Method for estimating lake water age based on hydrogen and oxygen stable isotope technology

Abstract

The invention discloses a method for estimating the age of lake water based on a hydrogen and oxygen stable isotope technology, and belongs to the technical field of hydrology and stable isotopes. According to the method, the lake water isotope mass balance model is constructed, the lake water age calculation formula is exported, various key parameters required by the lake water age calculation formula are determined and substituted into the formula for solving, the lake water age corresponding to each lake water sampling point position is output, the result is displayed, and lake water age estimation is completed. Compared with traditional water age simulation based on a lake hydrodynamic model, the method is simple in principle and efficient in operation, the dependency of an existing hydrological model on lake hydrological monitoring data during water age simulation is overcome, and the method is easily applied to water age estimation of shallow lakes.

Description

Technical Field

[0001] This invention belongs to the field of hydrology and stable isotope technology, specifically relating to a method for estimating the age of lake water based on hydrogen and oxygen stable isotope technology. Background Technology

[0002] When describing the hydraulic conditions of lakes, the water exchange cycle is often used to measure the hydrological renewal cycle of a lake. However, the lake water exchange cycle is only a theoretical value, reflecting the theoretical time required for one water replacement in the lake. It can be roughly estimated by dividing the lake volume V by the inflow runoff I. The water exchange cycle treats the lake as a homogeneous whole and does not take into account the spatial heterogeneity of the hydrodynamic conditions within the lake. In contrast, lake age is a local concept that quantifies the age distribution differences of water masses at different locations within the lake, effectively reflecting the spatial distribution of lake hydrodynamics. If the age of inflow runoff (such as river water) is defined as 0 days, then the lake age represents the cumulative time (residence) experienced by the inflow runoff after it enters the lake and forms a local water mass, driven by the lake flow field, until it leaves (flows out of the lake). Therefore, accurately estimating the lake age is a key focus in lake hydrological research and is crucial for studying the impact of lake hydrological changes on lake ecosystems.

[0003] Current methods for estimating lake age typically involve simulating the lake's hydrodynamic age using hydrodynamic models. This method is time-consuming and labor-intensive, making it difficult to implement in lakes lacking detailed hydrological monitoring data. Simulating lake age based on hydrodynamic models requires extensive meteorological and hydrological monitoring data as boundary conditions; the model parameters are numerous, complex to set, and computationally intensive. Data such as underwater topography and inflow / outflow monitoring data are often needed, rendering hydrodynamic simulations infeasible for some lakes lacking sufficient observational data. Furthermore, the reliability of the simulation results heavily depends on the quality of the input data. Hydrogen and oxygen stable isotopes are natural tracers in the water cycle, and lake water isotopic signals record crucial information about lake hydrological processes. Therefore, a method for retrieving lake age using hydrogen and oxygen isotopes is urgently needed. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for estimating the age of lake water based on hydrogen-oxygen stable isotope technology.

[0005] To achieve the above technology, the steps include: S1. Construct a formula for calculating the age of lake water, including the following steps: S1.1 Collect lake water samples from the target area and perform isotope measurements; Specifically, the distribution and number of sampling points are determined based on the characteristics of the lake and the on-site sampling conditions; water samples are collected by boat along the planned route and locations; during sampling, a water sampler is used to collect surface water (0.5m below the water surface), and the latitude and longitude information of each sampling point is recorded simultaneously; the collected water samples are filled into 20ml plastic bottles, and the samples should be sealed and frozen before analysis; the hydrogen and oxygen isotope composition (i.e., δ¹⁸) of the lake water is measured using a water isotope analyzer (such as a Picarro 2140-i). 8 O and δ²H), uniformly corrected to the VSMOW (Vienna Standard Mean Seawater) standard; S1.2 Construct the lake water balance equation, and based on the water balance equation, construct the lake isotope mass balance equation; For a lake in a hydrologically stable state (i.e., its water storage remains relatively stable on an interannual scale), its annual water storage variable dV / dt can be expressed as: In the formula, V represents the lake's water storage capacity; I represents the average annual inflow into the lake; E represents the average annual evaporation; and Q represents the average annual outflow from the lake. Based on the lake's water balance, the expression for the lake's isotopic mass balance is as follows: In the formula, δ L Indicates the isotopic composition of the lake water; δ I Indicates the weighted average isotopic composition of inflow into the lake; δ E Indicates the isotopic composition of water vapor evaporating from the lake surface; δ Q The isotopic composition of the lake's flow (lake water); S1.3. Based on the lake isotope mass balance equation, derive the formula for calculating the age of lake water; Assuming the lake water is homogeneous (i.e., without spatial heterogeneity), isotopic fractionation during evaporation leads to continuous enrichment of lake water isotopes. The dynamic changes in lake water isotopes during this process can be described by the following formula: In the formula, δ L(i+1) This indicates that after one hydrological exchange, the lake's hydrological values ​​relative to the previous δ step... L(i) The updated iteration value; ΔI represents the water balance at one time step, i.e., the water cycle; x =E / I represents the ratio of annual evaporation to the inflow into the lake (i.e., the evaporation ratio). Formula for dynamic changes in lake water isotopes δ L(i+1) Integrating over time and combining the results, we obtain the following formula: In the formula, δ Sδ represents the value at which the lake water reaches an isotopic stable state under specific water balance conditions (i.e., given E / I values); δ0 represents the initial isotopic composition of the lake water. m Indicates the evaporation enrichment coefficient of an isotope; t It represents the number of time steps; I / V is equal to the reciprocal of V / I (i.e., the theoretical water exchange cycle of the lake), and is defined as the time unit of the lake water cycle. One I / V represents one unit of time step of water cycle, corresponding to ΔI. By performing an inverse function operation on the integral formula, we obtain the formula for calculating the age of the lake, as shown below: In the formula, WA (Water Age) represents the age of the lake water.

[0006] S2. Determine the key parameters for the formula to calculate the age of lake water; The calculation steps for each parameter in the constructed formula for calculating the age of lake water include: S2.1 Determine the value δ when the lake water reaches isotopic stability under specific water balance conditions (i.e., given E / I values). S ; The method to determine this is: calculate δ S 18 O and δ S 2 H, thus determining the steady-state point (δ) S 18 O, δ S 2 H) falls on the lake evaporation line, thus ensuring the internal self-consistency of the model; δ S 18 O is calculated using the following formula: δ S 18 O=δ L 18 O max +0.1 In the formula, δ L 18 O max This represents the maximum isotope enrichment value observed (measured) in a certain sampling; 0.1 represents the instrument's measurement error (‰). Based on δ S 18 O, determine δ S 2 H, expressed as follows: δ S 2 H=δ S 18 O *Slope+Intercept In the formula, Slope and Intercept represent the slope and intercept of the lake evaporation line LEL, respectively; Furthermore, the lake water has an excessive deuterium value δ S The expression for (d-excess) is as follows: δ S (d-excess)=δ S 2 H-8*δ S 18 O S2.2 Determine the lake evaporation line (LEL) and the weighted average inflow runoff isotope δ¹⁸. I ; The method for determining the lake evaporation line (LEL) is as follows: Linear regression was used to derive the hydrogen and oxygen isotope relationship line for all sampling points in a given period, i.e., the lake evaporation line (LEL). The linear characteristics of the LEL were statistically analyzed, including the slope, intercept, and coefficient of determination (R²). 2 and residual RMSE; Determine the delta isotope of the runoff flowing into the lake I The method is as follows: determine the value by the intersection of the lake evaporation line (LEL) and the local atmospheric water line (LMWL). If there is no local atmospheric water line (LMWL), the global atmospheric water line (GMWL) can be used instead, with the formula δ²H = 8 * δ¹. 8 O+10; Additionally, for lakes where the isotopic composition of the inflowing river water has been monitored simultaneously, the average isotopic value of the river water can be used instead of δ. I .

[0007] S2.3 Determine the δ¹⁸O isotope of water vapor evaporating from the lake surface. E ; Estimate δ using the Craig-Gordon isotopic evaporation model E The calculation formula is as follows: In the formula, α + This represents the isotopic equilibrium fractionation coefficient at the steam-water evaporation interface; h The relative humidity of the atmosphere is expressed as the multi-year average value of the weather stations near the lake; δ A Indicates the isotopic composition of atmospheric water vapor; ε k =(1 h)*C k Represents the isotopic kinetic fractionation factor; where C k The kinetic fractionation constant is commonly used for oxygen and hydrogen, with values ​​of 14.2‰ (δ¹). 8 O) and 12.5‰ (δ 2 H); ε + =(α+ 1) 1000 represents the equilibrium fractionation factor; the equilibrium fractionation coefficients for oxygen and hydrogen are calculated using the following formulas: Oxygen fractionation coefficient α + ( 18 O): Hydrogen fractionation coefficient α + ( 2 H): In the formula, T represents the lake water temperature (°C), which is converted to Kelvin temperature by adding 273.15; The annual average water temperature of a lake can be obtained by taking measurements at specific locations within the lake. Atmospheric water vapor isotope δ A It can be obtained through instrument measurement or indirect calculation; Instrumental measurement method: Direct measurement is performed using an instrument (such as Picaro 2130-i), or indirect measurement is performed by condensing atmospheric water vapor using a condenser and then using a water isotope analyzer. Indirect calculation: Using the known slope of the lake evaporation line (LEL), we can deduce the unique atmospheric water vapor isotope value that could produce that slope. Details are as follows: First, a preliminary estimate of the oxygen isotope value δ of atmospheric water vapor is made. A 18 O: In the formula, δ P This indicates the isotopic composition of the average annual precipitation in the watershed where the lake is located; k δ P With δ A The effective fractionation coefficient between them ranges from 0.5 to 1.0; when other parameters are given, δ E It can be represented as δ A The function will be based on δ A δ obtained from simulation E The slope of the measured evaporation line is fitted using the following formula: In the formula, S LEL This represents the measured slope of the evaporation line; Based on δ A δ obtained from simulation E Must be located at δ S and δ I On the evaporation line formed by the two points (i.e., δ) S δ I and δ EOnly when the three points are collinear can the simulated evaporation line match the measured evaporation line; from this, the relationship for constraining the atmospheric hydrogen and oxygen isotope composition can be derived: δ A 2 H=a·δ A 18 O+b In the formula, δ A 2 H represents the hydrogen isotope value of atmospheric water vapor; a and b represent the slope and intercept of the constraint relation, respectively; δ is precisely constrained through the constraint relation. A 2 The value of H is chosen to make the E / I values ​​estimated for hydrogen and oxygen consistent.

[0008] S2.4 Determine the isotope evaporation enrichment coefficient m ; Evaporation enrichment coefficient m This describes the enrichment rate of lake water isotopes per unit time step, which is related to atmospheric relative humidity. h The function is calculated using the following formula: In the formula, δ * This represents the theoretical maximum isotopic enrichment value that a body of water can achieve when it is completely evaporated to dryness under given atmospheric isotopic composition and humidity conditions. The calculation formula is as follows: In the formula, ε = ε + + ε k This represents the total enrichment factor.

[0009] S2.5 Determine the evaporation ratio and water exchange cycle; The lake evaporation ratio E / I is calculated as follows: Furthermore, the water exchange cycle V / I of the lake can be calculated as follows: E / V represents the relative evaporation rate of a lake, which is the percentage of the lake's volume that is evaporated each year.

[0010] S3. Substitute the key parameters determined in S2 into the lake water age calculation formula constructed in S1 to solve the problem, output the lake water age corresponding to each sampling point, and intuitively display the spatial distribution characteristics of lake water isotopes and water age through spatial interpolation and probability distribution statistics, which is convenient for analysis and application.

[0011] Beneficial effects of the present invention This invention provides a rapid, direct, and efficient water age estimation scheme by measuring lake water isotope signals to invert the age of lake water. It is particularly suitable for quantitatively analyzing the spatiotemporal changes in water age and hydrodynamics of large shallow lakes before and after the implementation of water diversion projects, and provides technical support for evaluating the hydrological benefits of water replenishment projects. Attached Figure Description

[0012] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is a schematic diagram illustrating the relationship between lake water isotopes and lake water age according to the present invention. Figure 3 This is a schematic diagram illustrating the evaporation lines of lake water and river water isotopes in a certain lake in a certain year and month, as shown in this invention; wherein, Figure 3 (a) represents δ 18 O and δ 2 The relationship of H, Figure 3 (b) represents δ 18 The relationship between O and d-excess; Figure 4 The spatial variation of isotopes and water age of Dianchi Lake water in the embodiments of the present invention is shown; wherein (a) and (b) are the results in November 2022, and (c) and (d) are the results in May 2024; Figure 5 The spatial variation of isotopes and water age of Qilu Lake is shown in the embodiments of the present invention; wherein (a) and (b) are the results in August 2023, and (c) and (d) are the results in December 2024; Figure 6 The spatial variation of isotopes and water age of Yilong Lake is shown in the embodiments of the present invention; wherein (a) and (b) are the results in September 2023, and (c) and (d) are the results in May 2024. Detailed Implementation

[0013] The invention will now be described in further detail with reference to examples.

[0014] like Figure 1 and Figure 2 As shown, a method for estimating the age of lake water based on hydrogen and oxygen stable isotope technology includes the following steps: S1. Construct a formula for calculating the age of lake water, including the following steps: S1.1 Collect lake water samples from the target area and perform isotope measurements; Water samples and isotope measurements were performed on the three example lakes. The sampling details and isotope measurement results for each lake are shown in Table 1.

[0015] Table 1: Sampling data and isotope measurement results for each lake S1.2 Construct the lake water balance equation, and based on the water balance equation, construct the lake isotope mass balance equation (see instruction manual for details).

[0016] S2. Determine the key parameters for the lake age calculation formula; Determine the various model parameters in the water age formula sequentially according to the steps and methods described in the instruction manual.

[0017] S2.1, δ of each example lake s The results are shown in Table 2; Table 2: δ values ​​for each example lake s result S2.2 Evaporation lines and δ for each example lake I The results are shown in Table 3; Table 3: Evaporation lines and δ values ​​for each example lake I S2.3, δ of each example lake E The results of the relevant isotope fractionation coefficients are shown in Table 4; Table 4: δ values ​​for each example lake E and related isotopic fractionation coefficient results S2.4 Determine the evaporation enrichment coefficient of isotopes m (Results are shown in Table 5); S2.5 The results of the evaporation ratio E / I and water exchange cycle V / I for each example lake are shown in Table 5.

[0018] Table 5: Evaporation enrichment coefficients of each example lake m Evaporation ratio E / I and water exchange cycle V / I S3. Substitute the key parameters determined in S2 into the lake water age calculation formula constructed in S1 to solve for the lake water age corresponding to each sampling point. Through spatial difference and statistical analysis, the spatial distribution characteristics of lake water isotopes and water age are intuitively displayed, facilitating analysis and application. Specifically, the spatial distribution of lake water isotopes and water age is visualized using the pykrige toolkit in Python based on the latitude and longitude coordinates of the sample points; the spatial distribution of lake water isotopes and water age is then quantitatively displayed using the statistical probability density function PDF and cumulative probability distribution function CDF from the scipy toolkit.

[0019] To verify this invention, three plateau lakes in Yunnan Province, my country—Dianchi Lake, Qilu Lake, and Yilong Lake—are used as examples to demonstrate the water age estimation results obtained based on the method of this invention. Dianchi Lake, Qilu Lake, and Yilong Lake are all moderately eutrophic lakes. To control eutrophication, local governments have implemented lake water replenishment (inter-basin) water transfer projects, aiming to accelerate water replacement and create favorable hydrodynamic conditions for improving lake water quality. The water age estimation results can provide a scientific basis for optimizing lake water replenishment schemes.

[0020] Lake Introduction: Dianchi Lake (longitude: 102.716; latitude: 24.855; altitude: 1887m): It belongs to the Yangtze-Jinsha River system, with a water surface area of ​​approximately 298 km². 2 The average water depth is 5 meters, and the water storage capacity is 1.49 billion cubic meters. 3 .

[0021] Qilu Lake (Longitude: 102.777; Latitude: 24.166; Altitude: 1796m): It belongs to the Pearl River-Nanpan River system, with a water surface area of ​​approximately 37 km². 2 The average water depth is 4.2 meters, and the water storage capacity is 150 million cubic meters. 3 .

[0022] Yilong Lake (Longitude: 102.551; Latitude: 23.679; Altitude: 1414m): It belongs to the Pearl River-Nanpan River system, with a water surface area of ​​approximately 30 km². 2 The average water depth is 3.9 meters, and the water storage capacity is 120 million cubic meters. 3 .

[0023] Figure 4 Interpretation of Dianchi Lake water isotope and water age results: In November 2022, the lake water isotopes showed a trend of gradually increasing from north to south, δ¹ 8 The range of O is -7.4‰ to -5.5‰, with an average value of -6.2‰. Figure 4 (a) The spatial variation trend of lake water age is consistent with that of lake water isotopes, with the age gradually increasing from north to south, ranging from 179 to 779 days, and an average of 404 days. Figure 4 (b) 27% of the water area in the northern part of the lake has a water age less than the theoretical residence time, while the remaining 78% of the central and southern parts of the lake have a water age greater than the theoretical residence time. This indicates that the water replenishment project significantly enhanced the hydrodynamic conditions in the northern lake area and accelerated the water cycle in that area; however, the hydrodynamic conditions in the central and southern lake areas, which account for a larger area, have not been significantly improved.

[0024] Compared to November 2022, in May 2024, the average values ​​of lake water isotopes and water age increased to -3.8‰ and 822 days, respectively. Figure 4 (c) and Figure 4 (d) The water surface area with a water age greater than the theoretical residence time increased to 88%, which indicates that the reduced inflow during the dry season led to more closed lake hydrodynamic conditions.

[0025] Figure 5 Interpretation of isotope and water age results for Qilu Lake: In August 2023, the lake water isotopes showed a trend of gradual enrichment from southwest to northeast, δ¹ 8 The range of O is -4.0‰ to -3.4‰, with an average value of -3.7‰. Figure 5 (a)); The spatial variation trend of lake water age is consistent with that of lake water isotopes, with the water age gradually increasing from the southwest shore to the northeast shore, ranging from 561 to 951 days, with an average of 768 days. Figure 5 (b) δ¹ 8 Areas with relatively low water quality and shorter water age are concentrated at the mouths of major rivers flowing into the lake on the west bank, indicating the impact of rainy season runoff. In August, the water age across the entire lake exceeded the theoretical retention time for that month, indicating a severe shortage of inflow water resources in the basin.

[0026] Compared to August 2023, the spatial distribution trend of lake water isotopes and water age in December 2024 generally changed from a southwest-northeast direction to a north-south direction, and the average water age showed a slight decrease. Figure 5 (c) and Figure 5 (d) The reason is that the lake was artificially replenished through the northern water inlet before sampling. However, only 3% of the water area on the north bank had a water age less than the theoretical residence time for the month, indicating that the hydrological benefits of the single-point (inlet) water replenishment method are very limited.

[0027] Figure 6 Interpretation of isotope and water age results of Yilong Lake: In September 2023, the lake water isotopes showed a trend of gradual enrichment from west to east, δ¹ 8 The range of oxygen (O) was -5.1‰ to -2.5‰, with an average of -3.3‰. The spatial variation trend of the lake water age was consistent with that of the lake water isotopes, with the water age gradually increasing from the west bank to the east bank, ranging from 323 to 1133 days, with an average of 639 days. Figure 6 (a) and Figure 6 (b)). Lake water δ¹ 8Areas with relatively low water quality and shorter water age are concentrated at the estuaries of the main rivers flowing into the lake on the west bank, indicating that the inflow during the rainy season significantly enhances the hydrodynamic conditions of the estuary area. Meanwhile, in September, 78% of the area had water age less than the theoretical residence time for that month, suggesting a relatively abundant inflow of water into the lake during the rainy season.

[0028] Compared to September 2023, both the lake water isotopes and water age showed a significant increase in December 2024. The average δ¹⁸ for the entire lake... 8 O rose to -2.0‰, and the average water age increased to 976 days. Figure 6 (c) and Figure 6 (d) The area of ​​the lake with a water age less than the theoretical residence time of the month has shrunk to 18%, indicating that the reduction in the amount of water entering the lake during the dry season has greatly reduced the lake's hydrological renewal rate.

[0029] The above cases demonstrate that our invented water age calculation formula can be successfully applied to different types of shallow lakes, revealing and quantifying the differences in water age at different locations within the lake during different seasons (under different hydrological conditions), reflecting the spatial distribution of lake hydrodynamics, and providing a strong scientific basis for optimizing water replenishment strategies for specific lakes.

[0030] It should be noted that the above are merely preferred embodiments of this application and do not limit the scope of patent protection of this application. Any equivalent structural or procedural changes made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of this application.

Claims

1. A method for estimating the age of lake water based on hydrogen and oxygen stable isotope technology, characterized in that, Includes the following steps: S1. Construct a lake isotope mass balance model and derive a formula for calculating the age of lake water; S2. Determine the key parameters for the formula to calculate the age of lake water, including: The value of lake water when it reaches its isotopic stable state (δ) S ); isotopic composition of inflow runoff into the lake (δ) I ); Isotopic composition of water vapor evaporating from the lake surface (δ) E ); Isotope evaporation enrichment coefficient m ; Lake evaporation rate; Theoretical water exchange cycle of lakes; S3. Substitute the key parameters determined in S2 into the lake age calculation formula constructed in S1 to solve the problem, output the lake age corresponding to each sampling point, and visualize the results to complete the lake age estimation.

2. The method for estimating lake water age based on hydrogen and oxygen stable isotope technology according to claim 1, characterized in that: The steps for calculating the age of the lake water include: S1.1 Collect lake water samples from the target area and perform isotope measurements; S1.2 Construct the lake water balance equation; In the formula, V represents the lake's water storage capacity; I represents the average annual inflow into the lake; E represents the average annual evaporation; Q represents the average annual outflow from the lake; and dV / dt represents the annual water storage variable of the lake. Constructing a lake isotopic mass balance equation based on the lake water balance equation: In the formula, δ L Indicates the isotopic composition of the lake water; δ I Indicates the isotopic composition of runoff flowing into the lake; δ E Indicates the isotopic composition of water vapor evaporating from the lake surface; δ Q The isotopic composition of the lake's flow rate is indicated; S1.

3. Based on the lake water isotope mass balance equation, derive the formula for calculating lake water age; In the formula, δ L(i+1) This indicates that after one hydrological exchange, the lake's hydrological values ​​relative to the previous δ step... L(i) The updated iteration value; ΔI represents the water balance at one time step, i.e., the water cycle; x The evaporation ratio is expressed as... x=E / I ; Formula for dynamic changes in lake water isotopes δ L(i+1) Integrating over time and combining the results, we obtain the following formula: In the formula, δ S δ represents the value when the lake water reaches an isotopic stable state; δ0 represents the initial isotopic composition of the lake water. m I / V represents the isotope evaporation enrichment coefficient; I / V represents the water cycle over a time step. t Indicates the number of time steps; By performing an inverse function operation on the integral formula, we obtain the formula for calculating the age of the lake, as shown below: In the formula, WA represents the age of the lake water.

3. The method for estimating lake water age based on hydrogen and oxygen stable isotope technology according to claim 1, characterized in that: The oxygen isotope value δ when the lake water reaches an isotopic stable state S 18 O is calculated using the following formula: d S 18 O=d L 18 The max +0.1 In the formula, δ L 18 O max This represents the maximum isotope enrichment value observed in a particular sampling. 0.1 indicates the instrument's measurement error; Based on δ S 18 O determines the hydrogen isotope value δ when the lake water reaches a stable state. S 2 H, expressed as follows: d S 2 H=d S 2 O*Slope+Intercept In the formula, Slope and Intercept represent the slope and intercept of the lake evaporation line LEL, respectively.

4. The method for estimating lake water age based on hydrogen and oxygen stable isotope technology according to claim 1, characterized in that: The isotopic composition of the inflow runoff into the lake δ I The determination method is as follows: use linear regression to obtain the hydrogen and oxygen isotope relationship line, i.e., the lake evaporation line (LEL), for all sampling points, and determine it by the intersection with the local atmospheric water line (LMWL).

5. The method for estimating lake water age based on hydrogen and oxygen stable isotope technology according to claim 1, characterized in that: The isotopic composition of water vapor evaporated from the lake surface is δ E The method for determining δ is as follows: the Craig-Gordon isotope evaporation model is used to estimate δ. E The calculation formula is as follows: In the formula, δ L Indicates the isotopic composition of the lake water; α + α represents the isotopic equilibrium fractionation coefficient at the steam-water evaporation interface. + >1; h Indicates atmospheric relative humidity; δ A Indicates the isotopic composition of atmospheric water vapor; ε k Indicates the isotopic kinetic fractionation factor; ε + This represents the equilibrium fractionation factor.

6. The method for estimating lake water age based on hydrogen and oxygen stable isotope technology according to claim 1, characterized in that: The isotope evaporation enrichment coefficient m The determination method is as follows: isotope evaporation enrichment coefficient m It is atmospheric relative humidity h The function is calculated using the following formula: In the formula, δ L Indicates the isotopic composition of the lake water; δ E Indicates the isotopic composition of water vapor evaporating from the lake surface; δ * This represents the theoretical maximum isotopic enrichment value that a body of water can achieve when it is completely evaporated to dryness, given atmospheric isotopic composition and humidity conditions. h Indicates atmospheric relative humidity; ε k Indicates the isotopic kinetic fractionation factor; ε + Represents the equilibrium fractionation factor; α + This represents the isotopic equilibrium fractionation coefficient at the steam-water evaporation interface.

7. The method for estimating lake water age based on hydrogen and oxygen stable isotope technology according to claim 1, characterized in that: The methods for determining the evaporation ratio and water exchange cycle include: The formula for calculating the lake evaporation ratio E / I is as follows: In the formula, δ S The value representing the lake water at which it reaches an isotopic stable state; δ I Indicates the isotopic composition of runoff flowing into the lake; δ E This indicates the isotopic composition of water vapor evaporated from the lake surface; m Indicates the isotope evaporation enrichment coefficient; δ * This represents the theoretical maximum isotopic enrichment value that a body of water can achieve when it is completely evaporated to dryness, given atmospheric isotopic composition and humidity conditions. The lake water exchange cycle V / I can be calculated as follows: Where E / V represents the relative evaporation rate of a lake; I is the average annual inflow into the lake; E is the average annual evaporation; and V represents the lake's water storage capacity.

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