] Enter "100" as the return period year. At this point, a message will appear indicating that the site has limited data. You will then be taken to the correlation analysis page. Load the extreme high tide data of station B, a neighboring station of station A (synchronized with the data of station A, but not the overall data of station B). The data is as follows (unit: m): Station B: 2.32, 2.77, 2.62, 2.77, 2.72, 3.10, 2.80, 3.18, 2.94, 3.23, 3.11, 3.32, 3.18, 3.34, 3.32, 3.35, 3.24, 3.39, 3.10, 3.27, 2.96, 3.20, 2.87, 3.28, 2.70, 2.85, 2.66, 2.74, 2.78, 2.60.

[0102] Click "Calculate Correlation," and the system will automatically calculate and display the analysis results as shown in Table 2 below. Figure 5 As shown: Table 2

[0103] Simultaneously, a tide level correlation diagram of sample data from two stations was obtained for reference. Figure 7 .

[0104] At this point, input the entire 42-year data for Station B into the return period calculation page (the sample size is sufficient to directly calculate the design water level for a 100-year return period). The overall data sequence for Station B is as follows (unit: m): 2.37, 2.49, 2.39, 2.53, 2.41, 2.36, 2.51, 2.37, 2.46, 2.50, 2.43, 2.35, 2.32, 2.77, 2.6 2, 2.77, 2.72, 3.10, 2.80, 3.18, 2.94, 3.23, 3.11, 3.32, 3.18, 3.34, 3.32, 3.35, 3.24, 3.39, 3.10, 3.27, 2.96, 3.20, 2.87, 3.28, 2.70, 2.85, 2.66, 2.74, 2.78, 2.60.

[0105] Enter "100" as the return period year, click "Calculate", and you will get the design water level automatically recommended by the system: the system automatically recommends the Gumbel distribution, and the design water level is 4.06m.

[0106] In the correlation analysis interface, select the known station B for tide level estimation. The known station's design tide level is 4.06m. Click "Estimate another station," and you will get the design tide level of station A as approximately 4.137m (reference). Figure 6 ).

[0107] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment, characterized in that, Includes the following steps: S1. Obtain the annual extreme water level sequence data of the target station and record the sample size. ; S2. Parse the user-input list of recurrence periods. Calculate the upper limit of reliable return period ,Will The calculation result is rounded to an integer, and the maximum recurrence period input by the user is determined. Is it greater than ; like Then proceed to step S4; like If so, the user is prompted that the current data volume is limited, and step S3 is executed; S3. Calculate the design water level of the target station using the design water level of a highly correlated reference station; S4. Frequency analysis was performed on the current site data sequence using both Pearson Type III and Günbel distribution models. S5. The statistical parameters of the two distribution models are automatically estimated by combining the method of moments with the optimization fitting technique; For the Pearson type III distribution in step S5: Its probability density function is: ; Where, in the formula , , These are shape, scale, and location parameters, respectively, and the mean values ​​of hydrological parameters. Coefficient of variation and skewness coefficient The relationship is: ； The method of moments is used to estimate the sample mean. Coefficient of variation and skewness coefficient : ； ； ； Then, taking the minimization of the sum of squared deviations between empirical frequency data and the theoretical curve as the objective function, optimization is performed. Value; the objective function is: ； in, Let j be the j-th sample value arranged in descending order. For empirical frequency, The deviation coefficient is calculated using the following formula: ； In the formula It is the inverse function of the incomplete gamma function; In step S5, for the Gumbel distribution: Its probability distribution function is: ; Where, in the formula For scale parameters, For position parameters; the method of moments is used to estimate the parameters: ； in, , and for The mean and standard deviation, and The sample mean and standard deviation are calculated as follows: ； ； S6. Based on one or more recurrence periods input by the user. The system automatically calculates the corresponding water level value; S7. Calculate the root mean square error between the empirical frequency points and the theoretical curves of the two models, automatically recommend the optimal model based on the magnitude of the root mean square error, and draw a Hessian frequency grid to display the empirical data and the theoretical curves. S8. Output the design water level value of the recommended model.

2. The adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment according to claim 1, characterized in that, Step S3 specifically includes: S31. Load the synchronous observation data of the target station and the reference station respectively. ; S32. Calculate the Pearson correlation coefficient. The formula is: ； And perform a significance test to construct the t-statistic: ; S33. Select reference sites with a correlation coefficient absolute value higher than 0.8 and significant correlation, and establish a linear regression equation with the reference sites as independent variables and the target sites as dependent variables. ,in: ； S34. Using reference station data, perform the same frequency analysis steps as steps S4-S7 to obtain the design water level value of the reference station under the target return period. ; S35, Refer to the design water level value of the station Substitute the values ​​into the regression equation to calculate the design water level for the target site during the corresponding return period. ; S36. Draw a scatter plot and regression line between the target site and the reference site.

3. The adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment according to claim 1, characterized in that, Given a return period Corresponding frequency The design water level for Pearson type III distribution is... for: 。 4. The adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment according to claim 1, characterized in that, The formula for calculating the return period water level in the Gumbel distribution is: 。 5. The adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment according to claim 1, characterized in that, The formula for calculating the root mean square error in step S7 is as follows: ； And at the same time, the following suggestion message is displayed: "Data total..." Year, suggested estimate "Recurrence periods of 1 year or less are considered more reliable," among which... .

6. The adaptive calculation method for the return period of hydrological extreme values ​​based on data sufficiency judgment according to claim 1, characterized in that, In step S7, when drawing the Hessian frequency grid, the horizontal axis is converted to the standard normal quantile. ,in The vertical axis represents the inverse function of the standard normal distribution function, and the vertical axis represents the water level value. Plot empirical data scatter points and two theoretical frequency curves, Pearson Type III and Günbel Type, on graph paper; the horizontal axis scale is automatically converted to commonly used frequency values.

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