Downstream hydrological situation change degree estimation method based on joint distribution

Abstract

The invention provides a joint distribution-based downstream hydrological situation change degree estimation method, which comprises the following steps of: extracting a reference index from IHA indexes through a principal component analysis method, constructing joint distribution of the reference index and the IHA indexes by adopting a Copula function, and preferably selecting a probability density function with a good fitting effect; and respectively comparing the differences of the joint probability density functions of the two groups of series before and after the construction and operation of the cascade reservoir group, and further estimating the downstream hydrological situation variation condition considering the regulation and storage influence of the cascade reservoir group. The novel hydrological situation change degree estimation method is reasonable in technology, accords with objective laws, can be used for estimating the hydrological situation change degree of the downstream control section after being influenced by regulation and storage of the upstream reservoir group, and provides a technical basis for reservoir ecological regulation and water ecological environment protection.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological situation and water environment change assessment, and in particular to a method for estimating the degree of change of downstream hydrological situation based on joint distribution. Background Art

[0002] Affected by the combined effects of global climate change and human activities, the water ecosystem and hydrological regime of rivers and lakes have deviated from their natural state. The construction and operation of reservoirs have had a particularly significant impact on the ecological environment and hydrological regime of rivers. As the scale of upstream reservoirs gradually expands, the underlying surface of the basin has changed accordingly, resulting in major changes in the hydrological regime of downstream rivers, which may even threaten the safety of the downstream water ecological environment. Therefore, it is of great practical significance to scientifically and rationally estimate the degree of change in the downstream hydrological regime caused by the regulation of cascade reservoirs.

[0003] At present, the most commonly used hydrological situation assessment method is the IHA-RVA method, which has a clear principle and simple calculation. It has been widely used in practice and improved in research. For example, the invention patent with the authorization number CN202310719537.2 improves this method based on the distribution characteristics of cascade reservoirs, and calculates the cumulative impact of the eco-hydrological situation caused by the operation of the reservoir group; the invention patent with the authorization number CN201710780035.5 uses the projection dimension reduction method to mine the low-dimensional change characteristics of the indicator to reduce the impact of the IHA indicator noise, and proposes a hydrological situation assessment method for hydropower stations based on projection tracking. The invention patent with the authorization number CN201710236762.5 uses the maximum entropy principle and the minimum information entropy to select the univariate probability density function of the IHA indicator, which fully reflects the changes before and after the reservoir impact. However, the above hydrological situation estimation and evaluation system is based on the magnitude change of the IHA indicator itself, ignoring the internal connection between the IHA indicators, and cannot reflect the detailed distribution characteristics and coordinated changes of the flow indicator.

[0004] The invention patents with authorization numbers CN202110411487.2 and CN202211156565.X both introduce the fractal concept, further explore the morphological variability of hydrological indicators, and combine the RVA method to evaluate the degree of change in the hydrological situation caused by cascade reservoirs. The invention patent with patent number CN202410770630.0 also introduces the average annual runoff, calculates the hydrological change degree and slope change of each IHA hydrological indicator, and uses the TOPSIS method to obtain the comprehensive evaluation results of the river hydrological situation. The existing methods mainly focus on the expansion of hydrological indicators, without considering the representativeness of hydrological data and other hydrological information. The natural water inflow in the basin varies greatly from year to year, and wet, normal and dry years alternate. Among them, annual runoff is one of the important evaluation indicators of the hydrological situation, and it is also an important reference indicator for water resources planning and management and reservoir scheduling. According to the predicted changes in annual runoff, the reservoir scheduling operation of the year will be adjusted accordingly, which in turn affects all IHA indicators. Therefore, the estimation of hydrological conditions downstream of cascade reservoirs should take into account the coordinated changes in the IHA index and annual runoff.

[0005] In order to fully reflect the detailed distribution information of the statistical magnitude of hydrological indicators and take into account the synergistic influence of annual runoff on the distribution of various indicators, this paper is based on the joint probability density function of the IHA indicator and annual runoff, compares the changes in the joint probability density of the hydrological sequence before and after the impact of the reservoir, and proposes a method for estimating the hydrological situation downstream of cascade reservoirs based on joint distribution, which provides a technical reference for reservoir ecological scheduling and water ecological environment protection and management. Summary of the invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and provide a method for estimating the degree of change of downstream hydrological situation based on joint distribution.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] The present invention provides a method for estimating the degree of change of downstream hydrological situation based on joint distribution, comprising:

[0009] S1. Taking the downstream section of a cascade reservoir group in a certain river basin as the research object, collect the measured flow series data of the research section, calculate the IHA index, and determine the univariate marginal distribution before and after the reservoir impact;

[0010] S2. The principal component analysis method is used to process the IHA index, extract the principal components, and combine the measured hydrological data to demonstrate the physical meaning of the principal components and test the rationality of constructing the joint distribution with annual runoff as the reference indicator;

[0011] S3. On the basis of confirming the effectiveness of the reference indicators, construct the joint distributions of natural and non-natural IHA indicators and the reference indicators, compare different Copula joint distributions, and select the joint distribution with good fitting effect based on the Akaike information criterion;

[0012] S4. Compare the joint distributions of natural and non-natural IHA indicators and the reference indicators, calculate the non-overlapping part of the joint distribution function, and statistically analyze the hydrological alteration degree of single IHA indicators;

[0013] S5. Based on the hydrological alteration degree of single IHA indicators and combined with the results of principal component analysis, calculate the hydrological alteration degree of IHA groups and the overall situation.

[0014] Furthermore, the specific content of S1 is as follows:

[0015] S101. Divide the time periods based on the reservoir operation conditions, divide the flow data into natural and non-natural conditions, and calculate the IHA indicators under the natural and non-natural conditions respectively, including monthly average flow, the sum of the maximum and minimum flows for 1 day, 3 days, 7 days, 30 days, and 90 days per year, base flow index, number of days of water cut-off, moments of maximum and minimum flows, number and duration of high and low flow pulses, flow growth rate, reduction rate, and number of variations. At the same time, organize and statistically analyze the annual runoff series;

[0016] S102. Use the kernel density estimation theory to evaluate the marginal distributions of IHA indicators and annual runoff under natural and non-natural conditions:

[0017]

[0018] where x is the indicator variable; f(x) is the marginal distribution of the indicator variable; n is the sample length of the divided IHA or annual runoff series; t is the sample length serial number; h is the bandwidth; is the sequence variance; IQR is the interquartile range of the sequence.

[0019] Furthermore, the specific content of S2 is as follows:

[0020] S201. Based on the IHA indicators of the entire series, construct a covariance matrix, solve the eigenvalues and the corresponding unit eigenvectors, then the vector product of all unit eigenvectors and each IHA indicator is the required principal component, and extract the principal components with large contribution rates according to the cumulative weighting of the eigenvalues;

[0021] S202. Draw a scatter plot of the annual average runoff and the extracted principal components, evaluate the correlation between the annual average runoff and the principal components, and demonstrate whether the annual runoff is closely related to each indicator and whether it can meet the requirements for constructing the joint distribution function.

[0022] Furthermore, the specific content of S3 is as follows:

[0023] S301. Calculate the initial estimated IHA indicators and the joint distribution function of annual runoff using hydrological analysis with Gumbel, Clayton, and Frank Copula. The corresponding Copula function formulas are as follows:

[0024] C G = exp{-[(-lnu) θ + (-lnv) θ 1 / θ} τ = 1 - 1 / θ (3);

[0025] C C = (u -θ + v -θ - 1) 1 / θ τ = θ / (θ + 2) (4);

[0026]

[0027] Among them, C G , C C , C F are the Gumbel, Clayton, and Frank Copula functions respectively; u, v are the cumulative probabilities of IHA indicators and annual runoff; θ is the Copula correlation parameter; τ is the rank correlation coefficient;

[0028] S302. Calculate the AIC values of each joint distribution, and select the joint distribution with the smaller AIC value according to the Akaike information criterion. The AIC value calculation formula for the bivariate Copula function is:

[0029] AIC = 2 + 2nln(RMSE) (6);

[0030] Among them, RMSE is the root mean square error between the theoretical frequency and the empirical frequency calculated by Copula.

[0031] Furthermore, the specific content of S4 is as follows:

[0032] S401. Based on the joint distribution of the calibrated reference indicators and IHA indicators, compare the hydrological alteration degree D i :

[0033]

[0034] f(x i , y) = c(u i , v)f X (x i )f Y (y) (8);

[0035] Among them, x i ​x and y are the i-th IHA index and the reference index; f X (x i ) and f Y (y) are the marginal distribution probability densities; f pre,i (x i , y) and f post,i (x i , y) are the joint distribution probability densities in the natural and non-natural states, and c(u i , v) is the probability density of the proposed copula function.

[0036] Further, the specific content of S5 is as follows:

[0037] S501. Calculate the principal component weighted change degree D of the group or overall hydrological index according to the m-th principal component screened by S2 PCm :

[0038]

[0039] where i0 and i1 are the start and end numbers of the IHA group or all IHA indexes; α m,i is the coefficient corresponding to the i-th IHA index in the unit eigenvector of the m-th principal component; D i is the hydrological change degree of the i-th IHA index calculated by S4;

[0040] S502. Calculate the influence weight ω of the m-th principal component on the change degree of the group index or overall index according to the contribution rate of the screened principal component PCm :

[0041]

[0042] where |λ m | is the eigenvalue size of the m-th principal component; M is the total number of screened principal components;

[0043] S503. Combine the principal component weighted change degree and influence weight calculated in S501 and S502 to calculate the change degree D of the group index or overall index:

[0044]

[0045] The beneficial effects of the present invention are as follows: It solves the problem that the existing calculation method of hydrological regime change degree cannot fully reflect the comprehensive variability of indexes;

[0046] By introducing the joint probability distribution of IHA indexes and annual average runoff, analyzing the differences between the natural situation and the non-natural situation after the influence of the reservoir, to evaluate the hydrological regime change degree downstream of cascade reservoir groups, providing a new analysis idea for hydrological regime estimation.

[0047] Scientifically reasonable and more in line with engineering needs: It fully considers the joint distribution of index variables. While covering all their distribution information as much as possible, it selects annual runoff as the reference index, reflects the internal connection of IHA indicators, echoes the actual needs of reservoir operation, reflects the morphological changes of hydrological regimes, and has important practical significance for reservoir ecological operation, water ecological environment protection and governance. Brief Description of the Drawings

[0048] Figure 1 It is a flowchart of a method for estimating the change degree of downstream hydrological regime based on joint distribution;

[0049] Figure 2 It is a schematic diagram of the upstream hydrological station at Cuntan and the upstream reservoir group;

[0050] Figure 3(a) shows the runoff and annual runoff variation processes of a certain month during the flood season at the design section;

[0051] Figure 3(b) shows the probability density of runoff of a certain month during the flood season at the design section before and after the influence of reservoir regulation and storage;

[0052] Figure 4 It is the principal component analysis result of IHA indicators at the design section;

[0053] Figure 5(a) shows the joint probability density distribution diagram of runoff of a certain month during the dry season and annual runoff before the influence of reservoir group regulation and storage;

[0054] Figure 5(b) shows the joint probability density distribution diagram of runoff of a certain month during the dry season and annual runoff after the influence of reservoir group regulation and storage;

[0055] Figure 6 It is the IHA indicator groups and the overall hydrological change degree at the design section. Specific Embodiment

[0056] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0057] Please refer to Figure 1 , a method for estimating the change degree of downstream hydrological regime based on joint distribution, including:

[0058] S1. Taking the downstream section of a cascade reservoir group in a certain basin as the research object, collecting the measured flow series data of the research section, calculating the IHA indicators, and determining the univariate marginal distributions before and after the influence of the reservoir;

[0059] S2. Using the principal component analysis method to process the IHA indicators, extracting the principal components, and combining the measured hydrological data to demonstrate the physical meaning of the principal components and verify the rationality of constructing the joint distribution with the annual runoff as the reference index;

[0060] S3. On the basis of confirming the effectiveness of the reference indicators, construct the joint distributions of natural and non-natural IHA indicators and the reference indicators, compare different Copula joint distributions, and select the joint distribution with good fitting effect based on the Akaike information criterion;

[0061] S4. Compare the joint distributions of natural and non-natural IHA indicators and the reference indicators, calculate the non-overlapping part of the joint distribution function, and statistically analyze the hydrological alteration degree of single IHA indicators;

[0062] S5. Based on the hydrological alteration degree of single IHA indicators and combined with the results of principal component analysis, calculate the IHA group and the overall hydrological alteration degree.

[0063] The specific content of S1 is as follows:

[0064] S101. Divide the time periods based on the reservoir operation conditions, divide the flow data into natural and non-natural conditions, and calculate the IHA indicators under the natural and non-natural conditions respectively, including the monthly average flow, the sum of the maximum and minimum flows for 1 day, 3 days, 7 days, 30 days, and 90 days per year and the base flow index, the number of days of water interruption, the moments of the maximum and minimum flows, the number and duration of high and low flow pulses, the flow growth rate, reduction rate, and variation times. At the same time, organize and statistically analyze the annual runoff series;

[0065] S102. Use the kernel density estimation theory to evaluate the marginal distributions of IHA indicators and annual runoff under natural and non-natural conditions:

[0066]

[0067] where \(x\) is the indicator variable; \(f(x)\) is the marginal distribution of the indicator variable; \(n\) is the sample length of the divided IHA or annual runoff series; \(t\) is the sample length serial number; \(h\) is the bandwidth; is the sequence variance; IQR is the interquartile range of the sequence.

[0068] The specific content of S2 is as follows:

[0069] S201. Based on the IHA indicators of the entire series, construct a covariance matrix, solve the eigenvalues and the corresponding unit eigenvectors, then the vector product of all unit eigenvectors and each IHA indicator is the required principal component, and extract the principal components with large contribution rates according to the cumulative weights of the eigenvalues;

[0070] S202. Draw a scatter plot of the annual average runoff and the extracted principal components, evaluate the correlation between the annual average runoff and the principal components, and demonstrate whether the annual runoff is closely related to each indicator and whether it can meet the requirements for constructing the joint distribution function.

[0071] The specific content of S3 is as follows:

[0072] S301. Calculate the initial estimated IHA indicators and the joint distribution function of annual runoff using hydrological analysis for Gumbel, Clayton, and Frank Copula. The corresponding Copula function formulas are as follows:

[0073] C G = exp{-[(-lnu) θ + (-lnv) θ 1 / θ} τ = 1 - 1 / θ (3);

[0074] C C = (u -θ + v -θ - 1) 1 / θ τ = θ / (θ + 2) (4);

[0075]

[0076] Among them, C G 、C C 、C F are the Gumbel, Clayton, and Frank Copula functions respectively; u, v are the cumulative probabilities of IHA indicators and annual runoff; θ is the Copula correlation parameter; τ is the rank correlation coefficient;

[0077] S302. Calculate the AIC values of each joint distribution, and select the joint distribution with the smaller AIC value according to the Akaike information criterion. The AIC value calculation formula for the bivariate Copula function is:

[0078] AIC = 2 + 2nln(RMSE) (6);

[0079] Among them, RMSE is the root mean square error of the theoretical frequency and empirical frequency calculated by Copula.

[0080] The specific content of S4 is as follows:

[0081] S401. Based on the joint distribution of the calibrated reference indicators and IHA indicators, compare the hydrological alteration degree D i :

[0082]

[0083] f(x i , y) = c(u i , v)f X (x i )f Y (y) (8);

[0084] Among them, x i ​x and y are the i-th IHA index and the reference index; f X (x i ) and f Y (y) are the marginal distribution probability densities; f pre,i (x i , y) and f post,i (x i , y) are the joint distribution probability densities in natural and non-natural states, and c(u i , v) is the probability density of the proposed copula function.

[0085] Specifically, S5 is as follows:

[0086] S501. Calculate the principal component weighted change degree D of the group or overall hydrological index according to the m-th principal component screened in S2 PCm :

[0087]

[0088] where i0 and i1 are the start and end numbers of the IHA group or all IHA indexes; α m,i is the coefficient corresponding to the i-th IHA index in the unit eigenvector of the m-th principal component; D i is the hydrological change degree of the i-th IHA index calculated in S4;

[0089] S502. Calculate the influence weight ω of the m-th principal component on the change degree of the group index or overall index according to the contribution rate of the screened principal component PCm :

[0090]

[0091] where |λ m | is the eigenvalue size of the m-th principal component; M is the total number of screened principal components;

[0092] S503. Combine the principal component weighted change degree and influence weight calculated in S501 and S502 to calculate the change degree D of the group index or overall index:

[0093]

[0094] Example 1

[0095] As Figure 2As shown in the figure, in the embodiment, the Cuntan section, an important flood control control node in the Sichuan-Chongqing section of the Yangtze River, is taken as the research object. There are a total of 22 key large reservoirs upstream of the designed section, including 6 in the middle reaches of the Jinsha River (Liyuan, Ahai, Jin'anqiao, Longkaikou, Ludila, Guanyinyan), 3 in the Yalong River (Lianghekou, Jinping I, Ertan), 4 in the lower reaches of the Jinsha River (Wudongde, Baihetan, Xiluodu, Xiangjiaba), 5 in the Min River (Zipinpu, Houziyan, Changheba, Dagangshan, Pubugou), and 4 in the Jialing River (Bikou, Baozhusi, Tingzikou, Caojie).

[0096] By collecting the long-term flow observation data of the Cuntan Hydrological Station, according to the completion and operation of the reservoirs, the flow data series is divided into natural flow sequence and non-natural flow sequence, and the IHA indicators are calculated respectively, namely monthly average flow, maximum and minimum 1-day, 3-day, 7-day, 30-day, 90-day flows, base flow index, dry-up days, maximum and minimum flow times, high and low flow pulse numbers and durations, flow growth rate, reduction rate and variation times. At the same time, the annual runoff of the two groups of sequences is sorted and statistically analyzed. The univariate probability density of each hydrological index in the natural and non-natural states is calculated by kernel density estimation respectively. Figures 3(a) and 3(b) show the change processes and probability density distribution curves of the runoff in a certain month and the annual runoff before and after the impact of reservoir regulation. It can be seen that after the construction of the reservoir, the runoff in the flood season is significantly reduced and the distribution is more discrete.

[0097]

[0098] S2. Extract the principal components of IHA, explore the actual physical meaning of the principal components, and determine the reference index. The principal components are extracted by solving the eigenvalues and eigenvectors of the IHA indicators as Figure 4 , and it is found by comparison that except for the 5th principal component, the remaining 1st to 4th, 6th to 8th principal components all have a good linear relationship with the annual runoff. It shows that the annual runoff can well reflect the internal connection of the IHA indicators, and can be used as a reference index to construct the joint distribution;

[0099] S3. Construct the joint distribution of the reference index and the IHA indicators. After determining the annual runoff as the reference index, the joint distributions of the annual runoff and each IHA indicator in the natural and non-natural states are constructed in turn, and the Archimedean copula function family is used for fitting, and the AIC value is calculated according to the following formula:

[0100] AIC = 2 + 2nln(RMSE);

[0101] Select the Copula fitting joint distribution with the smallest AIC value.

[0102] S4: Calculate the hydrological regime change degree of different indicators in the natural and non-natural states, and statistically analyze its variability according to the following formula:

[0103]

[0104] Figures 5(a) and 5(b) show the joint probability density distribution diagrams of monthly runoff and annual runoff during the dry season before and after the regulation and storage impact of the designed section reservoir group. It can be found that under the regulation and storage impact of the reservoir group, the joint distribution shows an obvious bimodal structure, and the sample distribution shifts to the upper right corner.

[0105] S5: Combine the 8 principal components extracted in Step S2 and the change degrees of the 33 IHA indicators calculated in Step S4 to calculate the weighted change degree DPCm and influence weight ωPCm of each principal component, and further statistically calculate the weighted average value D of each group and overall indicators. The specific formula is as follows:

[0106]

[0107] Solve the hydrological change degree of each group and the overall hydrological change degree as Figure 6 shown.

[0108] The above-described embodiments only represent the implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be based on the appended claims.

Claims

1. A method for estimating the change degree of downstream hydrological regime based on joint distribution, characterized in that Including: S1. Taking the downstream section of a cascade reservoir group in a certain basin as the research object, collecting the measured flow series data of the research section, calculating the IHA indicators, and determining the univariate marginal distributions before and after the influence of the reservoir; S2. Using the principal component analysis method to process the IHA indicators, extracting the principal components, and combining the measured hydrological data to demonstrate the physical meaning of the principal components and test the rationality of constructing the joint distribution with the annual runoff as the reference index; S3. On the basis of confirming the effectiveness of the reference index, constructing the joint distributions of natural and non-natural IHA indicators and the reference index, comparing different Copula joint distributions, and selecting the joint distribution with good fitting effect based on the Akaike information criterion; S4. Comparing the joint distributions of natural and non-natural IHA indicators and the reference index, calculating the non-overlapping part of the joint distribution function, and statistically analyzing the hydrological alteration degree of single IHA indicators; S5. Based on the hydrological alteration degree of single IHA indicators and combining the results of principal component analysis, calculating the IHA group and the overall hydrological alteration degree.

2. The method for estimating the change degree of downstream hydrological regime based on joint distribution according to claim 1, wherein The specific content of S1 is as follows: S101. Dividing the time period based on the operation of the reservoir, classifying the flow data into natural and non-natural conditions, and respectively calculating the IHA indicators under the natural and non-natural conditions, including the monthly average flow, the sum of the maximum and minimum flows for 1 day, 3 days, 7 days, 30 days, and 90 days per year, the base flow index, the number of days of no flow, the moments of the maximum and minimum flows, the number and duration of high and low flow pulses, the flow growth rate, reduction rate, and variation times. At the same time, organizing and statistically analyzing the annual runoff series; S102. Using the kernel density estimation theory to evaluate the marginal distributions of IHA indicators and annual runoff under natural and non-natural conditions: Among them, x is the index variable; f(x) is the marginal distribution of the index variable; n is the sample length of the IHA or annual runoff series divided; t is the sample length serial number; h is the broadband; is the sequence variance; IQR is the interquartile range of the sequence.

3. The method for estimating the degree of change in downstream hydrological regime based on joint distribution according to claim 2, characterized in that, The specific content of S2 is as follows: S201. Based on the full series of IHA indicators, constructing a covariance matrix, solving the eigenvalues and the corresponding unit eigenvectors. Then, the vector product of all unit eigenvectors and each IHA indicator is the required principal component. Extract the principal components with large contribution rates according to the cumulative weighting of the eigenvalues; S202. Drawing a scatter plot of the annual average runoff and the extracted principal components, evaluating the correlation between the annual average runoff and the principal components, and demonstrating whether the annual runoff is closely related to each indicator and whether it can meet the requirements for constructing the joint distribution function.

4. The method for estimating the change degree of downstream hydrological regime based on joint distribution according to claim 3, wherein The specific content of S3 is as follows: S301. Using hydrological analysis to calculate the joint distribution functions of Gumbel, Clayton, and Frank Copula for the initial estimation of IHA indicators and annual runoff. The corresponding Copula function formulas are as follows: C G = exp{-[(-lnu) θ + (-lnv) θ 1 / θ}; τ = 1 - 1 / θ (3);​ C C = (u -θ + v - θ - 1) 1 / θ τ = θ / (θ + 2) (4); Among them, C G , C C , C F are the Gumbel, Clayton, and Frank Copula functions respectively; u and v are the IHA indicators and the annual runoff cumulative probability; θ is the Copula correlation parameter; τ is the rank correlation coefficient; S302. Calculating the AIC values of each joint distribution, and selecting the joint distribution with a small AIC value according to the Akaike information criterion. The AIC value calculation formula for the binary Copula function is: AIC = 2 + 2nln(RMSE) (6); where RMSE is the root mean square error of the theoretical frequency and empirical frequency calculated by Copula.

5. The method for estimating the change degree of downstream hydrological regime based on joint distribution according to claim 4, characterized in that The specific content of S4 is as follows: S401. Compare the hydrological alteration degree D under the influence of reservoir regulation and storage based on the joint distribution of the calibrated reference index and IHA index i : f(x i , y) = c(u i , v)f X (x i )f Y (y) (8); where x i and y are the i-th IHA index and the reference index; f X (x i ) and f Y (y) are the marginal distribution probability densities; f pre,i (x i , y) and f post,i (x i , y) are the joint distribution probability densities in the natural and non-natural states, and c(u i , v) is the probability density of the proposed copula function.

6. The estimation method for the degree of change in downstream hydrological regime based on joint distribution according to claim 5, characterized in that, The specific content of S5 is as follows: S501. Calculate the principal component weighted change degree D of the group or overall hydrological index according to the m-th principal component screened by the S2 PCm : where, i0 and i1 are the starting and ending numbers of the IHA groups or all IHA indicators; α m,i is the coefficient corresponding to the i-th IHA indicator in the unit eigenvector of the m-th principal component; D i is the degree of hydrological alteration of the i-th IHA indicator calculated by S4; S502. Calculate the influence weight ω of the m-th principal component on the change degree of the group index or the overall index according to the contribution rate of the selected principal components. PCm : where |λ m | is the eigenvalue of the m-th principal component; M is the total number of selected principal components; S503. Combining the weighted alteration degree of the principal components and the influence weights calculated in S501 and S502, calculating the alteration degree D of the group index or the overall index:

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