Method for determining optimal water level of lake considering coexistence relationship between water level and hydrological connectivity

Abstract

The present invention relates to the field of water resources planning and management, and particularly to a method for determining the optimal water level of a lake considering the coexistence relationship between water level and hydrological connectivity. The method comprises the following steps: analyzing and processing remote sensing images of a set lake to obtain hydrological connectivity data; obtaining water level data of the set lake; calculating the correlation coefficient between hydrological connectivity and water level to determine the correlation between the hydrological connectivity and water level series; respectively constructing the marginal distribution functions of hydrological connectivity and water level; using the Copula function to obtain the joint probability distribution function of the two; combining the requirements of lake water replenishment management and ecological restoration objectives, setting different water replenishment scenarios for hydrological connectivity and water level, and determining the optimal water level of the lake by using joint probability and conditional probability analysis. The present invention considers the coexistence relationship between water level and hydrological connectivity and the uncertainty generated by it for water replenishment management, determines the optimal water level of the lake, and provides a quantitative basis for the water replenishment management of the lake.

Description

Technical Field

[0001] The present invention relates to the field of water resources planning and management, and particularly to a method for determining the optimal water level of a lake considering the coexistence relationship between water level and hydrological connectivity. Background Art

[0002] Water level is a key factor determining the eco-hydrological status of a lake, which determines the composition characteristics of the lake biological community. The reasonable determination of the optimal water level of a lake is an important basis for the optimal allocation and planning management of regional water resources. Currently, most studies on the determination of the ecological water level of a lake generally adopt methods such as curve correlation method, water level-area method, natural water level data method, lake morphology analysis method, and biological space minimum demand method, etc. After the implementation of the ecological water replenishment project, the runoff increases, resulting in a rise in water level and an expansion of the inundated area, further affecting the distribution of hydrological connectivity. Usually, the water level is considered to be the hydrological index with the greatest impact on hydrological connectivity, and there is an inseparable coexistence relationship between the two. This coexistence relationship will be fed back to the water replenishment regulation process, bringing challenges to water replenishment management. Therefore, it is urgent to reveal the coexistence relationship between hydrological connectivity and water level, and consider the combined effect in water replenishment management to provide a quantitative basis for the determination of the optimal ecological water level of the lake. The current research methods have obvious drawbacks, that is, they fail to comprehensively consider the coexistence relationship between hydrological connectivity and water level, and fail to consider the uncertainty brought by the coexistence relationship to water replenishment management, thus unable to provide a quantitative basis for the determination of the optimal ecological water level of the lake. Summary of the Invention

[0003] In view of this, aiming at the deficiencies that the existing methods for determining the optimal ecological water level of a lake fail to effectively characterize the uncertainty of the water replenishment management system and cannot accurately quantify the coexistence relationship between the lake's hydrological connectivity and water level, a method for determining the optimal water level of a lake considering the coexistence relationship between water level and hydrological connectivity is proposed, providing a reliable basis for further realizing the optimal allocation of water resources.

[0004] To achieve the above object, the present invention mainly provides the following technical solutions:

[0005] A method for determining the optimal water level of a lake considering the coexistence relationship between water level and hydrological connectivity, comprising the following steps:

[0006] Step 1: Perform geostatistical analysis on the remote sensing images of the set lake to obtain the hydrological connectivity data of the lake;

[0007] Step 2: Obtain the water level data of the lake;

[0008] Step 3: Calculate the correlation coefficients between hydrological connectivity and water level respectively, and determine the correlation between hydrological connectivity and water level;

[0009] Step 4: For the hydrological connectivity and water level data that meet the correlation requirements, use the parameter estimation method of a single variable to construct the marginal distribution function of hydrological connectivity and water level, and obtain its optimal marginal distribution form according to the goodness-of-fit test;

[0010] Step 5: Use the Copula function to connect the marginal distributions of hydrological connectivity and water level to obtain the joint probability distribution function;

[0011] Step 6: Set up different water replenishment scenarios for hydrological connectivity and water level, calculate the joint probability and conditional probability of different water replenishment scenarios, and determine the optimal lake water level in combination with the water replenishment management requirements and ecological restoration goals.

[0012] In the above method for determining the optimal lake water level, in Step 1, perform geostatistical analysis on the remote sensing images of the set lake to obtain the connection probability between any two target water areas of the lake along a certain direction and distance range, and obtain the hydrological connectivity data of the lake.

[0013] In the above method for determining the optimal lake water level, in Step 3, test the correlation between the hydrological connectivity and water level data sequences through the Spearman coefficient, Pearson coefficient, and Kendall coefficient. The greater the absolute value of the correlation coefficient value, the stronger the dependence between variables. Among them: a correlation coefficient value less than 0.2 can be regarded as extremely weak correlation or no correlation, and a correlation coefficient value greater than 0.6 is a strong correlation.

[0014] In the above method for determining the optimal lake water level, the single variable refers to the data sequence of hydrological connectivity or water level; the multi-variable refers to the data sequences of hydrological connectivity and water level; the types of the marginal distribution function include beta distribution, gamma distribution, Weibull distribution, generalized Pareto distribution, generalized extreme value distribution, lognormal distribution, or normal distribution; the types of the joint probability distribution function include Frank, T, Gaussian, Clayton, and Gumbel Copula functions.

[0015] In the above method for determining the optimal lake water level, in Step 4, the process of obtaining the marginal distribution function includes: first, use the maximum likelihood method to solve and determine the unknown parameters of the single-variable marginal distribution function, and test the goodness-of-fit of alternative marginal distribution functions such as the beta distribution through the AIC and BIC criteria. The smaller the AIC and BIC values, the better the fitting effect of the selected marginal function and the empirical distribution function, and thus the optimal marginal distribution type of hydrological connectivity and water level data is selected.

[0016] In the above method for determining the optimal lake water level, in Step 5, the expression of the joint probability distribution function is:

[0017]

[0018] where: x is the hydrological connectivity data, and y is the water level data, is the marginal distribution function of the hydrological connectivity sequence, is the marginal distribution function of the water level sequence, is the joint probability distribution function of hydrological connectivity and water level, is the type of Copula function satisfied by the joint probability distribution function.

[0019] In the above method for determining the optimal water level of the lake, in step 5, different types of Copula functions are selected to fit the joint probability distribution between the hydrological connectivity and water level sequences, and the Copula function type with the best fitting effect is selected based on the principle of the minimum AIC and BIC values.

[0020] In the above method for determining the optimal water level of the lake, in step 6, different water replenishment scenarios for hydrological connectivity and water level are set up. The process of calculating the joint probability and conditional probability of different water replenishment scenarios is as follows: According to the quartile method, the hydrological connectivity and water level data sequences are respectively divided into four levels: (1) 0 - 25%, (2) 25% - 50%, (3) 50% - 75%, (4) 75% - 100%. The hydrological connectivity and water level data sequences of different levels are combined into 16 scenarios in sequence, and the joint probability of different water replenishment scenarios and the conditional probability results that the hydrological connectivity result belongs to a certain connectivity level at a specific water level are calculated.

[0021] In the above method for determining the optimal water level of the lake, in step 6, the water replenishment management requirements and ecological restoration goals refer to meeting the requirements such as flood control safety of the lake, minimum ecological flow, maintaining biodiversity, and protecting biological habitats, so as to ensure the survival and reproduction of organisms.

[0022] In the above method for determining the optimal water level of the lake, the water level interval range in the conditional probability distribution result obtained in step 6 that is conducive to the transformation of low connectivity level events to high connectivity level events is the optimal water level of the target lake.

[0023] In the above method for determining the optimal water level of the lake, through step 6, according to the joint probability distribution, conditional probability distribution, lake water replenishment management requirements, and ecological restoration goals, the probabilities of hydrological connectivity and water level grades in different scenario combinations, as well as the conditional probability distribution results that the hydrological connectivity result belongs to a certain connectivity level at a specific water level are calculated, and the water level interval range that is conducive to the transformation of low connectivity level events to high connectivity level events is obtained, thereby determining the optimal water level of the lake.

[0024] By means of the above technical solution, the method for determining the optimal water level of the lake in the present invention has at least the following advantages:

[0025] 1) By taking advantage of the Copula function's ability to solve multi-variable probability problems and its suitability for characterizing non-linear relationships between variables, the present invention quantifies the coexistence relationship between hydrological connectivity and water level based on the Copula function. Different water replenishment scenarios for hydrological connectivity and water level are established, and the joint probability and conditional probability of different water replenishment scenarios are calculated. Combining the requirements of water replenishment management and the goals of ecological restoration, the water level range that is conducive to the transformation of low connectivity level events to high connectivity level events is determined as the optimal water level of the target lake. This method effectively quantifies the correlation between hydrological connectivity and water level, improving the scientificity and rationality of water replenishment management.

[0026] 2) The present invention comprehensively considers the uncertainty in water replenishment management caused by the coexistence of hydrological connectivity and water level, with high accuracy, providing a quantitative basis for the optimal allocation of regional water resources.

[0027] The above description is only an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and implement it in accordance with the content of the specification, the following further details the preferred embodiments of the present invention in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flowchart of the method for determining the optimal water level of the lake in the present invention;

[0029] Figure 2 is the marginal distribution function of hydrological connectivity calculated in the embodiment of the present invention;

[0030] Figure 3 is the marginal distribution function of water level calculated in the embodiment of the present invention;

[0031] Figure 4 is the joint distribution contour map of hydrological connectivity and water level calculated in the embodiment of the present invention;

[0032] Figure 5 is the joint probability distribution map of hydrological connectivity and water level;

[0033] Figure 6 is the conditional probability distribution map of hydrological connectivity and water level. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following details the specific implementation manners, structures, features, and effects of the present invention in accordance with the accompanying drawings and preferred embodiments.

[0035] Taking the water replenishment management of Baiyangdian as an example, the method for determining the optimal water level of the lake in the present invention is further described.

[0036] Baiyangdian is located in the Daqing River Basin and is the largest shallow lake wetland in North China. After the 1990s, the Ministry of Water Resources and Hebei Province replenished water to Baiyangdian 38 times through projects such as upstream reservoir water replenishment, "diverting the Yellow River to replenish Baiyangdian", "diverting the Yue River to replenish Baiyangdian", and the middle route of the South-to-North Water Diversion Project, with a total water inflow of 2.19 billion cubic meters. Since the establishment of Xiongan New Area in 2017, the ecological water replenishment sources and paths in Baiyangdian have become more diversified, and the amount and frequency of ecological water replenishment have also been increasing. Ecological water replenishment will affect the hydrological connectivity distribution characteristics and water area pattern of Baiyangdian and improve its ecological water level; at the same time, there is a coexistence relationship between hydrological connectivity and water level, and this feedback relationship and uncertainty will pose challenges to the water replenishment management of Baiyangdian. Therefore, it is necessary to consider the coexistence relationship between hydrological connectivity and water level, determine the optimal ecological water level of the lake, and provide a quantitative basis for the lake water replenishment management.

[0037] As Figure 1 shown, a method for determining the optimal water level of a lake considering the coexistence relationship between water level and hydrological connectivity provided in this embodiment includes the following steps: Step 1: Conduct geostatistical analysis on the remote sensing images of the set lake to obtain the hydrological connectivity data of the lake; Step 2: Obtain the water level data of the set lake from the official website of the Ministry of Water Resources; Step 3: Calculate the correlation coefficients between hydrological connectivity and water level respectively to determine the correlation between the hydrological connectivity and water level series; Step 4: Use the parameter estimation method of a single variable to construct its marginal distribution function, and obtain its optimal marginal distribution form according to the goodness-of-fit test, with the abscissa being the hydrological connectivity or water level data and the ordinate being the corresponding probability; Step 5: Use the Copula function to connect the marginal distributions of hydrological connectivity and water level to obtain the joint probability distribution function; Step 6: Set different water replenishment scenarios for hydrological connectivity and water level, calculate the joint probability and conditional probability of different water replenishment scenarios, and combine the water replenishment management requirements and ecological restoration goals. According to the conditional probability distribution result that the hydrological connectivity result at a specific water level belongs to a certain connectivity level, determine the water level interval range that is conducive to the transformation of low connectivity level events to high connectivity level events as the optimal water level of the target lake.

[0038] The method for determining the optimal water level of the lake provided in this embodiment starts from analyzing the hydrological connectivity and water level data series of the lake, determines the correlation between the two data series, constructs the marginal distribution function, and conducts joint probability and conditional probability distribution analysis, so as to fully consider the coexistence relationship between hydrological connectivity and water level and the uncertainty brought by this feedback relationship, and provide a more scientific and reasonable quantitative basis for the water replenishment management of the lake. This method effectively quantifies the correlation and dependence relationship between hydrological connectivity and water level, comprehensively considers the uncertainty brought to water replenishment management due to the feedback relationship, has high accuracy, and provides a quantitative basis for the optimal allocation of regional water resources.

[0039] Preferably, in step 3, the correlation between hydrological connectivity and water level data series is tested by Spearman coefficient, Pearson coefficient and Kendall coefficient. The larger the absolute value of the correlation coefficient, the stronger the dependence between variables. Among them, when the correlation coefficient is less than 0.2, it can be regarded as extremely weak correlation or no correlation, and when the correlation coefficient is greater than 0.6, it is a strong correlation. In specific implementation, when the correlation coefficient is greater than 0.2, the correlation requirement is satisfied, and subsequent analysis can be carried out.

[0040] In step 4, the process of obtaining the marginal distribution function includes: first, the maximum likelihood method is used to solve and determine the unknown parameters of the univariate marginal distribution function, and the goodness of fit of alternative marginal distribution functions such as beta distribution is tested by AIC and BIC criteria. The smaller the AIC and BIC values, the better the selected marginal function fits the empirical distribution function, and thus the optimal marginal distribution type of hydrological connectivity and water level data is selected.

[0041] The process of obtaining the marginal distribution function includes: first, the maximum likelihood method is used to solve and determine the unknown parameters of the univariate marginal distribution function, and the goodness of fit of alternative marginal distribution functions such as beta distribution is tested by AIC and BIC criteria. The smaller the AIC and BIC values, the better the selected marginal function fits the empirical distribution function, and thus the optimal marginal distribution type of hydrological connectivity and water level data is selected.

[0042] The principle of the maximum likelihood method is that a random sample satisfies a certain probability distribution, but the specific parameters are unknown. By observing the results of multiple experiments and using these experimental observation results to estimate the approximate values of the parameters, the possibility of the selected sample appearing in the selected population is maximized. Maximum likelihood estimation is based on the idea that a given parameter can maximize the probability of the sample occurring, and by giving up choosing other samples with smaller probabilities, this parameter is directly used as the estimated true value. The AIC (Akaike Information Criterion) is a statistical method based on the concept of entropy that can balance the complexity of the estimated model and the goodness of fit of this model to the data, and is applicable to the test of the Copula model obtained by maximum likelihood estimation. The BIC (Bayesian Information Criterion) will increase the likelihood function, increase the model complexity, and continuously improve the model accuracy, and has a more sensitive response to overestimated models. Its calculation formula is as follows:

[0043]

[0044]

[0045]

[0046] In the formula, x is the hydrological connectivity data series; y is the water level data series; is the empirical distribution function, and its value is the empirical frequency value; is the selected Copula distribution function (theoretical distribution function), and its value is the theoretical frequency value; MSE is the error between the empirical distribution function and the theoretical distribution function; n is the statistic; k is a constant.

[0047] In step 5, the expression of the joint probability distribution is:

[0048]

[0049] In the formula: x is the hydrological connectivity data, and y is the water level data, is the marginal distribution function of the hydrological connectivity sequence, is the marginal distribution function of the water level sequence, is the joint probability distribution function of hydrological connectivity and water level, is the type of Copula function satisfied by the joint probability distribution function. The types of the marginal distribution functions include beta distribution, gamma distribution, Weibull distribution, generalized Pareto distribution, generalized extreme value distribution, lognormal distribution or normal distribution; the types of the joint probability distribution functions include Frank, T, Gaussian, Clayton and Gumbel Copula functions.

[0050] In step 5, different types of Copula functions are selected to fit the joint probability distribution between the hydrological connectivity and the water level sequence, and the Copula function type with the best fitting effect is selected according to the principle of the minimum AIC and BIC values; the univariate refers to the data sequence of hydrological connectivity or water level; the multivariate refers to the data sequences of hydrological connectivity and water level.

[0051] In step 6, the steps to determine the optimal water level of the lake are as follows: different water replenishment scenarios of hydrological connectivity and water level are set up, and the process of calculating the joint probability and conditional probability of different water replenishment scenarios is as follows: according to the quartile method, the hydrological connectivity and water level data sequences are respectively divided into four levels: (1) 0 - 25%, (2) 25% - 50%, (3) 50% - 75%, (4) 75% - 100%, and the hydrological connectivity and water level data sequences of different levels are combined into 16 scenarios in sequence, and the joint probability of different water replenishment scenarios and the conditional probability results that the hydrological connectivity result belongs to a certain connectivity level at a specific water level are calculated.

[0052] In step 6, the water replenishment management requirements and ecological restoration goals refer to meeting the requirements such as flood control safety of the lake, minimum ecological flow, maintaining biodiversity and protecting biological habitats, so as to ensure the survival and reproduction of organisms.

[0053] In step 6, according to the joint probability distribution, conditional probability distribution, lake water replenishment management requirements and ecological restoration objectives, calculate the probabilities of hydrological connectivity and water level grades under different scenario combinations, as well as the conditional probability distribution results that the hydrological connectivity results at a specific water level belong to a certain connectivity grade, obtain the water level interval range conducive to the transition of low connectivity grade events to high connectivity grade events, and then determine the optimal water level of the lake.

[0054] In this embodiment, the calculated Spearman coefficient between the hydrological connectivity of Baiyangdian and the water level data sequence is 0.2888, the Pearson coefficient is 0.2727, and the Kendall coefficient is 0.2545, indicating that there is a certain positive correlation between the hydrological connectivity and the water level data. The correlation coefficients in this embodiment can be obtained by inputting the data (hydrological connectivity and water level data) through SPSS or MATLAB software and performing correlation analysis.

[0055] In practical applications, after obtaining the Copula function of hydrological connectivity and water level, use the expression of the Copula function and the joint distribution contour map, divide different grades by the quartile method, calculate the joint probability and conditional probability of hydrological connectivity and water level grades under different scenario combinations, obtain the water level interval range conducive to the transition of low connectivity grade events to high connectivity grade events, and then determine the optimal water level of the lake.

[0056] The above steps are described in detail as follows:

[0057] (1) Obtain the hydrological connectivity and water level data of the lake

[0058] Through lake water resources investigation and data collection, combined with the geostatistical analysis method for the interpretation of remote sensing images, obtain the connection probability between any two target waters of the lake along a certain direction and distance range, and determine the hydrological connectivity and water level data sequence of the lake.

[0059] (2) Discriminate the correlation between the hydrological connectivity and water level data sequence

[0060] Since whether there is a correlation between variables is the criterion for judging whether a Copula function can be used to construct a bivariate joint distribution model. Examine the correlation between the hydrological connectivity and water level data sequence through Spearman coefficient, Pearson coefficient, Kendall coefficient, etc.

[0061] (3) Construct the joint probability distribution function between the hydrological connectivity and water level data sequence of the lake that meets the correlation requirements in (2)

[0062] Estimate the parameters of a single variable using the maximum likelihood method, construct its marginal distribution function, and perform a goodness-of-fit test according to the AIC and BIC criteria to obtain the optimal marginal distribution form; select an appropriate Copula function type based on the principle of the minimum AIC and BIC to construct the joint probability distribution function of the hydrological connectivity and water level data series, so as to fully consider the uncertainty brought by the coexistence relationship between hydrological connectivity and water level to the lake water replenishment management, and determine the optimal water level of the lake in combination with the water replenishment management requirements and ecological restoration goals.

[0063] The goodness-of-fit test, also known as the adaptability test, is to test the established prediction model and compare the compliance of its prediction results with the actual occurrence. Usually, multiple prediction models are tested simultaneously, and a better goodness of fit is selected for the experiment. The goodness-of-fit evaluation of parameters can be completed by comparing the AIC and BIC values. The goodness-of-fit test determines the degree of fit between the test fitting model and the sample observation data points by constructing a statistic that can characterize the degree of fit; the constructed test statistic is the sample observation value. The corresponding function can calculate the statistical values of all test objects, then select a comparison standard to obtain the test conclusion, and then judge the degree of fit of the fitting model. Common methods for evaluating the goodness of fit include the K-S test, A-D test, etc. The K-S test is based on the cumulative distribution function, which tests whether the distribution satisfies the theoretical distribution or compares the significant differences between two empirical distributions. The one-sample K-S test is used to test whether the empirical distribution of the observed data conforms to a known theoretical distribution. The two-sample K-S test is sensitive to the differences in the location and shape parameters of the empirical distribution functions of the two samples, making it one of the most useful and commonly used non-parametric methods for comparing two samples.

[0064] (4)Determine the optimal water level of the target lake

[0065] According to the quartile method, divide the hydrological connectivity and water level into four grades, analyze the joint probability and conditional probability of hydrological connectivity and water level under different scenario combinations, calculate the conditional probability results that the hydrological connectivity results belong to a certain connectivity grade at a specific water level, and combine the water replenishment management requirements and ecological restoration goals to obtain the water level interval range that is conducive to the transformation of low connectivity grade events to high connectivity grade events, and then determine the optimal water level of the lake.

[0066] Through the Copula function, connect the marginal distribution functions of hydrological connectivity and water level to obtain their joint probability distribution function, that is, the Copula function that hydrological connectivity and water level will ultimately satisfy a certain expression, such as: .

[0067] Based on the hydrological connectivity and water level data series of the studied lake, construct their marginal distribution functions respectively ( and ), and they each follow the beta distribution and the generalized Pareto distribution type; then construct their joint probability distribution function (Frank Copula), 2.00 is the parameter estimation result. Combining the joint probability and conditional probability analysis results of hydrological connectivity and water level under different scenario combinations, obtain the water level range conducive to the transition of low connectivity level events to high connectivity level events, and then determine the optimal water level of the lake.

[0068] The results calculated by the above method for determining the optimal water level of the lake are as follows:

[0069] 1) Correlation discrimination

[0070] Through the previous data collection and remote sensing image interpretation, the obtained data include: the hydrological connectivity data sequence of Baiyangdian (1990 - 2020) and the water level data sequence of Baiyangdian (1990 - 2020). Calculate the rank correlation coefficient between the hydrological connectivity and water level data of Baiyangdian pairwise (see Table 1 below). The results show that the Spearman coefficient of the hydrological connectivity and water level data sequence of Baiyangdian is 0.2888, the Pearson coefficient is 0.2727, and the Kendall coefficient is 0.2545, indicating that there is a certain positive correlation between the hydrological connectivity and water level data, and the Copula function can be used for the distribution of joint probability and conditional probability.

[0071] Table 1. Results of correlation discrimination between the hydrological connectivity and water level data sequence of Baiyangdian

[0072]

[0073] 2) Construction of univariate marginal distribution functions

[0074] Select the beta distribution, gamma distribution, Weibull distribution, generalized Pareto distribution, generalized extreme value distribution, lognormal distribution or normal type to simulate the distribution characteristics of the hydrological connectivity and water level data sequences of Baiyangdian respectively. The statistical results of AIC and BIC are shown in Table 2. Among them, for the hydrological connectivity data sequence, the AIC and BIC results of the beta distribution are the smallest and pass the K - S test; for the water level data sequence, the AIC and BIC statistical results of the generalized Pareto distribution are the smallest and pass the K - S test; therefore, the beta distribution and the generalized Pareto distribution are respectively selected as the marginal distribution functions of hydrological connectivity and water level (see Figure 2 and Figure 3 ).

[0075] Table 2. Statistical results of AIC and BIC of univariate marginal distribution functions

[0076]

[0077] 3) Hydrological connectivity - water level joint probability distribution function

[0078] The Frank, T, Gaussian, Clayton, and Gumbel Copula functions were selected to fit the joint distribution of hydrological connectivity and water level. Combining the AIC and BIC criteria, the optimal Copula type was determined to be the Frank Copula function. The statistical results of AIC and BIC are shown in Table 3. Using Matlab software, the Frank Copula function with a parameter of 2.00 was plotted, and the joint distribution contour of hydrological connectivity and water level was obtained as Figure 4 shown.

[0079] Table 3. AIC and BIC statistical results of the joint probability distribution function of multiple variables

[0080]

[0081] 4) Hydrological connectivity - water level joint probability analysis

[0082] According to the quartile method, the hydrological connectivity and water level data series were respectively divided into four grades: (1) 0 - 25%, (2) 25% - 50%, (3) 50% - 75%, (4) 75% - 100%. The hydrological connectivity and water level data series of different grades were sequentially combined into 16 scenarios, and the joint probabilities of different water replenishment scenarios were calculated. The calculation results of the joint probabilities of 16 water replenishment scenarios were plotted using origin plotting software (see Figure 5 ). The results show that the highest joint probability (0.10) appears in the events of excellent water level and good hydrological connectivity, while the joint probability of low water level and good hydrological connectivity events is the lowest (0.03). With the improvement of hydrological connectivity, the variation laws of the joint probabilities of the same low, medium, high, and excellent water level events are different. In addition, the joint probability of the synchronous combination of hydrological connectivity and water level (low - low, medium - medium, good - high, and excellent - excellent) is 0.31, indicating a strong synchronous relationship between the hydrological connectivity and water level in Baiyangdian. Therefore, considering the joint probability results, it is recommended that lake managers should take measures to regulate the water level and improve hydrological connectivity according to whether the joint events are beneficial to the ecological environment, in order to restore the ecology of Baiyangdian and manage the water replenishment of Xiongan New Area.

[0083] 5) Hydrological connectivity - water level conditional probability analysis

[0084] Calculate the conditional probabilities of different water replenishment scenarios, analyze the conditional probabilities that the hydrological connectivity results at a specific water level belong to a certain connectivity grade, and plot the calculation results of the conditional probabilities using origin plotting software (see Figure 6). The results show that as the water level increases, the probability of low hydrological connectivity events decreases, while the probabilities of medium, good, and excellent hydrological connectivity events increase. When the water level is below 7 m, the probability of low hydrological connectivity events is the highest, followed by medium and good hydrological connectivity events, and the probability of excellent hydrological connectivity events is the lowest. However, when the water level exceeds 8 m, the results are exactly the opposite. When the water level is 7–7.5 m, the occurrence probability of medium hydrological connectivity events exceeds that of low hydrological connectivity events, indicating that the occurrence probability of medium hydrological connectivity events is the highest at 7–7.5 m. Therefore, 7–8 m is the key water level range for the transition of the hydrological connectivity state of Baiyangdian Lake. When the water level exceeds 7 m, the hydrological connectivity of Baiyangdian Lake gradually improves, and when the water level exceeds 8 m, it improves more, which is consistent with the previous research results.

[0085] In April 2018, the "Outline of the Plan for Xiongan New Area in Hebei Province" required that the normal water level of Baiyangdian Lake be adjusted to within 6.5 - 7.0 m. The results of this study verify the rationality of the government's decision-making management. Therefore, in combination with the "Plan for the Management and Protection of the Ecological Environment of Baiyangdian Lake (2018 - 2035)", managers should establish a multi-source water replenishment mechanism, make an overall plan for ecological water resources including in-basin and cross-basin rivers, reservoir water, and reclaimed water, and through effective water replenishment management, ensure that the annual ecological water replenishment volume of Baiyangdian Lake should be 3 more than 300 million m³, and the water level should be maintained above 7 m to maintain good hydrological connectivity and restore the ecological environment.

[0086] Due to the coexistence relationship between hydrological connectivity and water level, it will bring challenges to lake water replenishment management. Previous studies have ignored the feedback relationship between hydrological connectivity and water level, so the lake water replenishment management is not scientific and reasonable enough, and the lake water level cannot effectively shift from low connectivity level events to high connectivity level events. The present invention overcomes this limitation, can effectively quantify the coexistence relationship between hydrological connectivity and water level, objectively reflect the uncertainty brought by the feedback relationship between hydrological connectivity and water level, determine the optimal ecological water level by calculating the joint probability and conditional probability of different water replenishment scenarios, with high accuracy, and provide reliable basic data support for the optimal allocation of water resources and the decision-making of water supply scheduling planning, thereby improving the scientificity and effectiveness of lake water replenishment management.

[0087] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for determining the optimal water level of a lake considering the coexistence relationship between water level and hydrological connectivity, characterized in that, it includes the following steps: Step 1: Conduct geostatistical analysis on the remote sensing images of the set lake to obtain the connection probability between any two target waters of the lake along a certain direction and distance range, and obtain the hydrological connectivity data of the lake; Step 2: Obtain the water level data of the lake; Step 3: Calculate the correlation coefficients between hydrological connectivity and water level respectively, and judge the correlation between hydrological connectivity and water level; Step 4: For the hydrological connectivity and water level data that meet the correlation requirements, use the parameter estimation method of univariate variables to construct the marginal distribution functions of hydrological connectivity and water level, and obtain their optimal marginal distribution forms according to the goodness-of-fit test; Step 5: Use the Copula function to connect the marginal distributions of hydrological connectivity and water level to obtain the joint probability distribution function, and the Copula function solves the multi-variable probability problem; Step 6: Set up different water replenishment scenarios for hydrological connectivity and water level, calculate the joint probability and conditional probability of different water replenishment scenarios, and determine the optimal water level of the lake in combination with the water replenishment management requirements and ecological restoration goals. The water replenishment management requirements and ecological restoration goals refer to meeting the requirements of flood control safety, minimum ecological flow, maintaining biodiversity and protecting biological habitats of the lake to ensure the survival and reproduction of organisms.

2. The method for determining the optimal water level of a lake according to claim 1, characterized in that, in Step 1, conduct geostatistical analysis on the remote sensing images of the set lake to obtain the connection probability between any two target waters of the lake along a certain direction and distance range, and obtain the hydrological connectivity data of the lake.

3. The method for determining the optimal water level of a lake according to claim 1, characterized in that, in Step 3, test the correlation between hydrological connectivity and water level data sequences through Spearman coefficient, Pearson coefficient and Kendall coefficient. The greater the absolute value of the correlation coefficient value, the stronger the dependence between variables. Among them: when the correlation coefficient value is less than 0.2, it can be regarded as extremely weak correlation or no correlation, and when the correlation coefficient value is greater than 0.6, it is a strong correlation.

4. The method for determining the optimal water level of a lake according to claim 1, characterized in that, the univariate variable refers to the data sequence of hydrological connectivity or water level; the multi-variable variables refer to the data sequences of hydrological connectivity and water level; the types of the marginal distribution functions include beta distribution, gamma distribution, Weibull distribution, generalized Pareto distribution, generalized extreme value distribution, lognormal distribution or normal distribution; the types of the joint probability distribution functions include Frank, T, Gaussian, Clayton and Gumbel Copula functions.

5. The method for determining the optimal water level of a lake according to claim 1, characterized in that, In step 4, the process of obtaining the marginal distribution function includes: First, use the maximum likelihood method to solve and determine the unknown parameters of the univariate marginal distribution function, and test the goodness of fit of alternative marginal distribution functions such as the beta distribution through the AIC and BIC criteria. The smaller the AIC and BIC values, the better the selected marginal function fits the empirical distribution function, so as to select the optimal marginal distribution type for hydrological connectivity and water level data.

6. The method for determining the optimal water level of a lake according to claim 1, characterized in that, in step 5, the expression of the joint probability distribution function is: ； In the formula: x is the hydrological connectivity data, y is the water level data, is the marginal distribution function of the hydrological connectivity sequence, is the marginal distribution function of the water level sequence, is the joint probability distribution function of hydrological connectivity and water level, is the type of Copula function satisfied by the joint probability distribution function.

7. The method for determining the optimal water level of a lake according to claim 1, characterized in that, in step 5, different Copula function types are selected to fit the joint probability distribution between hydrological connectivity and water level sequences, and the Copula function type with the best fitting effect is selected according to the principle of the smallest AIC and BIC values.

8. The method for determining the optimal water level of a lake according to claim 1, characterized in that, in step 6, different water replenishment scenarios of hydrological connectivity and water level are set up. The process of calculating the joint probability and conditional probability of different water replenishment scenarios is as follows: According to the quartile method, the hydrological connectivity and water level data sequences are respectively divided into four levels: (1) 0 - 25%, (2) 25% - 50%, (3) 50% - 75%, (4) 75% - 100%. The hydrological connectivity and water level data sequences of different levels are combined into 16 scenarios in sequence, and the joint probability and conditional probability of different water replenishment scenarios, as well as the conditional probability that the hydrological connectivity result belongs to a certain connectivity level at a specific water level, are calculated.

9. The method for determining the optimal water level of a lake according to claim 1, characterized in that, the water level interval range in the conditional probability distribution result obtained in step 6 that is beneficial to the transition of low connectivity level events to high connectivity level events is the optimal water level of the target lake.

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