Small watershed design flood calculation method based on unified recurrence period

Abstract

The invention discloses a small watershed design flood reckoning method based on a unified return period, and the method comprises the steps: building a unified flow-area-return period relation of a region, fusing the information of a reference station and a plurality of survey sections, breaking through the limitation that the areas of single stations must be similar, and achieving the robust extension of a flood law from large and medium watershed to small watershed; a physical mechanism is formed based on regional flood, and the consistency of rules is ensured through multi-frequency data joint calibration; the calculation process only needs the catchment area and the design standard of the target small watershed, does not need to actually measure a rainstorm or flood sequence, is particularly suitable for the grassroots water conservancy department, and is high in practicability and easy to popularize in areas with similar climate and underlying surface conditions.

Description

Technical Field

[0001] This invention belongs to the field of hydrological analysis technology for water conservancy projects, and relates to a method for estimating design floods in small watersheds based on a unified return period. Background Technology

[0002] Small watershed water conservancy projects are crucial infrastructure for flood prevention and rural water supply security. The accuracy of their design flood parameters directly determines the project's flood control capacity and the rationality of its investment. Currently, for watersheds with a catchment area generally not exceeding 500 km²... 2 In small mountainous watersheds, design flood projection faces the dual bottlenecks of "data scarcity" and "scale mismatch." Specific problems are as follows: 1. Data scarcity: These small watersheds generally lack hydrological stations, making it impossible to directly apply frequency analysis methods based on measured sequences.

[0003] 2. Scale mismatch: Existing extrapolation methods all have significant limitations: Hydrological analogy method: Its applicability is based on the premise that the reference watershed and the design watershed have similar hydrological conditions and similar areas. In engineering practice, when the area difference exceeds ±30%, the nonlinear differences in the flood formation mechanism will lead to a sharp increase in estimation errors, making direct application risky. Moreover, the control area of ​​available hydrological stations in the region is usually much larger than many target small watersheds, resulting in a serious scale mismatch.

[0004] Heavy rainfall projection method: It relies on designing heavy rainfall parameters in small watersheds. These parameters are often obtained by interpolation from sparse rain gauge networks, which are inherently uncertain and will amplify the error in the final flood calculation.

[0005] Regional empirical formulas are mostly based on fitting data from limited hydrological stations. The formula structure (such as the area index) does not consider the unified laws under multiple frequencies, resulting in poor adaptability and no guarantee of accuracy when extended to watersheds of different areas.

[0006] Therefore, there is an urgent need for a calculation method that can overcome the limitations of single-station area and is based on a unified physical mechanism of regional flood formation, so as to achieve robust estimation of design floods in small watersheds without data. Summary of the Invention

[0007] The purpose of this invention is to provide a method for estimating design floods in small watersheds based on a unified return period, which solves the problem of large errors in estimating design floods in small watersheds due to mismatched areas of reference stations and scarcity of rainstorm data in the prior art.

[0008] The technical solution adopted in this invention is a method for estimating design floods in small watersheds based on a unified return period, applicable to catchment areas of no more than 500 km². 2 For small watersheds in mountainous areas where no measured hydrological data is available, the specific steps include: Step 1: Construct a regional reference system and determine basic parameters; the regional reference system includes at least one benchmark station and two survey sections within the target hydrological area; Step 2: Calculate the return periods for different survey sections. Design peak flow ; Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding frequency parameters ; Step 4: Establish frequency coefficients With recurrence period Association model; Step 5: Calculate the design peak flow of the target frequency in the small watershed using the power function model and the correlation model.

[0009] The invention is further characterized by: In step 1, the reference station is a hydrological station with a long series of measured annual maximum flood peak flow data; the survey section is a section with reliable historical flood survey information; the basic parameters include flood statistical parameters of the target hydrological area and historical flood survey information of the survey section; the flood statistical parameters include the coefficient of variation. and skewness coefficient Historical flood survey information includes peak flow rates. With recurrence period .

[0010] The flood statistical parameters of the survey section and the benchmark station are the same, and the statistical parameters for the target hydrological area are obtained as follows: , .

[0011] The specific process in step 2 is as follows: Step 2.1: Determine the multi-year average peak flood discharge of each survey section by back-calculation through frequency analysis. ; Step 2.2, based on the reverse calculation and statistical parameters within the target hydrological region , The hydrological frequency curves were used to calculate the hydrological frequency curves at various cross sections with different return periods. Design peak flow .

[0012] In step 2.1, the reverse calculation The specific process is as follows: based on the return period of the flood at the survey section... Find the deviation coefficient from the mean of the P-III type frequency curve. The result is obtained by reverse calculation using formula (1). , (1), In formula (1), For the corresponding frequency The modulus ratio.

[0013] Step 3 specifically involves: The survey section under different return periods With the corresponding catchment area A power function was used for fitting, and the goodness of fit R0 was obtained. 2 Greater than 0.9; Establish a power function relationship model: (2), In formula (2), This is the area index, with a value ranging from 0.65 to 0.75; This corresponds to the frequency.

[0014] The goodness of fit R² for the power function relationship model for each return period data is no less than 0.9.

[0015] In step 4, the association model exhibits a significant logarithmic function relationship, specifically: (3); Goodness of fit R of the correlation model 2 Greater than 0.9.

[0016] The specific steps in step 5 are as follows: Step 5.1: Determine the catchment area of ​​the target small watershed. and design recurrence period ; Step 5.2: Calculate the corresponding return period correlation coefficient using the frequency coefficient association model; Step 5.3: Substitute the values ​​into the multi-frequency peak flow-area power function model to calculate the design peak flow for the small watershed. .

[0017] The target small watershed and the hydrological region where the regional reference system is constructed are located in the same hydro-meteorological consistency zone.

[0018] The beneficial effects of this invention are: 1. Solved the scale mismatch problem: This invention integrates the information of the benchmark station with multiple survey sections by constructing a unified "flow-area-return period" relationship in the region, breaking through the limitation that the area of ​​a single station must be similar, and realizing a robust extension of flood patterns from large and medium watersheds to small watersheds; 2. High accuracy and strong reliability: The method is based on the physical mechanism of regional flood formation and ensures the consistency of the patterns through joint calibration of multi-frequency data; 3. Highly practical and easy to promote: The calculation process only requires the catchment area and design standards of the target small watershed, without the need for measured rainstorm or flood sequences, making it particularly suitable for grassroots water conservancy departments. In areas with similar climate and underlying surface conditions, only one model parameter calibration is required before it can be extended to small watersheds without data. Attached Figure Description

[0019] Figure 1 This is a graph showing the relationship between the multi-frequency peak flow and catchment area of ​​the Jialing River main stream in Embodiment 1 of the present invention. Figure 2 The main stream of the Jialing River in Embodiment 1 of this invention Correlation curve between value and return period. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0021] This invention provides a method for estimating design floods in small watersheds based on a unified return period, applicable to catchment areas not exceeding 500 km². 2 For small watersheds in mountainous areas where no measured hydrological data is available, the following steps will be taken based on the standardization of regional flood patterns: Step 1: Construct a regional reference system and determine basic parameters; The regional reference system includes at least one reference station and two survey sections within the target hydrological area; the reference station is a hydrological station with a long series of measured annual maximum flood peak flow data; and the survey section is a section with reliable historical flood survey information.

[0022] The basic parameters include flood statistics for the target hydrological area and historical flood survey information for the survey sections; the flood statistics parameters include the coefficient of variation. and skewness coefficient Historical flood survey information includes peak flow rates. With recurrence period .

[0023] Determine flood statistical parameters using frequency analysis results from reference stations. , The flood statistical parameters of the survey section are the same as those of the benchmark station, meaning the statistical parameters within the target hydrological area are... , .

[0024] Step 2: Calculate the return periods for different survey sections. Design peak flow ; Step 2.1: Determine the multi-year average peak flood discharge of each survey section by back-calculation through frequency analysis. Specifically, this refers to: based on the return period of floods at the survey cross-section. Find the deviation coefficient from the mean of the P-III type frequency curve. The result is obtained by reverse calculation using formula (1). , (1), In formula (1), For the corresponding frequency (or recurrence period) The modulus ratio; Step 2.2, based on the reverse calculation and statistical parameters within the target hydrological region , The hydrological frequency curves were used to calculate the hydrological frequency curves at various cross sections with different return periods. ( Design peak flow rates for different frequencies .

[0025] Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding correlation coefficient during the return period .

[0026] By jointly fitting multiple sets of data with different return periods, that is, by combining the data from all survey sections obtained in step 2 under different return periods... With the corresponding catchment area A power function was used for fitting, and the goodness of fit R0 was obtained. 2 Greater than 0.9; Establish a power function relationship model: (2), In formula (2), This is the area index, with a value ranging from 0.65 to 0.75; This corresponds to the frequency.

[0027] Based on the physical mechanism of regional flood formation (manifested as a fixed area index) By combining and calibrating multi-frequency data, the consistency of the patterns was ensured.

[0028] Step 4: Establish frequency coefficients With recurrence period Association model; Under each recurrence period The correlation curves on a log-log scale are a pair of parallel lines, representing the correlation coefficient over the return period. With recurrence period Change; Establishment With recurrence period The correlation model exhibits a significant logarithmic functional relationship. The correlation model is as follows: (3), Goodness of fit R of the correlation model 2 Greater than 0.9.

[0029] Step 5: Calculate the design peak flow rate of the target small watershed frequency.

[0030] For extrapolating the data for a target small watershed within a region where no data is available, the specific procedure is as follows: Step 5.1: Determine the catchment area of ​​the target small watershed. and design recurrence period The design return period is determined according to standard SL252-2017. Step 5.2: Calculate the corresponding coefficient values ​​using the frequency coefficient correlation model; Step 5.3: Substitute the values ​​into the multi-frequency peak flow-area power function model to calculate the design peak flow for the small watershed. .

[0031] Step 6: Verify the calculation results of Step 5 using historical flood survey values ​​of the target small watershed or adjacent watersheds.

[0032] Example 1 This embodiment uses a small-basin design flood estimation method based on a unified return period for the main stream and tributaries of the Jialing River (Huangniupu to Ciba section), and is implemented according to the following steps: Step 1: Construct a regional reference system and determine basic parameters; Step 1.1: Select Fengzhou Hydrological Station (catchment area 688 km²) 2 Using a long series of data as the base station, and supplementing it with two historical flood survey sections, Huangniupu and Honghuapu, together they constitute the reference system for this river section; through frequency analysis, the statistical parameters of Fengzhou station were determined. =1.15、 =3.45 ( =3.0), and these two parameters were transferred to the Huangniupu and Honghuapu sections.

[0033] Step 2: Calculate the multi-frequency design peak flow; Step 2.1: Taking the Huangniupu section as an example, its maximum historical flood return period is known to be 220 years, and the peak flood flow is 806 m³ / s; by back-calculating using the P-III type frequency curve, the cross-section can be obtained. =112.1 m³ / s; Step 2.2: Based on the theory in "Principles of Hydrology" (4th Edition, by Rui Xiaofang) that "the peak flow of a mountain watershed has a power function relationship with the catchment area," and based on the determined locations of Huangniupu and Honghuapu... Values ​​and statistical parameters ( =1.15、 =3.45), calculate different frequencies .

[0034] Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding correlation coefficient during the return period ; Based on the design peak flow results of Fengzhou Station and Ciba Station, the peak flow at different frequencies at four cross-sections was fitted to establish a multi-frequency peak flow-area power function model. ;like Figure 1 As shown in the graph, the horizontal axis of the graph depicting the relationship between the multi-frequency peak flow and the catchment area of ​​the main stream of the Jialing River (Huangniupu to Ciba section) represents the catchment area. (km) 2 The vertical axis represents the peak flow rate. (m) 3 The graph contains six curves: a 10-year, 20-year, 50-year, 100-year, and 220-year return period curve, and the average curve, each labeled with its corresponding power function formula.

[0035] Step 4: Establish a frequency coefficient correlation model Goodness of fit R 2 =0.9999; for example Figure 2 As shown, the main stream of the Jialing River In the curve graph showing the relationship between return value and return period, the horizontal axis represents the return period. (Year), with the vertical axis as .

[0036] Step 5: Calculate the design peak flow rate for the target small watershed frequency; With a catchment area of ​​210 km² 2 Taking a small watershed (without hydrological stations) as an example: if the design return period is 50 years ( =50), calculate first Substitute =13.59×210 0.68 =516m 3 / s; and the adjacent Huangniupu section (210km) 2 50-year return period design value (527m) 3 The deviation of only 2.2% ( / s) meets the accuracy requirements of hydrological analysis, verifying the effectiveness of the method.

[0037] Example 2 In this embodiment, the method for estimating design floods in small watersheds based on a unified return period is applied to the Baliguan section (F=107km²) of the Beizhan River, a left-bank tributary of the Baohe River, a tributary of the Han River. The specific implementation steps are as follows: Step 1: Construct a regional reference system and determine basic parameters; Baliguan is located in Liuba County, Hanzhong City, Shaanxi Province, with a catchment area of ​​F=107km². 2 It belongs to the mid-mountain canyon landform of the Qinba Mountains and has a similar hydrological underlying surface height to the Huangniupu-Ciba section of the main stream of the Jialing River (both belong to the Qinba Mountains, with a difference of ≤10% in topography and vegetation characteristics). It was also the center of the "Hanzhong-Baoji" super rainstorm in 1981 ("Investigation Report on the 1981 Super Flood in Shaanxi Province"). The causes and spatial and temporal distribution of the rainstorm are completely consistent, and the flood formation mechanism is the same.

[0038] Confirmation of 1981 Historical Flood Data and Recurrence Period: According to the "Shaanxi Province Flood Survey Data", the flood at Baliguan on August 21, 1981, was the largest flood during the survey period, with a peak flow of 471 m³ / h. 3 This flood, along with the 1981 floods at Fengzhou and Ciba stations on the main stream of the Jialing River, was caused by the same torrential rain and originated from the same source. Therefore, the recurrence period of the 1981 flood in the Baliguan small watershed is determined to be consistent with that of the Fengzhou and Ciba floods, which is a 220-year return period, i.e., the design recurrence period. =220 years.

[0039] Step 2: Calculate the multi-frequency design peak flow.

[0040] Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region, and obtain the correlation coefficient of return period for different return periods. .

[0041] Step 4: Establish a correlation model between frequency coefficients and return periods.

[0042] Step 5: Calculate the design peak flow rate for the target small watershed frequency; Design flood calculation: =20.16×107 0.68 =484m 3 / s.

[0043] Step 6: Verify the estimation results of Step 5 using historical flood survey values ​​from the target small watershed or adjacent watersheds; Design value 484m 3 / s, compared to the survey value of 471m 3 The deviation is 2.8%, which meets the accuracy requirements.

[0044] The above typical examples show that the deviation between the calculated results and the historical flood survey values ​​or the design values ​​of adjacent sections can be controlled within 5%, which is significantly better than the traditional hydrological analogy method.

[0045] Example 3 The method for estimating design floods in small watersheds based on a unified return period in this embodiment is applicable to catchment areas of no more than 500 km². 2For small watersheds in mountainous areas where no measured hydrological data is available, the following steps should be followed: Step 1: Construct a regional reference system and determine basic parameters; The regional reference system includes at least one reference station and two survey sections within the target hydrological area; The reference station is a hydrological station with a long series of measured annual maximum flood peak flow data; the survey section is a section with reliable historical flood survey information; The basic parameters include flood statistics for the target hydrological area and historical flood survey information for the survey sections; the flood statistics parameters include the coefficient of variation. and skewness coefficient Historical flood survey information includes peak flow rates. With recurrence period ; The flood statistical parameters of the survey section and the benchmark station are the same, and the statistical parameters for the target hydrological area are obtained as follows: , .

[0046] Step 2: Calculate the return periods for different survey sections. Design peak flow .

[0047] Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding frequency parameters .

[0048] Step 4: Establish frequency coefficients With recurrence period The association model.

[0049] Step 5: Calculate the design peak flow of the target frequency in the small watershed using the power function model and the correlation model.

[0050] Example 4 The method for estimating design floods in small watersheds based on a unified return period in this embodiment is applicable to catchment areas of no more than 500 km². 2 For small watersheds in mountainous areas where no measured hydrological data is available, the following steps should be followed: Step 1: Construct a regional reference system and determine basic parameters; The regional reference system includes at least one reference station and two survey sections within the target hydrological area; The reference station is a hydrological station with a long series of measured annual maximum flood peak flow data; the survey section is a section with reliable historical flood survey information; The basic parameters include flood statistics for the target hydrological area and historical flood survey information for the survey sections; the flood statistics parameters include the coefficient of variation. and skewness coefficient Historical flood survey information includes peak flow rates. With recurrence period ; The flood statistical parameters of the survey section and the benchmark station are the same, and the statistical parameters for the target hydrological area are obtained as follows: , .

[0051] Step 2: Calculate the return periods for different survey sections. Design peak flow .

[0052] The specific process in step 2 is as follows: Step 2.1: Determine the multi-year average peak flood discharge of each survey section by back-calculation through frequency analysis. ; Reverse push The specific process is as follows: based on the return period of the flood at the survey section... Find the deviation coefficient from the mean of the P-III type frequency curve. The result is obtained by reverse calculation using formula (1). , (1), In formula (1), For the corresponding frequency The modulus ratio; Step 2.2, based on the reverse calculation and statistical parameters within the target hydrological region , The hydrological frequency curves were used to calculate the hydrological frequency curves at various cross sections with different return periods. Design peak flow .

[0053] Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding frequency parameters .

[0054] Step 4: Establish frequency coefficients With recurrence period The association model.

[0055] Step 5: Calculate the design peak flow of the target frequency in the small watershed using the power function model and the correlation model.

[0056] Example 5 The method for estimating design floods in small watersheds based on a unified return period is applicable to catchment areas of no more than 500 km². 2 For small watersheds in mountainous areas where no measured hydrological data is available, the following steps should be followed: Step 1: Construct a regional reference system and determine basic parameters; The regional reference system includes at least one benchmark station and two survey sections within the target hydrological area.

[0057] Step 2: Calculate the return periods for different survey sections. Design peak flow .

[0058] Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding frequency parameters ; The survey section under different return periods With the corresponding catchment area A power function was used for fitting, and the goodness of fit R0 was obtained. 2 Greater than 0.9; Establish a power function relationship model: (2), In formula (2), This is the area index, with a value ranging from 0.65 to 0.75; For the corresponding frequency; The goodness of fit R² for the power function relationship model for each return period data is no less than 0.9.

[0059] Step 4: Establish frequency coefficients With recurrence period Association model; The association model exhibits a significant logarithmic functional relationship, specifically: (3); Goodness of fit R of the correlation model 2 Greater than 0.9.

[0060] Step 5: Calculate the design peak flow of the target frequency in the small watershed using the power function model and the correlation model.

[0061] Example 6 The method for estimating design floods in small watersheds based on a unified return period, as described in this embodiment, is applicable to catchment areas of no more than 500 km². 2 For small watersheds in mountainous areas where no measured hydrological data is available, the following steps should be followed: Step 1: Construct a regional reference system and determine basic parameters; The regional reference system includes at least one reference station and two survey sections within the target hydrological area; Step 2: Calculate the return periods for different survey sections. Design peak flow ; Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding frequency parameters ; Step 4: Establish frequency coefficients With recurrence period Association model; Step 5: Calculate the design peak flood discharge of the target frequency in the small watershed using a power function model and a correlation model; the target small watershed and the hydrological region where the regional reference system is constructed are located in the same hydro-meteorological consistency zone; the specific operation is as follows: Step 5.1: Determine the catchment area of ​​the target small watershed. and design recurrence period ; Step 5.2: Calculate the corresponding return period correlation coefficient using the frequency coefficient association model; Step 5.3: Substitute the values ​​into the multi-frequency peak flow-area power function model to calculate the design peak flow for the small watershed. .

Claims

1. A method for estimating design floods in small watersheds based on a unified return period, applicable to catchment areas not exceeding 500 km². 2 Furthermore, in small mountain watersheds where no measured hydrological data is available, the characteristic is that... The specific steps are as follows: Step 1: Construct a regional reference system and determine basic parameters; The regional reference system includes at least one reference station and two survey sections within the target hydrological area; Step 2: Calculate the return periods for different survey sections. Design peak flow ; Step 3: Establish a multi-frequency peak flow-area power function model for the target hydrological region to obtain the results for different return periods. Corresponding frequency parameters ; Step 4: Establish frequency coefficients With recurrence period The association model; Step 5: Calculate the design peak flow of the target frequency in the small watershed using the power function model and the correlation model.

2. The method for estimating small watershed design floods based on a unified return period according to claim 1, characterized in that, In step 1, the reference station is a hydrological station with a long series of measured annual maximum flood peak flow data; the survey section is a section with reliable historical flood survey information. The basic parameters include flood statistics for the target hydrological area and historical flood survey information for the survey sections; the flood statistics parameters include the coefficient of variation. and skewness coefficient Historical flood survey information includes peak flow rates. With recurrence period .

3. The method for estimating small watershed design floods based on a unified return period according to claim 2, characterized in that, The flood statistical parameters of the survey section are the same as those of the benchmark station, and the statistical parameters obtained for the target hydrological area are as follows: , .

4. The method for estimating small watershed design floods based on a unified return period according to claim 3, characterized in that, The specific process in step 2 is as follows: Step 2.1: Determine the multi-year average peak flood discharge of each survey section by back-calculation through frequency analysis. ; Step 2.2, based on the reverse calculation and statistical parameters within the target hydrological region , The hydrological frequency curves were used to calculate the hydrological frequency curves at various cross sections with different return periods. Design peak flow .

5. The method for estimating small watershed design floods based on a unified return period according to claim 4, characterized in that, The reverse calculation in step 2.1 The specific process is as follows: based on the return period of the flood at the survey section... Find the deviation coefficient from the mean of the P-III type frequency curve. The result is obtained by reverse calculation using formula (1). , （1）， In formula (1), For the corresponding frequency The modulus ratio.

6. The method for estimating small watershed design floods based on a unified return period according to claim 1, characterized in that, Step 3 specifically involves: The survey section under different return periods With the corresponding catchment area A power function was used for fitting, and the goodness of fit R0 was obtained. 2 Greater than 0.9; Establish a power function relationship model: （2）， In formula (2), This is the area index, with a value ranging from 0.65 to 0.75; This corresponds to the frequency.

7. The method for estimating small watershed design floods based on a unified return period according to claim 6, characterized in that, The goodness of fit R² of the power function relationship model for each return period data is no less than 0.

9.

8. The method for estimating small watershed design floods based on a unified return period according to claim 1, characterized in that, In step 4, the association model exhibits a significant logarithmic function relationship, specifically: （3）； Goodness of fit R of the correlation model 2 Greater than 0.

9.

9. The method for estimating small watershed design floods based on a unified return period according to claim 1, characterized in that, The specific operation of step 5 is as follows: Step 5.1: Determine the catchment area of ​​the target small watershed. and design recurrence period ; Step 5.2: Calculate the corresponding return period correlation coefficient using the frequency coefficient association model; Step 5.3: Substitute the values ​​into the multi-frequency peak flow-area power function model to calculate the design peak flow for the small watershed. .

10. The method for estimating small watershed design floods based on a unified return period according to claim 9, characterized in that, The target small watershed and the hydrological region where the regional reference system is constructed are located in the same hydro-meteorological consistency zone.

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