Drainage basin flood law analysis method considering plum rain temporal and spatial variation

Abstract

The invention discloses a basin flood law analysis method considering plum rain temporal and spatial variation. The method comprises the following steps: step 1, obtaining index parameter characteristic relations of plum entering and exiting time, plum rain amount and plum rain intensity of plum rain in the middle and lower reaches of the Yangtze River through a time sequence analysis method; 2, utilizing a Copula function to carry out the flood encountering risk assessment process of the upstream main and tributaries of the Yangtze River; 3, according to a mathematical statistical method, the plum rain characteristics and the encounter law of the stage flood in the upstream flood season are explored; certain reference can be provided for construction management of water conservancy projects, a scientific basis is provided for improving flood control capacity of a drainage basin and guaranteeing flood control safety, and effective support is provided for formulating a feasible strategy for efficient utilization of water resources for a reservoir group.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological statistics of hydrology and water resources, in particular to a method for analyzing the laws of basin floods considering the spatio-temporal variation of plum rains. Background Art

[0002] The impounding and utilization of flood resources can effectively reduce flood pressure and alleviate the contradiction between water supply and demand, which is an important measure to ensure flood control safety and a practical choice for "developing new sources" of water resources. Under such a background, it is of great practical significance to identify the characteristics of basin rainstorms and floods, analyze the spatio-temporal laws of rain-flood encounters, and on this basis, reasonably divide the flood season boundaries and scientifically regulate the flood resources of cascade reservoirs. However, there are still few studies on how basin rainstorms and floods trigger flood encounters, affect the characteristics of flood season staging, and influence the selection of water conservancy project scheduling times. The exploration of the underlying mechanisms behind these problems also needs to be further deepened.

[0003] In summary, studying the spatio-temporal variation laws of basin rainfall and floods, revealing the internal connections between rain-flood characteristic attributes, conducting basin hydrological analysis and calculation, and quantitatively evaluating the flood encounter risks of main and tributary rivers are of great significance for flood control and water utilization in the basin. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above deficiencies and provide a method for analyzing the laws of basin floods considering the spatio-temporal variation of plum rains, aiming to provide certain references for the implementation, construction and management of water conservancy projects, provide a scientific basis for improving the flood control ability and ensuring flood control safety in the basin, and provide effective support for formulating feasible strategies for efficient utilization of water resources in reservoir groups.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a method for analyzing the laws of basin floods considering the spatio-temporal variation of plum rains, which includes the following steps:

[0006] Step 1, obtaining the characteristic relationship between the entering and leaving times of plum rains, the plum rain amount and the plum rain intensity index parameters in the middle and lower reaches of the Yangtze River through time series analysis method;

[0007] Step 2, carrying out the process of evaluating the flood encounter risks of the main and tributary rivers in the upper reaches of the Yangtze River by using the Copula function;

[0008] Step 3, exploring the encounter laws between plum rain characteristics and the staged floods in the upper reaches during the flood season according to mathematical statistics methods.

[0009] Preferably, Step 1 further includes the following sub-steps:

[0010] (1.1), analyzing the basic climate characteristics of plum rains based on the historical multi-year plum rain characteristic quantity data provided by the climate center, including the entering and leaving times of plum rains, the length of the plum rain season, the rainfall amount and the plum rain intensity index;

[0011] (1.2) Adopt the Mann-Kendall test method, Pettitt detection method, and Morlet continuous wavelet transform time series analysis method to analyze the change trends, mutation situations, and periodic laws of the plum rain duration and plum rain amount series.

[0012] Preferably, step 2 further includes the following sub-steps:

[0013] (2.1) Construct the marginal distributions of the flood occurrence time and flood magnitude respectively based on the mixed von Mises distribution and P-III distribution;

[0014] (2.2) Use the Archimedean Copula function family to construct the two-dimensional joint distribution of the flood occurrence times between any two hydrological control stations in the main and tributary basins, and the two-dimensional joint distribution of the flood magnitudes, as shown in the following formulas:

[0015] F(t i ,t j ) = C(T i ,T j ) (1);

[0016] F(q i ,q j ) = C(Q i ,Q j ) (2);

[0017] In formulas (1)-(2), i and j represent any gauging stations, and station j is downstream of station i; T i represents the annual maximum flood occurrence time at station i; Q i represents the annual maximum flood magnitude at station i; T j represents the annual maximum flood occurrence time at station j; Q j represents the annual maximum flood magnitude at station j;

[0018] Where:

[0019] In formula (3), C θ (·) is the Copula function; θ is the parameter of the Copula function; and are the marginal distribution functions, satisfying

[0020] Preferably, step 3 further includes the following sub-steps:

[0021] (3.1) Select the years with basin-wide large floods as typical years, analyze in detail the rainfall process and rainfall characteristics during the plum rain period, and study the historical encounter laws between the plum rain and basin floods.

[0022] (3.2) Use the cause analysis method and mathematical statistics method to conduct flood season staging for floods at hydrological control stations; and on this basis, further explore the relationship between the plum rain and the flood in the flood season staging, in order to provide a theoretical basis and reference for the scheduling of water conservancy projects in the basin.

[0023] Advantages of the present invention:

[0024] 1. The method of the present invention is scientific and reasonable, and can deeply analyze the distribution mechanism of rainfall and flood in the basin: The present invention uses common hydrological statistical methods to analyze the rainfall situation and rainfall characteristics during the plum rain period in the basin, and can be promoted and studied in any basin; studying the spatio-temporal distribution mechanism of plum rain and staged floods in the same period can not only enrich the scientific theoretical basis of rainstorm research, but also provide strong support for the identification and prediction of floods in the basin;

[0025] 2. The present invention can provide important scientific references and bases for the optimal operation and management of water conservancy projects in the basin: It can consider using the condition of the end time of plum rain in the basin to predict the subsequent water and rainfall trends in the basin. On the premise of ensuring flood control safety, water conservancy project scheduling measures such as dynamic control of reservoir operation water levels and early water storage are adopted to improve the comprehensive utilization benefits of the basin. Description of the drawings

[0026] Figure 1 is the specific flow chart of the method of the present invention;

[0027] Figure 2 is the scatter plot of the entry and exit times of plum rain and the cumulative plum rain amount in the basin;

[0028] Figure 3 is the relationship diagram between the daily flow in the flood season and the plum rain amount at Yichang Station in 1998;

[0029] Figure 4 is the relationship diagram between the flood season staging results of the 7-day and 15-day annual maximum flood volumes of the Three Gorges Reservoir and the plum rain in the basin. Detailed implementation manners

[0030] The following further describes the present invention in detail in conjunction with the drawings and specific embodiments.

[0031] Starting from the perspective of hydrological analysis and calculation, taking the Yangtze River Basin in China as an example, the present invention first obtains the parameter characteristic relationships such as the entry and exit times of plum rain, the plum rain amount, and the plum rain intensity index in the middle and lower reaches of the Yangtze River through time series analysis methods, then uses the Copula function to carry out the flood encounter risk assessment of the main and tributary rivers in the upper reaches of the Yangtze River, and finally explores the encounter law between the plum rain characteristics and the staged floods in the upper reaches during the flood season based on mathematical statistics methods.

[0032] Example 1: As Figure 1As shown in the figure, a method for analyzing the laws of basin floods considering the spatio-temporal variations of the plum rains, and the specific implementation process is shown in Figure 1 , and the steps are as follows:

[0033] Step 1: Obtain the parameter characteristic relationships such as the beginning and ending times of the plum rains, the amount of plum rain, and the plum rain intensity index in the middle and lower reaches of the Yangtze River through time series analysis methods.

[0034] Step 1 further includes the following sub-steps:

[0035] (1.1) Analyze the basic climate characteristics of the plum rains, such as the beginning and ending times of the plum rains, the length of the plum rain season, the rainfall amount, and the plum rain intensity index, based on the historical multi-year plum rain characteristic quantity data provided by the National Climate Center of the China Meteorological Administration, as shown in Figure 2 the figure.

[0036] (1.2) Use time series analysis methods such as the Mann-Kendall test method, the Pettitt test method, and the Morlet continuous wavelet transform to analyze the change trends, mutation situations, and periodic laws of the plum rain duration and plum rain amount series.

[0037] In the specific implementation manner, assume that X 1 , X 2 , …, X n is a time series with a sample length of n, and S is the test statistic defined by the Mann-Kendall method, and its expression is as follows:

[0038]

[0039] In formulas (1)-(2): x i and x j respectively represent the i-th and j-th data values of the time series; sgn() is the sign function.

[0040] Standardize the statistic S to construct a new statistic Z, and Z follows a normal distribution:

[0041]

[0042] In formula (3), when Z is greater than 0, it indicates that the sequence has an upward trend, and when Z is less than 0, it indicates that the sequence has a downward trend. Given the confidence level, when the absolute value of Z is greater than or equal to 1.28, 1.64, and 2.32, it indicates that the hypothesis tests with confidence levels of 90%, 95%, and 99% are passed in sequence.

[0043] The mutation test statistic U t,n defined by the Pettitt method is:

[0044]

[0045] In Equation (4), U t,n is a new sequence formed by counting the number of times the first sample sequence exceeds the second sample sequence. In the original hypothesis H 0 of the Pettitt method, there is no mutation point in the sequence. If the τ moment satisfies:

[0046] K τ = |U τ,n | = max|U t,n | (5)

[0047] Then the τ point is the mutation occurrence point, and the statistic p can be obtained:

[0048]

[0049] In Equation (6), if p is less than or equal to 0.05, it means that from a statistical sense, the detected mutation point τ is significant. The τ point is the first-level mutation occurrence point of the sequence to be detected. Taking it as the segmentation point, the original sample sequence can be split into two new time series, and the above method is repeated to detect new mutation occurrence points, and finally multiple mutation points can be obtained.

[0050] For the Morlet wavelet transform, a translation transformation and a scaling transformation can be performed on a certain mother wavelet function to construct a set of wavelet functions

[0051]

[0052] In Equation (7), a, b, and t are the scale, position, and time parameters in turn.

[0053] For an energy-limited signal f(t) ∈ L 2 (R), its continuous wavelet function can be obtained by using the convolution of a set of wavelet scaling and translation:

[0054]

[0055] In Equation (8), W f (a, b) is the wavelet coefficient; is the complex conjugate function of.

[0056] The mother wavelet function defined in this embodiment is as follows:

[0057]

[0058] In Equation (9): w 0 is the dimensionless frequency. If w 0 is equal to 6, the wavelet scale and the Fourier period are generally the same.

[0059] According to different time-scale parameters a, the power spectral density under the wavelet frequency spectrum can detect periods, and the calculation formula is as follows:

[0060]

[0061] In Equation (10), n is the data length.

[0062] In summary, the periodic change trends of the plum rain duration and plum rain amount sequences in the basin over the historical years can be comprehensively analyzed.

[0063] Step 2: Use the Copula function to conduct a flood encounter risk assessment for the main and tributary rivers in the upper reaches of the Yangtze River.

[0064] Step 2 further includes the following sub-steps:

[0065] (2.1) Construct the marginal distributions of flood occurrence time and flood magnitude respectively based on the mixed von Mises distribution and the P-III distribution.

[0066] Convert the flood occurrence time to radians x, x = 2πD j / L, where L is the total length of the flood season, and D j represents the j-th day of the flood occurrence in the flood season. The probability density function of the flood occurrence time X is:

[0067]

[0068] In Equation (11), p i is the coefficient of the mixing ratio; k i is the scale parameter; u i is the location parameter; I 0 (k i ) is the Bessel function of the 0th order; m is the order of the finite mixture von Mises distribution, and here m = 3. Estimate the above parameters using the maximum likelihood method.

[0069] Assume that the annual maximum flood magnitude follows the P-III distribution, and its probability density function is:

[0070]

[0071] In Equation (12), α, β, and δ represent the shape, scale, and location parameters of the P-III distribution respectively; Γ(·) represents the gamma function. Estimate the above parameters using the linear moment method. The following relationships exist among these three parameters and the statistical characteristic parameters Ex (mean), Cv (coefficient of variation), and Cs (skewness coefficient):

[0072]

[0073] Adopt the Kolmogorov-Smirnov (K-S) test, χ2 The fitting tests for the fitting marginal distributions are carried out by means of tests, root mean square error (RMSE) and AIC information criterion.

[0074] (2.2) Use the Archimedean Copula function family to construct the two-dimensional joint distribution of the flood occurrence times between any two hydrological control stations of the main and tributary rivers in the basin, as well as the two-dimensional joint distribution of the flood magnitudes, as shown in the following formula:

[0075] F(t i ,t j ) = C(T i ,T j ) (14)

[0076] F(q i ,q j ) = C(Q i ,Q j ) (15)

[0077] In formulas (14)-(15), i and j represent any gauging stations, and station j is downstream of station i; T i represents the occurrence time of the annual maximum flood; Q i represents the annual maximum flood magnitude.

[0078] For the Archimedean Copula function group, the three most commonly used Copulas are Clayton Copula, Gumbel-Hougaard Copula and Frank Copula. Their general structural form is:

[0079]

[0080] In formula (16), C θ (·) is the Copula function; θ is the parameter of the Copula function; and are the marginal distribution functions, satisfying

[0081] Step 3: According to the mathematical statistics method, explore the encounter law between the Meiyu characteristics and the flood in the upstream flood season staging.

[0082] Step 3 further includes the following sub-steps:

[0083] (3.1) Select the years with basin-wide large floods as typical years, analyze in detail the rainfall process and rainfall characteristics during the Meiyu period, and focus on studying the historical encounter law between Meiyu and basin floods (such as the hydrological control stations of large reservoirs), such as Figure 3Relationship diagram between the plum rain amount in the upper reaches of the Yangtze River in 1998 and the daily flow during the flood season at Yichang Station

[0084] (3.2) Combine the cause analysis method and the mathematical statistics method to conduct flood season staging for the floods at the hydrological control stations; and on this basis, further explore the relationship between the plum rain and the flood during the flood season staging, in order to provide a theoretical basis and reference for the water conservancy project scheduling in the basin.

[0085] Sample the flood season at the basin control hydrological stations, such as calculating the 7(15)-day maximum flood volume sequence (N 1 , N 2 , …, N n ) with each day as the center for 7(15) days. Assume it satisfies the normal distribution,

[0086] X i = μ i + e i , i = 1, 2, …, n (17)

[0087] If there exists:

[0088]

[0089] In formula (18), 1 < m 1 < m 2 < … < m q ≤ n, e i is a random error (expectation is 0, variance is equal). When b j ≠ b j+1 , m j is a change point to be found.

[0090] The specific operation steps for analyzing the mean change point using the least squares method in this embodiment are as follows:

[0091] First, determine the number of change points q, and roughly estimate the position of the change point, let m 0 = 1, m q+1 = n + 1;

[0092] Then, fix the two points m j-1 and m j+1 , and move m j-1 < m j < m j+1 within the interval of m j , and minimize the function S j ,

[0093]

[0094] In formula (19), y j is the estimated value of the mean b j , and it satisfies:

[0095]

[0096] When S j reaches its minimum value, the initial m j is replaced by m j '.

[0097] Repeat the above steps until m j ' and m j are exactly the same and then terminate. The finally obtained m j is the estimate of the q change points of the time series.

[0098] According to the results of the change points of the mean value during the flood season at the basin control station, explore the relationship between the staged flood and the plum rain. As Figure 4 shown, consider using the judgment condition of the plum rain withdrawal time of the basin, that is, obtain the plum rain withdrawal time according to the meteorological forecast, predict the subsequent water regime trends of the basin, and under the premise of ensuring flood control safety, adopt water conservancy project dispatching measures such as dynamic control of the reservoir operation water level and early water storage to improve the comprehensive utilization efficiency of the basin.

[0099] In summary, starting from the perspective of hydrological analysis and calculation, this embodiment first obtains the parameter characteristic relationships such as the entry and withdrawal times of the plum rain, the plum rain amount, and the plum rain intensity index of the middle and lower reaches of the Yangtze River through time series analysis methods, then uses the Copula function to carry out the flood encounter risk assessment of the main and tributary rivers in the upper reaches of the Yangtze River, and finally, based on mathematical statistics methods, explores the encounter law between the plum rain characteristics and the staged flood in the upper reaches during the flood season. The purpose of this invention is to reveal the temporal and spatial distribution and encounter characteristics of rain and flood, and provide important scientific references and bases for the operation and management of basin water conservancy dispatching projects.

[0100] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention should be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, the equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A basin flood law analysis method considering the temporal and spatial variation of plum rain, characterized by: It includes the following steps: Step 1, using time series analysis method to obtain the characteristic relationship between the start and end time of the plum rain in the middle and lower reaches of the Yangtze River, the plum rain amount and the plum rain intensity index parameter; Step 2: Use Copula function to carry out flood risk assessment process for the main and tributary rivers in the upper reaches of the Yangtze River; Step 3: Based on mathematical statistics methods, explore the characteristics of plum rain and the encounter patterns of staged floods in the upstream flood season.

2. A basin flood law analysis method considering the temporal and spatial variation of plum rain according to claim 1, characterized in that: Step 1 further includes the following sub-steps: (1.1) Analyze the basic climate characteristics of the Meiyu season based on the historical Meiyu characteristic data provided by the Climate Center, including the start and end time of the Meiyu season, the length of the Meiyu season, the rainfall, and the Meiyu intensity index; (1.2) The Mann-Kendall test method, Pettitt test method and Morelet continuous wavelet transform time series analysis method are used to analyze the changing trend, mutation and periodicity of the plum rain duration and plum rain amount series.

3. The method for analyzing basin flood rules considering the temporal and spatial variation of plum rain according to claim 1 is characterized by: Step 2 further includes the following sub-steps: (2.1) According to the mixed von Mises distribution and P-III type distribution, the marginal distribution of flood occurrence time and flood magnitude is constructed respectively; (2.2) The Archimedean Copula function family is used to construct the two-dimensional joint distribution of flood occurrence time between the hydrological control stations of the main and tributary rivers in the basin, as well as the two-dimensional joint distribution of flood magnitude, as shown in the following formula: F(t i ,t j )=C(T i ,T j ) (1); F(q i ,q j )=C(Q i ,Q j ) (2); In formulas (1)-(2), i and j represent any measuring stations, and station j is downstream of station i; T i represents the time of the annual maximum flood at station i; Q i represents the annual maximum flood magnitude at station i; T j represents the time of the maximum flood in the year at station j; Q j represents the maximum annual flood magnitude at station j; in: In formula (3), C θ (·) is the Copula function; θ is the parameter of the Copula function; and u2 is the marginal distribution function, satisfying 4. A basin flood law analysis method considering the temporal and spatial variation of plum rain according to claim 1, characterized in that: Step 3 further includes the following sub-steps: (3.1) Select the years when major floods occurred in the river basin as typical years, analyze the rainfall process and rainfall characteristics during the plum rain period in detail, and study the historical encounter patterns between plum rain and river basin floods. (3.2) Combine the cause analysis method and mathematical statistics method to divide the flood season of the hydrological control station; and on this basis, further explore the relationship between the plum rain and the flood season stages, in order to provide a theoretical basis and reference basis for the scheduling of water conservancy projects in the basin.

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