Method for determining design low water level variation range of river channel downstream of large reservoir

Abstract

This invention relates to the field of hydrological technology, and in particular to a method for determining the variation range of the design low-water level in the downstream channel of a large reservoir. The method includes the following steps: plotting the relationship curve between the daily average water level and the cumulative frequency for each year; selecting the low-water level value corresponding to the guarantee rate determined by the engineering design standards from the relationship curve to form a low-water level sequence; selecting two normalized variables from the low-water level sequence to construct covariates; using multiple probability distribution models to calculate the time-varying parameter values ​​of the low-water level sequence; selecting an optimal model and determining the number of days of previous low-water flow statistics based on the time-varying parameter values; and calculating the variation range of the design low-water level value in the downstream channel of a large reservoir under changing conditions based on the design low-water level value corresponding to the return period. This invention can reflect the non-uniform low-water level under changing environments, providing a scientific basis for engineering planning and design.

Description

Technical Field

[0001] This invention relates to the field of hydrological technology, and in particular to a method for determining the range of design low water level changes in downstream channels of large reservoirs. Background Technology

[0002] The design low water level is a fundamental design parameter in water conservancy and water transport projects such as pumping stations, gates, waterways, ports, and wharves. Its value directly determines the project cost and operational efficiency, making it a crucial parameter for engineering designers. The design low water level of natural rivers is determined through hydrological analysis and calculation, using either the comprehensive duration curve method or the guarantee rate frequency method. However, these methods rely on the assumption that the water level sample sequence must meet the interannual consistency condition, i.e., the independent and identically distributed sample assumption required by traditional hydrological frequency calculations. Under the influence of high-intensity human activities and water conservancy project construction, the physical conditions for the formation of the watershed hydrological cycle and river water level processes have changed significantly, resulting in variability in hydrological processes and hydrological design values. For example, the construction of a large reservoir upstream alters the water and sediment conditions of the downstream river channel, thus affecting the low water level. After the Three Gorges Project was completed and began to regulate water levels during high and low seasons, it altered the annual hydrological process, significantly increasing the flow during the dry season in the downstream river channel. Furthermore, due to reduced sediment, the downstream river channel experienced varying degrees of erosion, leading to significant changes in the river cross-section. Under the combined influence of low-flow-rate and cross-sectional area changes, the low-water level of the Jingjiang River downstream has also undergone significant fluctuations, even threatening the eco-hydrological processes of Dongting Lake and Poyang Lake. If the traditional comprehensive duration curve method and guarantee rate frequency method based on sample consistency are continued to be used to design the low-water level, the designed water level value will not meet actual requirements. To adapt to the demands of environmental change on hydrological analysis and calculation, some scholars have begun to explore methods for determining the design low-water level under changing conditions, including the flow method, reduction method, elimination method, and hydrological analogy method. These methods essentially involve replacing or extracting data from a single station or a specific river section. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a method for determining the variation range of the design low water level in the downstream channel of a large reservoir. This method can reflect the non-uniform low water level under changing environmental conditions, providing a scientific basis for engineering planning and design.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for determining the design low water level variation range of a downstream channel of a large reservoir includes the following steps:

[0006] S1. Plot the relationship between daily average water level and cumulative frequency for each year;

[0007] S2. Based on the guarantee rate specified in the engineering design standards, select the low water level value corresponding to the guarantee rate from the relationship curve to form a low water level sequence;

[0008] S3. Select two normalized variables from the low water level sequence to construct covariates;

[0009] S4. Calculate the time-varying parameter values ​​of the low water level sequence using multiple probability distribution models;

[0010] S5. Select the preferred model and determine the number of days for the previous dry season flow statistics by using time-varying parameter values;

[0011] S6. Calculate the variation range of the design low water level value of the downstream channel of the large reservoir under changing conditions based on the design low water level value corresponding to the return period.

[0012] In step S1, the daily average water level data of the long series of river design cross sections are obtained. For a certain year's water level sample data, the annual water level sample data is divided into several levels according to the difference between the highest and lowest values ​​in the sample data. The cumulative frequency of each level is obtained by the number of times the annual water level sample data appears in each level.

[0013] Using hydrological elements as the vertical axis and cumulative frequency as the horizontal axis, the cumulative frequency values ​​are plotted at the lower limit of each level. By connecting the points, the relationship curve between the daily average water level and the cumulative frequency is obtained.

[0014] Further, in step S2, the low water level value corresponding to the guarantee rate for each year is selected from the relationship curve to obtain the low water level series: ,in, , For the number of years of hydrological monitoring; This refers to the number of years of hydrological monitoring.

[0015] Further, in step S3, the two normalized variables are:

[0016]

[0017]

[0018] in, Low water level series The average low-water flow rate of this river section on day D prior; For the first Annual water level The following is the actual cross-sectional area of ​​the river channel.

[0019] Further, in step S4, the low water level sequence is represented by a probability function, where the covariates characterize the changes in location and scale parameters. The maximum value of the probability function and the corresponding time-varying parameter values ​​are calculated using multiple probability distribution models. The probability function is:

[0020] Formula (1)

[0021] in, Let be the probability function of the low water level sequence. For two time-varying parameter values, The location parameters of the probability distribution. is the scaling parameter of the probability distribution;

[0022] Formula (2)

[0023] in, It is a constant coefficient.

[0024] Further, in step S5, the maximum value is obtained based on multiple probability distribution models, the corresponding evaluation index is calculated, and the probability distribution model with the smallest evaluation index is selected as the preferred model. The average dry flow of the river section before the dry water level series is determined through the preferred model.

[0025] Furthermore, in step S5, the evaluation index is calculated as follows:

[0026] Formula (3)

[0027] in, As evaluation indicators; This is the maximum value of the probability function; For the penalty function; This represents the overall degrees of freedom in the model.

[0028] Further, in step S6, based on the average low-water flow of the river section D days prior to the low-water series, two normalized variables are determined to calculate the probability density function and probability distribution function of the preferred model. Based on the inverse function of the probability distribution function of each sample's year, the design low-water level value corresponding to the specified return period is calculated. Based on the design low-water level value corresponding to the return period, the variation range of the design low-water level value of the downstream river of the large reservoir under changing conditions is calculated.

[0029] Furthermore, the calculation method for the magnitude of the change is as follows:

[0030] Formula (4)

[0031] in, The range of change; The number of years before the reservoir was built. The number of years since the reservoir was built, and ; This specifies the design low water level value corresponding to the specified return period.

[0032] Furthermore, the calculation method for the design low water level corresponding to the specified return period is as follows:

[0033] Formula (5)

[0034] in, It is the inverse function of the probability distribution function of the year in which each sample is located; To specify the return period; The time-varying parameter value corresponding to the maximum value of the probability function obtained by calculating the optimal model.

[0035] The beneficial effects of this invention are:

[0036] By plotting hydrological elements on the ordinate and cumulative frequency on the abscissa, each cumulative frequency value is plotted at the lower limit corresponding to each level. Connecting these points forms a daily average water level-cumulative frequency relationship curve, thus creating an annual low water level sequence corresponding to a specific guarantee rate. For rivers with large reservoirs regulating upstream, the low water level series in adjacent downstream sections exhibits significant trends due to the combined influence of low water flow and changes in river cross-section. By constructing covariates using two normalized variables in the low water level sequence, these covariates can reflect changes in low water flow and river cross-section. Distributions that reflect the changing characteristics of the low water level sequence, such as Gumbel distribution, Weibull distribution, Gamma distribution, Logistic distribution, Log-normal distribution, and Normal distribution, are employed. The probability distribution model of Bu et al. uses continuous distributions of two time-varying parameters as candidate probability distribution sets, and fits low water level series with different distributions to estimate the time-varying parameter values ​​of the distribution. The changes in location parameters and scale parameters are characterized by covariates. The optimal model is selected from the probability distribution models using evaluation indicators to determine the value of the statistical days D of the previous low water flow, thereby determining two normalized variables. Using the known normalized variables, the design low water level value corresponding to the specified return period is calculated by the inverse function of the probability distribution function of the optimal model. Furthermore, by comparing the average design low water level before and after the reservoir is built, the variation range of the design low water level value of the downstream river channel of the large reservoir under changing conditions can be calculated. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to a preferred embodiment of the present invention. Detailed Implementation

[0038] 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.

[0039] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0040] See Figure 1 A preferred embodiment of the present invention provides a method for determining the design low water level variation range of a downstream channel of a large reservoir, comprising the following steps:

[0041] S1. Plot the relationship between the daily average water level and the cumulative frequency for each year.

[0042] In step S1, the daily average water level data of the long series of river design cross sections are obtained. For a certain year's water level sample data, the annual water level sample data is divided into several levels according to the difference between the highest and lowest values ​​in the sample data. The cumulative frequency of each level is obtained by the number of times the annual water level sample data appears in each level.

[0043] Using hydrological elements as the vertical axis and cumulative frequency as the horizontal axis, the cumulative frequency values ​​are plotted at the lower limit of each level. By connecting the points, the relationship curve between the daily average water level and the cumulative frequency is obtained.

[0044] In this embodiment, the high and low water levels are typically defined as 5 cm to 10 cm per level, and the medium water level is defined as 20 cm per level. By statistically analyzing the number of times the sample appears in different levels, the cumulative frequency of the sample is calculated from high to low.

[0045] S2. Based on the guarantee rate specified in the engineering design standards, select the low water level value corresponding to the guarantee rate from the relationship curve to form a low water level sequence.

[0046] In step S2, the low water level values ​​corresponding to the guarantee rate for each year are selected from the relationship curve to obtain the low water level series: ,in, , For the number of years of hydrological monitoring; This refers to the number of years of hydrological monitoring.

[0047] S3. Select two normalized variables from the low water level series to construct covariates.

[0048] In step S3, the two normalized variables are:

[0049]

[0050]

[0051] in, Low water level series The average low-water flow rate of this river section on day D prior; For the first Annual water level The following is the actual cross-sectional area of ​​the river channel.

[0052] In this embodiment, the cross-section was calculated from the measured river channel cross-section diagram in the hydrological yearbook. Since the river channel cross-section is constantly changing due to scouring, therefore... It has also been constantly changing.

[0053] S4. Calculate the time-varying parameter values ​​of the low water level sequence using multiple probability distribution models.

[0054] In step S4, the low water level sequence is represented by a probability function, with covariates characterizing the changes in location and scale parameters. The maximum value of the probability function and the corresponding time-varying parameter values ​​are calculated using multiple probability distribution models. The probability function is:

[0055] Formula (1)

[0056] in, Let be the probability function of the low water level sequence. For two time-varying parameter values, The location parameters of the probability distribution. is the scaling parameter of the probability distribution;

[0057] Formula (2)

[0058] in, It is a constant coefficient, and its value can be determined through optimization.

[0059] In this embodiment, the probability distribution models include Gumbel distribution, Weibull distribution, gamma distribution, logistic distribution, log-normal distribution, and normal distribution, which can reflect the characteristics of low water level series changes. These models are used as candidate probability distribution sets for the low water level series. Statistical modeling is performed, and the time-varying parameter values ​​of the model are estimated using the maximum likelihood method.

[0060] Inconsistent low water level sequence The probability density function can be expressed as Covariates are used to characterize the changes in location and scale parameters. The log-likelihood function is calculated mathematically. maximum value and the corresponding time-varying parameter values .

[0061] S5. Select the preferred model and determine the number of days for the previous dry season flow statistics by using time-varying parameter values.

[0062] In step S5, the maximum value is obtained based on multiple probability distribution models, the corresponding evaluation index is calculated, and the probability distribution model with the smallest evaluation index is selected as the preferred model. The average flow rate of the river section during the dry season D days before the dry season series is determined by the preferred model.

[0063] In step S5, the evaluation index is calculated as follows:

[0064] Formula (3)

[0065] in, As evaluation indicators; This represents the maximum value of the probability function. For the penalty function; This represents the overall degrees of freedom in the model.

[0066] In this embodiment, for alternative probability distributions such as Gumbel distribution, Weibull distribution, Gamma distribution, logistic distribution, lognormal distribution, and normal distribution, different statistical days D of previous low water flow, and different degrees of freedom, the corresponding evaluation indicators are calculated and compared. The size of the parameter is used to select the candidate probability distribution model that minimizes the evaluation index as the preferred model, and the value of the number of days D during the previous dry season is determined. The probability density function of the preferred model can be obtained using... In other words, the probability distribution function is represented by... express.

[0067] S6. Calculate the variation range of the design low water level value of the downstream channel of the large reservoir under changing conditions based on the design low water level value corresponding to the return period.

[0068] In step S6, based on the average low-water flow of the river section D days prior to the low-water series, two normalized variables are determined to calculate the probability density function and probability distribution function of the preferred model. Based on the inverse function of the probability distribution function of each sample year, the design low-water level value corresponding to the specified return period is calculated. Based on the design low-water level value corresponding to the return period, the variation range of the design low-water level value of the downstream river of the large reservoir under changing conditions is calculated.

[0069] The calculation method for the magnitude of change is as follows:

[0070] Formula (4)

[0071] in, The range of change; The number of years before the reservoir was built. The number of years since the reservoir was built, and ; This specifies the design low water level value corresponding to the specified return period.

[0072] The calculation method for the design low water level corresponding to a specified return period is as follows:

[0073] Formula (5)

[0074] in, It is the inverse function of the probability distribution function of the year in which each sample is located; To specify the return period; The time-varying parameter value corresponding to the maximum value of the probability function obtained by calculating the optimal model.

[0075] In this embodiment, the return period T is determined according to the design standards for water conservancy projects. Then, for the inconsistent low water level sequence, the probability distribution function of each sample's year is used... The inverse function is used to calculate the design low water level corresponding to a specified return period T.

[0076] Using the year when a large reservoir was built and began to play a regulatory role as a time node, the low water level data series is divided into two parts: the years before the reservoir was built and the years before the reservoir began to function. Year, after completion there will be By comparing the average annual design low water level before and after the reservoir's construction, the variation range of the design low water level in the downstream channel of a large reservoir under changing conditions can be calculated.

Claims

1. A method for determining the design low water level variation range of a downstream river channel of a large reservoir, characterized in that, Includes the following steps: S1. Plot the relationship between daily average water level and cumulative frequency for each year; S2. Based on the guarantee rate specified in the engineering design standards, select the low water level value corresponding to the guarantee rate from the relationship curve to form a low water level sequence; S3. Select two normalized variables from the low water level sequence to construct covariates; S4. Calculate the time-varying parameter values ​​of the low water level sequence using multiple probability distribution models; S5. Select the preferred model and determine the number of days for the previous dry season flow statistics by using time-varying parameter values; S6. Calculate the variation range of the design low water level value of the downstream channel of the large reservoir under changing conditions based on the design low water level value corresponding to the return period.

2. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 1, characterized in that: In step S1, the daily average water level data of the long series of river design cross sections are obtained. For a certain year's water level sample data, the annual water level sample data is divided into several levels according to the difference between the highest and lowest values ​​in the sample data. The cumulative frequency of each level is obtained by the number of times the annual water level sample data appears in each level. Using hydrological elements as the vertical axis and cumulative frequency as the horizontal axis, the cumulative frequency values ​​are plotted at the lower limit of each level. By connecting the points, the relationship curve between the daily average water level and the cumulative frequency is obtained.

3. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 1, characterized in that: In step S2, the low water level values ​​corresponding to the guarantee rate for each year are selected from the relationship curve to obtain the low water level series: ,in, , For the number of years of hydrological monitoring; This refers to the number of years of hydrological monitoring.

4. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 3, characterized in that: In step S3, the two normalized variables are: in, Low water level series The average low-water flow rate of this river section on day D prior; For the first Annual water level The following is the actual cross-sectional area of ​​the river channel.

5. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 4, characterized in that: In step S4, the low water level sequence is represented by a probability function, where the covariates characterize the changes in location and scale parameters. The maximum value of the probability function and the corresponding time-varying parameter values ​​are calculated using multiple probability distribution models. The probability function is: Official (1) in, Let be the probability function of the low water level sequence. For two time-varying parameter values, The location parameters of the probability distribution. is the scaling parameter of the probability distribution; Official (2) in, It is a constant coefficient.

6. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 5, characterized in that: In step S5, the maximum value is obtained based on multiple probability distribution models, the corresponding evaluation index is calculated, and the probability distribution model with the smallest evaluation index is selected as the preferred model. The average flow rate of the river section during the dry season D days before the dry season is determined through the preferred model.

7. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 6, characterized in that: In step S5, the evaluation index is calculated as follows: Official (3) in, As evaluation indicators; This is the maximum value of the probability function; For the penalty function; This represents the overall degrees of freedom in the model.

8. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 6, characterized in that: In step S6, based on the average low-water flow of the river section D days prior to the low-water series, two normalized variables are determined to calculate the probability density function and probability distribution function of the preferred model. Based on the inverse function of the probability distribution function of each sample's year, the design low-water level value corresponding to the specified return period is calculated. Based on the design low-water level value corresponding to the return period, the variation range of the design low-water level value of the downstream river of the large reservoir under changing conditions is calculated.

9. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 8, characterized in that: The calculation method for the magnitude of the change is as follows: Official (4) in, The range of change; The number of years before the reservoir was built. The number of years since the reservoir was built, and ; This specifies the design low water level value corresponding to the specified return period.

10. The method for determining the variation range of the design low water level in the downstream channel of a large reservoir according to claim 8, characterized in that: The calculation method for the design low water level corresponding to a specified return period is as follows: Official (5) in, It is the inverse function of the probability distribution function of the year in which each sample is located; To specify the return period; The time-varying parameter value corresponding to the maximum value of the probability function obtained by calculating the optimal model.

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