A method for calculating transformation amount of water resources in mining area based on nonlinear multi-terminal hybrid model

Abstract

The application discloses a kind of based on nonlinear multi-end element hybrid model's computing mining area water resource conversion quantity method, belong to water resource protection technical field, including carrying out research area regional geology, hydrogeological survey, obtain regional topography, rainfall, evaporation and other background data, identify all potential water sources in region, clarify the qualitative relationship of regional water resource circulation transformation;Select representative point to carry out water sample collection, carry out hydrogeochemical test;Using DBSCAN algorithm to eliminate abnormal samples, identify and confirm stable end member;Based on evaporation fractionation effect and mineral dissolution kinetics introduce nonlinear factor, construct nonlinear multi-end element hybrid model, the contribution rate calculation between different water sources;Bayesian hierarchical model is constructed, integrated verification measured data and contribution rate calculation result, output water source contribution rate confidence interval.The application can accurately find out regional water cycle quantitative relationship and circulation mode, realize water resource full utilization and protection repair.

Description

Technical Field

[0001] This invention relates to the field of water resource protection technology, and in particular to a method for calculating the water resource conversion in mining areas based on a nonlinear multi-terminal hybrid model. Background Technology

[0002] Open-pit coal mining often generates large amounts of mine water inflow, significantly impacting the native ecological environment, especially damaging shallow Quaternary aquifers. The transformation relationships among atmospheric precipitation, surface water, groundwater, and mine water under the influence of open-pit coal mining are a crucial research topic in regional water cycle models, providing an important basis for formulating scientific and efficient water-conserving coal mining strategies. Currently, the calculation of the transformation of these four waters in open-pit mines mainly relies on methods such as hydrogen and oxygen isotope analysis of water samples, hydrochemical testing, and the construction of linear mixing models. However, these methods suffer from limitations such as fragmented hydrological data and poor model adaptability. They only consider the absence of isotopic fractionation during short-term mixing and fail to quantify the evaporation effect and long-term water-rock interaction in the complex hydrological cycle of open-pit mines. The current lack of systematic and nonlinear global modeling methods for the transformation of these four waters in open-pit mines leads to low accuracy in water resource quantitative prediction and insufficient scientific rigor in regulation schemes, hindering the green development process of mining areas. Summary of the Invention

[0003] Technical Problem Solved: Addressing the issue of low accuracy in calculating water resource conversion during open-pit mining, this invention provides a method for calculating water resource conversion in mining areas based on a nonlinear multi-terminal hybrid model. This method comprehensively considers the geological and hydrogeological conditions of the mining area, as well as the effects of evaporation and water-rock interaction, establishing an accurate method for calculating water resource conversion. This method can precisely identify the quantitative relationship and cycle pattern of regional water circulation, effectively manage and utilize regional water resources, reduce negative environmental impacts, and provide a basis for formulating scientific and efficient water-conserving coal mining strategies.

[0004] Technical solution: The present invention provides a method for calculating the water resource conversion rate in mining areas based on a nonlinear multi-terminal hybrid model, the method comprising the following steps:

[0005] Step 1: Conduct regional geological and hydrogeological surveys of the study area to obtain background data on regional topography, rainfall, evaporation, and hydrogeological parameters; based on the regional background data, identify all potential water sources in the region and clarify the qualitative relationships of regional water resource cycle transformation.

[0006] Step 2: Select representative locations in the study area to collect water samples from all potential water sources and conduct hydrogeochemical tests; based on the test results, use the DBSCAN algorithm to remove outlier samples and identify and confirm stable endmembers;

[0007] Step 3: Based on the evaporation fractionation effect and mineral dissolution kinetics, introduce nonlinear factors to construct a nonlinear multi-terminal mixing model and calculate the contribution rate among different water sources;

[0008] Step 4: Construct a Bayesian hierarchical model, integrate and verify the measured data and contribution rate calculation results, and output the confidence interval of the water source contribution rate.

[0009] Preferably, the hydrogeological parameters in step 1 include, but are not limited to, the composition of Quaternary and bedrock aquifers, aquifer water level, aquifer permeability, aquifer storage coefficient, water inflow, water inflow point, and mining plan.

[0010] Preferably, all potential water sources in step 1 include atmospheric precipitation, surface water, groundwater, and coal mine water inflow, among which groundwater includes Quaternary loose layer water and bedrock water.

[0011] Preferably, the hydrogeochemical testing in step 2 includes conventional ion HCO3-. - C1 - SO4 2- CO3 2- Na + K + Ca 2+ Mg 2+ Trace components and stable isotopes of hydrogen and oxygen 2 H, 18 The test of O.

[0012] Preferably, the step 2 of the DBSCAN algorithm to remove abnormal samples is as follows:

[0013] Step 21: Based on the results of routine ion testing of water samples, determine the main components in the routine ion content of a specific water source to reduce dimensionality and construct a multidimensional dataset. X ={ x 1 , x 2 ,..., x n};

[0014] Step 22: Define the neighborhood radius eps of the DBSCAN algorithm: control the sample neighborhood range, determined by the k-distance curve k=min_samples-1;

[0015] Step 23: Define the minimum number of samples min_samples for the DBSCAN algorithm: the minimum number of neighborhood samples for determining the core object, where min_samples≥d+1, and d is the principal component dimension;

[0016] Step 24: Perform density clustering on the data points. If the number of samples in the neighborhood of point xi is greater than or equal to min_samples, then mark it as a core object; points not included in any cluster are marked as noise / outliers and excluded.

[0017] Preferably, the specific steps for constructing the nonlinear multi-terminal hybrid model in step 3 are as follows:

[0018] Step 31: Based on the evaporation fractionation effect, the Rayleigh isotope fractionation model is used, and its calculation formula is as follows:

[0019] ;

[0020] In the formula: ∆ i evap Rayleigh isotope fractionation model; α i E is the isotopic fractionation coefficient. i The proportion of evaporation loss from water source i;

[0021] Step 32: Based on the influence of water-rock interaction, a mineral dissolution kinetics correction term is used, the calculation formula of which is as follows:

[0022] ;

[0023] In the formula: ∆ i dissp k is a correction term for dissolution kinetics. i is the mineral dissolution rate constant; t is the water-rock interaction time; C mineral Mineral concentration;

[0024] Step 33: Based on the evaporation fractionation effect and mineral dissolution kinetics, define a nonlinear mixing equation, the calculation formula of which is as follows:

[0025] ;

[0026] Where: δ mix Isotope values ​​of mixed water / %; f i The contribution percentage of the i-th water source / %, Σf i =1;δ i The isotope value of the i-th water source is %.

[0027] Preferably, the specific steps for constructing the Bayesian hierarchical model in step 4 are as follows:

[0028] Step 41: Construct the data layer, with the likelihood function of the observed data being: y ~ N(g(f, θ), σ 2 I);

[0029] In the formula: y represents measured isotope and water chemistry data; g(⋅) is the nonlinear mixing function; θ represents the fractionation and dissolution parameters; σ2 I is the covariance matrix;

[0030] Step 42: Construct the process layer. The prior distribution of the water source contribution ratio is: f∼Dirichlet(β), β=(β1,...,β) n );

[0031] In the formula: f is the prior parameter, which is the expected contribution of other water sources based on geological and hydrogeological conditions; β is the concentration parameter of the Dirichlet distribution.

[0032] Step 43: Construct a hyperparameter layer where the fractionation coefficient and dissolution rate follow a multivariate normal distribution and a gamma distribution, respectively. Its hyperprior is: α i ~N(μ i ,τ α -1 ), k i ~Gamma(a,b);

[0033] Where: μ i τ is the prior mean; α -1 denoted as variance; a is the shape parameter; b is the rate parameter;

[0034] Step 44: Using Bayes' theorem, the posterior distribution is derived as: p(f,θ|y)∝p(y,f|θ)·p(f)·p(θ); the Hamilton-Monte Carlo (HMC) algorithm is used for sampling to estimate the marginal posterior distribution of the water source contribution, and then the confidence interval is calculated.

[0035] Compared with the prior art, the present invention has at least the following beneficial effects:

[0036] 1. Traditional linear hybrid models simply superimpose proportions between water source end-members. However, in reality, the water cycle is simultaneously affected by nonlinear processes such as evaporation and fractionation, and water-rock interaction. The method of this invention combines a nonlinear multi-end-member hybrid model (considering evaporation and fractionation effects and mineral dissolution kinetics) with a Bayesian hierarchical model (outputting confidence intervals), and introduces the DBSCAN algorithm to remove outlier samples. By introducing the isotope Rayleigh fractionation model and mineral dissolution kinetics correction term, a more realistic nonlinear hybrid model is constructed, providing a reliable basis for quantitative calculation of water resource transformation.

[0037] 2. The method of this invention integrates measured hydrochemical data and contribution rate calculation results through a Bayesian hierarchical model, and outputs a probabilistic expression to replace the traditional deterministic solution. It realizes the quantitative output of the confidence interval of the contribution rate in the water resource model of the mining area, solves the problem of model prediction ambiguity caused by strong uncertainty in the open-pit mine water cycle, significantly improves the prediction accuracy, and enhances the credibility of water resource assessment results.

[0038] 3. Traditional methods rely on manual experience to delineate water cycle units, making it difficult to quantify the conversion intensity of various potential water resources. This method implements a closed-loop technical system of "data acquisition-model calculation-verification and optimization." By integrating multi-source data and identifying stable end-members, it accurately identifies regional water cycle conversion paths, breaking through the spatial limitations of traditional hydrogeological experiments. This provides a more scientific basis for delineating water resource protection red lines and controlling mine water, supporting the remediation of groundwater and surface water in coal mining areas. In the process of water resource cycle conversion in open-pit mines, by calculating the quantitative conversion ratio of the "four waters" (atmospheric precipitation, surface water, groundwater, and mine water), it accurately identifies the quantitative relationship and cycle pattern of regional water cycle, providing a basis for identifying water pollution diffusion paths and for regional water resource protection and allocation.

[0039] 4. This method was actually applied in an open-pit mine in Inner Mongolia. In a specific case, the contribution rates of atmospheric precipitation, surface water, and groundwater to mine water were quantified (e.g., the contribution rate of groundwater was 45.3%~60.3%), and the technical steps were described in detail (e.g., DBSCAN parameter settings, nonlinear equation construction, and Bayesian hyperparameter selection). This can provide a basis for subsequent targeted regulation of water resources (e.g., limiting mining volume and strengthening drainage facilities). Attached Figure Description

[0040] Figure 1 This is a flowchart of the method for calculating the water resource conversion rate in mining areas based on a nonlinear multi-terminal hybrid model according to the present invention;

[0041] Figure 2 This is a diagram illustrating the "four waters" transformation relationship of atmospheric precipitation, surface water, groundwater, and mine water in open-pit mines, as presented in this invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will be described in conjunction with the accompanying drawings. Figures 1-2 The technical solutions of the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0043] Example 1: As Figures 1-2 As shown, this invention discloses a method for calculating the water resource conversion rate in mining areas based on a nonlinear multi-terminal hybrid model, the method comprising the following steps.

[0044] (I) Conduct regional geological and hydrogeological surveys of the study area to obtain background data on regional topography, rainfall, evaporation, and hydrogeological parameters. Hydrogeological parameters include, but are not limited to, the composition of Quaternary and bedrock aquifers, aquifer water levels, aquifer permeability, aquifer storage coefficient, water inflow, water inflow points, and mining plans. The regional topography and geomorphology map of the mining area will be obtained through remote sensing technology to obtain the regional topography and geomorphology map and stratigraphic columnar section. Contour maps of groundwater levels in the shallow Quaternary aquifers of the coal seam roof and the deep sandstone confined aquifers of the coal seam floor, as well as parameters such as mine water inflow and mine water inflow points, will be obtained through construction survey boreholes.

[0045] Based on regional background data, all potential water sources in the region were identified, and the qualitative relationships of regional water resource cycles and transformations were clarified. All potential water sources include atmospheric precipitation, surface water, groundwater, and coal mine water inflows, with groundwater further comprising Quaternary loose layer water and bedrock water. The qualitative relationships of cycles and transformations among potential water sources are as follows: Figure 2 As shown.

[0046] (II) Collect water samples (atmospheric precipitation, surface water, groundwater, and mine water) from representative locations within the study area and conduct hydrogeochemical tests. Hydrogeochemical tests include conventional ion HCO3-. - C1 - SO4 2- CO3 2- Na + K + Ca 2+ Mg 2+ Trace components and stable isotopes of hydrogen and oxygen 2 H, 18 The test of O.

[0047] The following example uses an open-pit mine in Inner Mongolia as an illustration:

[0048] A large amount of water inflow occurred during the mining of an open-pit mine in Inner Mongolia, resulting in significant water loss. Simultaneously, the extensive drainage caused the groundwater level to drop by more than 30 meters within a 5km radius of the mine pit. To alleviate the groundwater loss problem, the method for calculating water resource conversion volume of this invention was employed to accurately determine the quantitative relationship of the regional water cycle, enabling the scientific management and efficient utilization of regional water resources. The inflow volume of the mine pit was approximately 84,000 m³. 3 / d, a dynamic monitoring system for mine water inflow was established, and the specific characteristics of mine water inflow and water quality are shown in Table 1.

[0049] Table 1. Water quality characteristics of the four types of water in an open-pit mine in Inner Mongolia:

[0050] .

[0051] Based on the test results, the DBSCAN algorithm was used to remove abnormal samples and identify and confirm stable endmembers (taking mine water as an example). The steps of the DBSCAN algorithm to remove abnormal samples are as follows.

[0052] (1) Based on the results of routine ion testing of water samples, the main component Cl in the routine ion test of mine pit water was determined. - and SO4 2- To achieve dimensionality reduction to d=2 and construct a multidimensional dataset. X ={ x 1 , x 2 ,..., x n}

[0053] (2) Define the neighborhood radius eps of the DBSCAN algorithm: control the sample neighborhood range, and determine eps=1.2 by the k-distance curve k=min_samples-1.

[0054] (3) Define the minimum number of samples min_samples for the DBSCAN algorithm: the minimum number of neighborhood samples for determining the core object, min_samples≥d+1, where d is the principal component dimension, min_samples=4.

[0055] (4) Perform density clustering on the data points. If the number of samples in the neighborhood of point xi is ≥ min_samples=4, then mark it as a core object; points not included in any cluster, such as mine water 2# (taking mine water as an example), are noise / outliers and are excluded. Similarly, repeat the above steps to exclude the abnormal sample groundwater 4# from atmospheric precipitation, surface water, and groundwater.

[0056] (III) Based on the evaporation fractionation effect and mineral dissolution kinetics, a nonlinear multi-terminal mixing model is constructed to calculate the contribution rate between different water sources. The specific steps for constructing the nonlinear multi-terminal mixing model are as follows.

[0057] (1) Based on the evaporation fractionation effect, the Rayleigh isotope fractionation model is used, and the calculation formula is as follows:

[0058] ;

[0059] In the formula: ∆ i evap Rayleigh isotope fractionation model; α i α is the isotopic fractionation coefficient. i The value is 1.0; E i E represents the proportion of evaporation loss of water source i. i The value is 0.2; ∆ is calculated.i evap It is -0.22‰.

[0060] (2) Based on the influence of water-rock interaction, the mineral dissolution kinetics correction term is used, and its calculation formula is as follows:

[0061] ;

[0062] In the formula: ∆ i dissp k is a correction term for dissolution kinetics. i is the mineral dissolution rate constant; t is the water-rock interaction time; C mineral The mineral concentration is given; based on the average water-rock interaction in the study area (taking gypsum as an example), the gypsum dissolution rate constant k is... i The value is 0.01d. -1 The duration of action is t=100d, and the mineral concentration is C. 石膏 The value is taken as 5 mg / L, and ∆ is calculated. i dissp It is 5 mg / L (SO4²⁻).

[0063] (3) Based on the evaporation fractionation effect and mineral dissolution kinetics, a nonlinear mixing equation is defined, and its calculation formula is as follows:

[0064] ;

[0065] Where: δ mix Isotope values ​​of mixed water / %; f i The contribution percentage of the i-th water source / %, Σf i =1;δ i The isotope value of the i-th water source is %.

[0066] Taking mine water as an example, the contribution rate of mine water sources is calculated as shown in Table 2.

[0067] Table 2. Contribution Rate of Mine Water Sources:

[0068] .

[0069] (iv) Construct a Bayesian hierarchical model, integrate and verify the measured data and contribution rate calculation results, and output the confidence interval of the water source contribution rate; the specific steps for constructing the Bayesian hierarchical model are as follows.

[0070] (1) Construct the data layer, and the likelihood function of the observed data is: y ~ N(g(f, θ), σ 2 I);

[0071] In the formula: y represents measured isotope and water chemistry data; g(⋅) is the nonlinear mixing function; θ represents the fractionation and dissolution parameters; σ 2I is the covariance matrix.

[0072] (2) Constructing the process layer, the prior distribution of the water source contribution ratio is: f∼Dirichlet(β) = Dirichlet(f 大气降水 ,f 地表水 , f 地下水 ), β=(1,1,1);

[0073] In the formula: f is a priori parameter, which is the expected contribution of other water sources based on geological and hydrogeological conditions; β is the concentration parameter of the Dirichlet distribution.

[0074] (3) Construct a hyperparameter layer. The fractionation coefficient and dissolution rate follow a multivariate normal distribution and a gamma distribution, respectively. The hyperprior is: α i ~N(μ i ,τ α -1 =N(1.0,0.05) 2 ), k i ~Gamma(a,b)=Gamma(2,0.1);

[0075] Where: μ i τ is the prior mean; α -1 denoted as variance; a is the shape parameter; b is the rate parameter.

[0076] (4) The posterior distribution is derived using Bayes' theorem as: p(f,θ|y)∝p(y,f|θ)·p(f)·p(θ); the Hamilton Monte Carlo (HMC) algorithm is used for sampling to estimate the marginal posterior distribution of water source contribution, and then the range and confidence interval of the mine water source contribution rate are calculated as shown in Table 3.

[0077] Table 3. Range and confidence interval of contribution rate of mine water source:

[0078] .

[0079] This invention presents a method for calculating water resource conversion in mining areas based on a nonlinear multi-terminal hybrid model. This method can accurately identify the quantitative relationships and patterns of regional water cycles, effectively manage and utilize regional water resources, reduce negative environmental impacts, and provide a basis for formulating scientific and efficient water-conserving coal mining strategies. The method has been practically applied in an open-pit mine in Inner Mongolia. In a specific case, the contribution rates of atmospheric precipitation, surface water, and groundwater to mine water (e.g., groundwater contribution rate of 45.3%~60.3%) were quantified, and targeted control suggestions were proposed (e.g., limiting mining volume, strengthening interception...). The document details the technical steps (such as DBSCAN parameter settings, nonlinear equation construction, and Bayesian hyperparameter selection) for drainage facilities, demonstrating its operability. For example, it quantitatively identifies groundwater as the main source of mine water recharge in the study area, with an average contribution rate of 54.1%, necessitating strict limits on extraction (with a threshold set at a lower confidence limit of 45.3%). Surface water contributes an average of 31.1% to mine water, which may increase further during the rainy season, suggesting strengthened construction of interception and drainage facilities. Rainfall contributes an average of 14.8% to mine water, and its utilization rate can be improved through rainwater harvesting projects.

[0080] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating water resource conversion in mining areas based on a nonlinear multi-terminal hybrid model, characterized in that, The method includes the following steps: Step 1: Conduct regional geological and hydrogeological surveys of the study area to obtain background data on regional topography, rainfall, evaporation, and hydrogeological parameters; based on the regional background data, identify all potential water sources in the region and clarify the qualitative relationships of regional water resource cycle transformation. Step 2: Select representative locations in the study area to collect water samples from all potential water sources and conduct hydrogeochemical tests; based on the test results, use the DBSCAN algorithm to remove outlier samples and identify and confirm stable endmembers; Step 3: Based on the evaporation fractionation effect and mineral dissolution kinetics, a nonlinear factor is introduced to construct a nonlinear multi-terminal component mixing model to calculate the contribution rate among different water sources; the specific steps for constructing the nonlinear multi-terminal component mixing model are as follows: Step 31: Based on the evaporation fractionation effect, the Rayleigh isotope fractionation model is used, and its calculation formula is as follows: ； In the formula: Rayleigh isotope fractionation model; α i E is the isotopic fractionation coefficient. i The proportion of evaporation loss from water source i; Step 32: Based on the influence of water-rock interaction, a mineral dissolution kinetics correction term is used, the calculation formula of which is as follows: ； In the formula: k is a correction term for dissolution kinetics. i is the mineral dissolution rate constant; t is the water-rock interaction time; C mineral Mineral concentration; Step 33: Based on the evaporation fractionation effect and mineral dissolution kinetics, define a nonlinear mixing equation, the calculation formula of which is as follows: ； Where: δ mix Isotope values ​​of mixed water / %; f i The contribution percentage of the i-th water source / %, Σf i =1;δ i The isotope value of the i-th water source is %; Step 4: Construct a Bayesian hierarchical model, integrate and verify the measured data and contribution rate calculation results, and output the confidence interval of the water source contribution rate.

2. The method for calculating water resource conversion in mining areas based on a nonlinear multi-terminal hybrid model according to claim 1, characterized in that, The hydrogeological parameters in step 1 include, but are not limited to, Quaternary and bedrock aquifer composition, aquifer water level, aquifer permeability, aquifer storage coefficient, water inflow, water inflow point, and mining plan.

3. The method for calculating water resource conversion in mining areas based on a nonlinear multi-terminal hybrid model according to claim 1, characterized in that, All potential water sources in step 1 include atmospheric precipitation, surface water, groundwater, and coal mine water inflow. Groundwater includes Quaternary loose layer water and bedrock water.

4. The method for calculating the water resource conversion rate in mining areas based on a nonlinear multi-terminal hybrid model according to claim 1, characterized in that, Step 2 hydrogeochemical testing includes conventional ion HCO3-. - C1 - SO4 2- CO3 2- Na + K + Ca 2+ Mg 2+ Trace components and stable isotopes of hydrogen and oxygen 2 H, 18 The test of O.

5. The method for calculating the water resource conversion rate in a mining area based on a nonlinear multi-terminal hybrid model according to claim 4, characterized in that, The steps in step 2 of the DBSCAN algorithm to remove outlier samples are as follows: Step 21: Based on the results of routine ion testing of water samples, determine the main components in the routine ion content of a specific water source to reduce dimensionality and construct a multidimensional dataset. X ={ x 1 , x 2 ,..., x n }; Step 22: Define the neighborhood radius eps of the DBSCAN algorithm: control the sample neighborhood range, determined by the k-distance curve k=min_samples-1; Step 23: Define the minimum number of samples min_samples for the DBSCAN algorithm: the minimum number of neighborhood samples for determining the core object, where min_samples≥d+1, and d is the principal component dimension; Step 24: Perform density clustering on the data points. If the number of samples in the neighborhood of point xi is greater than or equal to min_samples, then mark it as a core object; points not included in any cluster are marked as noise / outliers and excluded.

6. The method for calculating the water resource conversion rate in mining areas based on a nonlinear multi-terminal hybrid model according to claim 1, characterized in that, The specific steps for constructing the Bayesian hierarchical model in step 4 are as follows: Step 41: Construct the data layer, with the likelihood function of the observed data being: y ~ N(g(f, θ), σ 2 I); In the formula: y represents measured isotope and water chemistry data; g(•) is the nonlinear mixing function; θ represents the fractionation and dissolution parameters; σ 2 I is the covariance matrix; Step 42: Construct the process layer. The prior distribution of the water source contribution ratio is: f ~ Dirichlet(β), β = (β1, ..., β2). n ); In the formula: f is the prior parameter, which is the expected contribution of other water sources based on geological and hydrogeological conditions; β is the concentration parameter of the Dirichlet distribution. Step 43: Construct a hyperparameter layer where the fractionation coefficient and dissolution rate follow a multivariate normal distribution and a gamma distribution, respectively. Its hyperprior is: α i ~N(μ i ,τ α -1 ), k i ~Gamma(a,b); Where: μ i τ is the prior mean; α -1 denoted as variance; a is the shape parameter; b is the rate parameter; Step 44: Using Bayes' theorem, the posterior distribution is derived as: p(f,θ|y)∝p(y,f|θ)·p(f)·p(θ); the Hamilton-Monte Carlo (HMC) algorithm is used for sampling to estimate the marginal posterior distribution of the water source contribution, and then the confidence interval is calculated.

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