A high-cold basin freeze-thaw hydrology-carbon coupling quantitative analysis method based on multi-isotope combined tracing

Abstract

This application relates to a quantitative analysis method for freeze-thaw hydrological-carbon coupling in high-altitude cold watersheds based on multi-isotope joint tracing. The method includes: using multi-isotope tracing technology, fitting the time-series isotope characteristics of water bodies to solve for gamma distribution parameters, calculating runoff retention time and fresh water ratio, and completing a quantitative analysis of the hydrological process; combining dual-model cross-validation to decompose the contribution ratio of rock weathering carbon sources, quantifying the contribution of carbon transport and the freeze-thaw transport contribution rate at different freeze-thaw periods; and finally constructing a structural equation model to analyze the causal coupling mechanism of freeze-thaw-hydrology-weathering-carbon transport. This method can accurately quantify the coupling law of hydrological cycle and carbon transport under freeze-thaw action in high-altitude cold watersheds, solving the problems of traditional methods being difficult to adapt to heterogeneous hydrological processes in high-altitude freeze-thaw areas and having low accuracy in carbon source analysis, effectively improving the accuracy and systematicness of quantitative analysis of hydrological-carbon coupling processes in high-altitude cold watersheds.

Description

Technical Field

[0001] This invention belongs to the field of isotope tracing and ecohydrology technology, and in particular relates to a quantitative analysis method for freeze-thaw hydrology-carbon coupling based on multi-isotope joint tracing in cold watersheds. Background Technology

[0002] With the development of isotope tracing and ecohydrological techniques, process analysis techniques based on single isotopes have emerged in high-altitude watersheds. This technique utilizes the natural abundance differences of specific isotopes to independently trace the source of water or the migration and transformation of carbon within the watershed, and is characterized by its ease of operation and clear objectives.

[0003] Traditional methods primarily employ single isotope indices to independently analyze water or carbon cycle processes. For example, using δD and δ¹ 8 O stable isotopes are used to identify the recharge relationships of precipitation, surface water, and groundwater, and to classify runoff components. δ¹³C is used to determine the sources of dissolved inorganic carbon in water and to calculate the contribution of carbonate rock weathering. Water cycle and carbon cycle studies are usually conducted separately; the analysis results of the water cycle and carbon cycle are then correlated through subsequent qualitative analysis.

[0004] However, current single-isotope analysis methods have significant limitations. First, they neglect the high coupling relationship between the water and carbon cycles during freeze-thaw cycles, making it impossible to simultaneously trace water and carbon sources. Second, they struggle to simultaneously separate multiple water source end-members, such as permafrost meltwater, groundwater, and precipitation, as well as multiple weathering end-members, such as silicate weathering and carbonate weathering. Finally, existing methods are mostly qualitative or semi-quantitative analyses, making it difficult to quantitatively calculate the specific contribution rates of seasonal freeze-thaw processes to rock chemical weathering intensity and river carbon transport flux, thus failing to fully characterize the hydrological-carbon coupling mechanism driven by freeze-thaw cycles. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for quantitative analysis of freeze-thaw hydrology-carbon coupling in cold watersheds based on multi-isotope joint tracing, which can simultaneously realize water source separation, carbon source identification, and weathering end-member differentiation, and complete the quantitative analysis of freeze-thaw hydrology-carbon coupling.

[0006] Firstly, this application provides a quantitative analysis method for freeze-thaw hydrology-carbon coupling based on multi-isotope joint tracing in cold watersheds, including:

[0007] S1. Obtain the δD isotope values ​​and δ¹ values ​​corresponding to various water sources within the high-altitude cold basin. 8 O isotope value, δ¹³C-DIC isotope value and 87 Sr / 86 Sr isotope values, and corresponding values ​​of representative end-member rock samples 87 Sr / 86Sr isotope values; where water sources include precipitation, permafrost water, and surface water;

[0008] S2. Based on the δD isotope values, calculate the mixing ratio of surface water and water above the permafrost layer;

[0009] S3, δ¹ of precipitation, surface water and permafrost water 8 The time series of O isotope values ​​were fitted with a sine wave to obtain δ¹ 8 Amplitude and phase of O isotope values; based on amplitude and phase, mean residence time of runoff and proportion of new water are calculated using a gamma distribution model, and the mixing ratio, mean residence time of runoff and proportion of new water are combined to obtain quantitative analysis results of hydrological processes;

[0010] S4, δ¹³C-DIC isotope values ​​based on water source and 87 Sr / 86 Sr isotope values, and representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to quantitatively decompose and cross-validate the sources of dissolved inorganic carbon in the high-altitude basin using a Bayesian isotope mixing model and a Monte Carlo river inversion model, so as to obtain the final contribution ratio of inorganic carbon sources from rock weathering.

[0011] S5. Based on the quantitative analysis results of hydrological processes, calculate the contribution rate of water resources to surface runoff, interflow, and groundwater runoff in the high-altitude cold basin during each freeze-thaw period; based on water resources... 87 Sr / 86 Sr isotope values ​​and representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to distinguish the contribution of silicate weathering and carbonate weathering to the carbon source of rock weathering in dissolved inorganic carbon. Based on the water source contribution rate, final contribution ratio, and contribution percentage, combined with the dissolved inorganic carbon concentration in the water source, the transport contribution rate of the freeze-thaw process to the transport of dissolved inorganic carbon in the high-altitude watershed was calculated. The freeze-thaw period included the freeze-thaw season, the pre-monsoon season, and the monsoon flood season.

[0012] S6. Input the water source contribution rate, average runoff residence time, fresh water ratio, contribution ratio, and transport contribution rate into the structural equation model for causal coupling integration analysis to obtain the causal coupling analysis results.

[0013] In one embodiment, the formula for calculating the mixing ratio is:

[0014] ;

[0015] in, This refers to the mixing ratio of surface water with water in the permafrost layer. This represents the mixing ratio of water above the permafrost layer with surface water. The δD isotope value of water above the permafrost layer. The δD isotope value of surface water. The δD isotope value is for precipitation.

[0016] In one embodiment, δ¹ of precipitation, surface water, and permafrost water 8 The time series of O isotope values ​​were fitted with a sine wave to obtain δ¹ 8 Amplitude and phase of O isotope values; based on amplitude and phase, mean residence time of runoff and proportion of fresh water are calculated using a gamma distribution model. Combining mixing ratio, mean residence time of runoff, and proportion of fresh water, quantitative analysis results of the hydrological process are obtained, including:

[0017] S11. Using the sine wave fitting method, the δ¹ values ​​of precipitation, surface water, and permafrost water are analyzed. 8 The time series of O isotope values ​​were fitted to obtain the amplitude and phase; the formula for calculating the sine wave fitting is as follows:

[0018] ;

[0019] in, δ¹ of surface water 8 O isotope fitting values δ¹ of precipitation 8 O isotope fitting values δ¹ of water above the permafrost layer 8 O isotope fitting values δ¹ of surface water 8 Amplitude of O isotope values δ¹ of precipitation 8 Amplitude of O isotope values δ¹ of water above the permafrost layer 8 Amplitude of O isotope values δ¹ of surface water 8 Phase of O isotope values δ¹ of precipitation 8 Phase of O isotope values δ¹ of water above the permafrost layer 8 Phase of O isotope values The annual cycle signal frequency, δ¹ of surface water 8 The mean term of the O isotope value with respect to the time series. δ¹ of precipitation 8 The mean term of the O isotope value with respect to the time series. δ¹ of water above the permafrost layer 8 The mean term of the O isotope value with respect to the time series. This represents the number of days since the start of sampling.

[0020] S12. Calculate the surface water amplitude ratio based on the amplitudes of surface water and precipitation, and calculate the surface water phase shift based on the phases of surface water and precipitation; calculate the frozen soil surface water amplitude ratio based on the amplitudes of water above the frozen soil layer and precipitation, and calculate the frozen soil surface water phase shift based on the phases of water above the frozen soil layer and precipitation; input the surface water amplitude ratio and surface water phase shift, and the frozen soil surface water amplitude ratio and frozen soil surface water phase shift into the gamma distribution model respectively, and iteratively solve the shape parameters and proportion parameters of surface water and water above the frozen soil layer;

[0021] S13. Multiply the shape parameter and proportion parameter of surface water to obtain the average residence time of surface water runoff; multiply the shape parameter and proportion parameter of water above the permafrost layer to obtain the average residence time of water above the permafrost layer; according to the incomplete gamma function under regularization, calculate the proportion of surface water and water above the permafrost layer with a residence time less than the preset age threshold in the total runoff of the high-altitude cold water basin to obtain the proportion of new water; where, the runoff residence time includes the time it takes for precipitation to become surface water through the watershed and the time it takes for precipitation to become water above the permafrost layer through the active permafrost layer; the proportion of new water includes the proportion of new surface water and the proportion of new water above the permafrost layer.

[0022] S14, combined with the mixing ratio, average residence time of surface water runoff, average residence time of water runoff above the frozen soil layer, proportion of fresh surface water and proportion of fresh water above the frozen soil layer, to obtain the quantitative analysis results of the hydrological process.

[0023] In one embodiment, based on the δ¹³C-DIC isotope value of the water source and 87 Sr / 86 Sr isotope values, and representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to quantitatively decompose and cross-validate the sources of dissolved inorganic carbon in high-altitude watersheds using a Bayesian isotope mixing model and a Monte Carlo river inversion model, yielding the final contribution ratio of inorganic carbon sources from rock weathering, including:

[0024] S21, the δ¹³C-DIC isotope values ​​corresponding to the water source and 87 Sr / 86 The Sr isotope values ​​are input into a Bayesian isotope mixing model, and the probability distribution of inorganic carbon sources in rock weathering is obtained by simulating the distribution with no information prior using the Markov chain Monte Carlo sampling method.

[0025] S22, the δ¹³C-DIC isotope values ​​corresponding to the water source and 87 Sr / 86 Sr isotope values ​​were used as data to be split, and representative end-member rock samples were analyzed. 87 Sr / 86Sr isotope values ​​were used as endmember constraints and input into the Monte Carlo river inversion model to obtain the preliminary contribution ratio of inorganic carbon sources from rock weathering.

[0026] S23. By comparing and cross-validating the probability distribution and the initial contribution ratio, the final contribution ratio of inorganic carbon sources from rock weathering is calculated.

[0027] In one embodiment, based on the quantitative analysis results of hydrological processes, the contribution rate of water sources to surface runoff, interflow, and groundwater runoff in the high-altitude watershed is calculated during each freeze-thaw period; based on the water source... 87 Sr / 86 Sr isotope values ​​and representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to differentiate the contribution of silicate weathering and carbonate weathering to the rock weathering carbon source in dissolved inorganic carbon. Based on the water source contribution rate, final contribution ratio, and contribution percentage, combined with the dissolved inorganic carbon concentration in the water source, the transport contribution rate of the freeze-thaw process to the transport of dissolved inorganic carbon in high-altitude watersheds was calculated, including:

[0028] S31. Based on the quantitative analysis results of hydrological processes, extract the δD isotope value characteristics and δ¹ values ​​of water sources during each freeze-thaw period. 8 O isotope value characteristics; based on δD isotope value characteristics and δ¹ 8 Based on the characteristics of O isotope values, the water source contribution rate to surface runoff, interflow and groundwater runoff was calculated using the endmember mixing method.

[0029] S32. Representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were statistically analyzed according to the classification of silicate and carbonate rocks to obtain the silicate rock end-members. 87 Sr / 86 Sr eigenvalues ​​and carbonate endmembers 87 Sr / 86 Sr eigenvalue; corresponding to the water source 87 Sr / 86 Sr isotope values ​​are associated with silicate and carbonate endmembers, respectively. 87 Sr / 86 By comparing Sr eigenvalues, the contribution ratio of silicate weathering and carbonate weathering to the rock weathering carbon source of dissolved inorganic carbon in water sources was calculated.

[0030] S33. Based on the water source contribution rate, final contribution ratio, and contribution percentage, and combined with the dissolved inorganic carbon concentration of the water source, calculate the contribution of rock weathering inorganic carbon sources to dissolved inorganic carbon transport in the high-altitude cold basin during the freeze-thaw season and the early monsoon season; subtract the contribution during the early monsoon season from the contribution during the freeze-thaw season to obtain the net increase in carbon transport; divide the net increase in carbon transport by the contribution during the freeze-thaw season to obtain the transport contribution rate.

[0031] In one embodiment, the water source contribution rate, average runoff residence time, fresh water ratio, contribution percentage, and transport contribution rate are input into a structural equation model for causal coupling integration analysis to obtain the causal coupling analysis results, including:

[0032] S41. Using the freeze-thaw intensity, hydrological connectivity, weathering intensity, and carbon release risk of high-altitude cold water basins as potential variables, and the water source contribution rate, average runoff residence time, fresh water ratio, contribution ratio, and transport contribution rate as observation variables, a measurement model of structural equation model is constructed.

[0033] S42. Define the causal paths from freeze-thaw intensity to hydrological connectivity, from hydrological connectivity to weathering intensity, and from weathering intensity to carbon release risk, and construct a structural equation model.

[0034] S43. Perform parameter estimation and fitting on the structural equation model to obtain the path coefficients and model fit of each causal path, and output the causal coupling analysis results of freeze-thaw hydrology-rock weathering-carbon transport.

[0035] The above-mentioned quantitative analysis method based on multi-isotope joint tracing in high-altitude watersheds using freeze-thaw hydrology-carbon coupling, through δD and δ¹, utilizes... 8 O, δ¹³C-DIC and 87 Sr / 86 Sr multi-isotope joint tracing breaks through the technical barrier that traditional single isotope analysis can only independently resolve water or carbon cycles. By dividing the research period into freeze-thaw season, pre-monsoon season, and monsoon flood season, the mixing ratio of surface water and permafrost water, average runoff retention time, and fresh water ratio are calculated in different time periods to accurately capture the evolution characteristics of hydrological connectivity at different freeze-thaw stages. Through cross-validation of Bayesian isotope mixing models and Monte Carlo river inversion models, the contribution ratio of inorganic carbon sources from rock weathering is quantitatively distinguished, solving the technical challenges of complex carbon sources and low source tracing accuracy in high-altitude permafrost regions. By quantifying the contribution rate of each water source, distinguishing the proportion of silicate and carbonate weathering, and calculating the transport contribution rate of the freeze-thaw process based on the carbon transport differences between the freeze-thaw season and the non-freeze-thaw season, a quantitative coupled analysis of the entire chain of hydrology-weathering-carbon transport driven by freeze-thaw is achieved. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1A schematic diagram illustrating the application environment of a quantitative analysis method based on multi-isotope joint tracing for freeze-thaw hydrology and carbon coupling in cold watersheds provided by this invention.

[0038] Figure 2 A flowchart illustrating a quantitative analysis method for freeze-thaw hydrology-carbon coupling in high-altitude watersheds based on multi-isotope joint tracing, provided by the present invention;

[0039] Figure 3 This is a schematic diagram of the process for generating the final contribution ratio in one optional embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0041] This application provides a quantitative analysis method for freeze-thaw hydrology and carbon coupling in high-altitude watersheds based on multi-isotope joint tracing, which can be applied to, for example... Figure 1 In the application environment shown, terminal 102 can communicate with server 101 via a network. A data storage system can store the data that server 101 needs to process. The data storage system can be integrated onto server 101 or located in the cloud or on other network servers. Server 101 can be used to perform freeze-thaw hydrological process analysis, carbon source splitting and cross-validation, freeze-thaw carbon transport contribution rate calculation, and causal coupling integration analysis on the sample data submitted by terminal 102. Terminal 102 can be used to submit sample data to server 101 and display the analysis results. Terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. Server 101 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0042] In one exemplary embodiment, such as Figure 2 As shown, a quantitative analysis method based on freeze-thaw hydrology and carbon coupling in high-altitude watersheds using multi-isotope joint tracing is presented, and this method is applied to... Figure 1 Taking server 101 as an example, the explanation includes the following steps:

[0043] S1. Obtain the δD isotope values ​​and δ¹ values ​​corresponding to various water sources within the high-altitude cold basin. 8 O isotope value, δ¹³C-DIC isotope value and 87 Sr / 86 Sr isotope values, and corresponding values ​​of representative end-member rock samples 87 Sr / 86Sr isotope values; where water sources include precipitation, permafrost water, and surface water.

[0044] Specifically, δD isotope values ​​and δ¹ 8 O isotope values ​​can refer to the stable isotope parameters of hydrogen and oxygen in water, δD isotope values, and δ¹⁴⁰ isotope values. 8 O isotope values ​​can be used to characterize water sources, runoff replenishment pathways, and water mixing characteristics; δ¹³C-DIC isotope values ​​can refer to the stable isotope parameters of dissolved inorganic carbon, and δ¹³C-DIC isotope values ​​can reflect the differences in the sources of dissolved inorganic carbon in high-altitude and cold water basins. 87 Sr / 86 Sr isotope values ​​refer to the strontium isotope ratios between water bodies and rock end-members, possessing good specificity for tracing the origin of rock weathering. 87 Sr / 86 Sr isotope values ​​can be used to distinguish the differences in contributions between silicate weathering and carbonate weathering; precipitation can refer to the atmospheric precipitation recharge end-member in high-altitude cold basins, which is the initial water source for the hydrological cycle in high-altitude cold basins; permafrost water can refer to the soil water stored in the upper part of the active permafrost layer, which is a key intermediate water body for hydrological regulation and carbon migration during the freeze-thaw process; surface water can refer to the surface water bodies in high-altitude cold basins, which can be transformed into surface runoff, interflow, and groundwater runoff through confluence; representative end-member rock samples can refer to rock samples collected within the research area of ​​high-altitude cold basins that can accurately represent the lithological characteristics of the main strata controlling the basin. Representative end-member rock samples include core lithological types such as silicate rocks and carbonate rocks, which are the benchmark end-member samples for tracing the origin of rock weathering.

[0045] Optionally, server 101 can read in batches the δD and δ¹ values ​​of various water sources detected by isotope detection equipment. 8 O, δ¹³C-DIC and 87 Sr / 86 Raw Sr isotope data, and representative end-member rock samples 87 Sr / 86 Raw Sr isotope data. Server 101 can perform outlier removal, spatiotemporal matching correction, and standardization on the raw isotope data, eliminating invalid data caused by sampling contamination and equipment detection errors, and constructing a multi-isotope dataset for high-altitude cold watersheds.

[0046] S2. Based on the δD isotope values, calculate the mixing ratio of surface water and water above the permafrost layer.

[0047] Specifically, the mixing ratio can refer to the percentage of mixing between different water sources. The mixing ratio can be used to quantify the mutual replenishment and mixing degree of surface water and permafrost water under freeze-thaw conditions.

[0048] Optionally, server 101 can retrieve valid δD isotope data corresponding to precipitation, permafrost water, and surface water, substitute them into a preset binary endmember mixing calculation formula, and iteratively solve for the mixing ratio of surface water in permafrost water and the mixing ratio of permafrost water in surface water, respectively. Server 101 can verify the rationality of the calculated mixing ratio results, remove abnormal results that exceed the 0-1 value range, and correct the data by combining the freeze-thaw hydrological recharge pattern of the high-altitude cold watershed to obtain the mixing ratio.

[0049] S3, δ¹ of precipitation, surface water and permafrost water 8 The time series of O isotope values ​​were fitted with a sine wave to obtain δ¹ 8 The amplitude and phase of the O isotope value; based on the amplitude and phase, the average residence time of runoff and the proportion of new water are calculated by the gamma distribution model. By combining the mixing ratio, the average residence time of runoff and the proportion of new water, the quantitative analysis results of the hydrological process are obtained.

[0050] Specifically, δ¹ 8 The time series of O isotope values ​​can refer to the set of oxygen isotope values ​​of precipitation, surface water, and permafrost water collected sequentially according to sampling time, δ¹ 8 O isotope values ​​can fully characterize the seasonal fluctuations of isotopes in water bodies of high-altitude cold regions with the freeze-thaw cycle; sine wave fitting can indicate the relationship between δ¹ 8 A periodic signal fitting method based on the temporal fluctuation characteristics of O isotopes, using sinusoidal wave fitting, can be used to extract the annual periodic variation of isotope time series and extract stable amplitude and phase parameters; amplitude can refer to the δ¹ of water bodies. 8 The amplitude of the O isotope value fluctuates within an annual cycle; this amplitude can be used to characterize the strength of fluctuations in water isotope replenishment by atmospheric precipitation; the phase can refer to the δ¹⁸ of the water body. 8 The lag offset of the O isotope value time series relative to the standard annual cycle signal, phase can be used to characterize the lag response characteristics of runoff recharge; the average residence time of runoff refers to the average time it takes for precipitation to be transformed into surface water and permafrost water after watershed recharge, and the average residence time of runoff can be used to quantify the watershed hydrological renewal rate and water turnover capacity; the fresh water ratio refers to the proportion of fresh precipitation runoff with a residence time less than a preset age threshold to the total runoff, and the fresh water ratio can be used to characterize the intensity of fresh water recharge in the watershed during the freeze-thaw period; the gamma distribution model refers to a probabilistic statistical model adapted to the distribution characteristics of watershed runoff residence time, and the gamma distribution model can characterize the time distribution patterns of precipitation infiltration, transport, and residence, with the δ¹ of surface water and permafrost water respectively compared with precipitation. 8Using the isotope amplitude ratio and phase difference as input constraints, the shape parameters and scale parameters of the model are obtained through iterative solution. The average residence time of runoff is calculated based on the product of the shape parameters and scale parameters. The runoff proportion within the preset age threshold is then solved by combining the incomplete gamma function under regularization, thereby realizing the quantitative inversion of the watershed runoff residence time and the ratio of new and old water bodies.

[0051] Optionally, server 101 can retrieve δ¹ values ​​of precipitation, surface water, and permafrost water. 8 The O-isotope value time series dataset uses a pre-defined sine wave fitting algorithm to fit the time series of isotope values ​​of precipitation, surface water, and permafrost water sequence by sequence. The mean and periodic fluctuation terms are removed, and the amplitude and phase parameters corresponding to precipitation, surface water, and permafrost water are extracted. Server 101 can calculate the amplitude ratio and phase difference of surface water and permafrost water relative to precipitation, respectively. Using the amplitude ratio and phase difference as constraints input to the gamma distribution model, the shape and scale parameters corresponding to the gamma distribution model are iteratively solved to calculate the average residence time of surface water and permafrost water runoff. Server 101 can statistically calculate the runoff proportion within a preset age threshold based on a regularized incomplete gamma function, obtaining the proportion of new water in the corresponding water body. Server 101 can integrate the mixing ratio, average residence time of runoff, and proportion of new water, performing parameter normalization matching and fusion to obtain quantitative analysis results of the hydrological process.

[0052] S4, δ¹³C-DIC isotope values ​​based on water source and 87 Sr / 86 Sr isotope values, and representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to quantitatively decompose and cross-validate the sources of dissolved inorganic carbon in the high-altitude basin using a Bayesian isotope mixing model and a Monte Carlo river inversion model, thus obtaining the final contribution ratio of inorganic carbon sources from rock weathering.

[0053] Specifically, the Bayesian isotope mixing model can refer to a probabilistic statistical source analysis model based on the principle of isotope mass conservation. Using Markov chain Monte Carlo sampling, iterative simulations are conducted with an informationless prior distribution. Under conditions where endmembers in high-altitude cold-climate watersheds are uncertain, the Bayesian isotope mixing model can simulate the contribution probability distribution of inorganic carbon sources from rock weathering, achieving a probabilistic quantitative decomposition of dissolved inorganic carbon sources. The Monte Carlo river inversion model can refer to a numerical inversion model adapted to the source tracing of river materials in high-altitude cold-climate watersheds. The Monte Carlo river inversion model can use water source isotope numbers... Using the sample to be decomposed as the representative end-member rock sample isotope data as the fixed constraint, the preliminary contribution ratio of inorganic carbon sources from rock weathering is solved through large-scale random sampling iterative calculation. The Monte Carlo river inversion model can be used to cross-validate the results with the Bayesian isotope mixing model to improve the accuracy and reliability of the carbon source decomposition results. Dissolved inorganic carbon refers to inorganic carbon components existing in dissolved form in the water bodies of high-altitude cold basins, which is the main form of carbon transport in the basin. Rock weathering inorganic carbon sources refer to the sources of dissolved inorganic carbon released by the weathering process of various rocks in the basin.

[0054] Optionally, server 101 can transmit the δ¹³C-DIC isotope value corresponding to the water source and 87 Sr / 86 Sr isotope values ​​are input into a Bayesian isotope mixing model. Using a Markov chain Monte Carlo sampling method, the probability distribution of inorganic carbon sources from rock weathering is simulated with an information-free prior distribution. Server 101 can then output the δ¹³C-DIC isotope values ​​corresponding to the water source. 87 Sr / 86 Sr isotope values ​​were used as data to be split, and representative end-member rock samples were analyzed. 87 Sr / 86 Using Sr isotope values ​​as endmember constraints, the Monte Carlo river inversion model is input to obtain the preliminary contribution ratio of inorganic carbon sources from rock weathering. Server 101 can perform cross-validation by comparing the probability distribution output by the Bayesian isotope mixing model and the preliminary contribution ratio output by the Monte Carlo river inversion model, calibrating the model calculation error, and obtaining the final contribution ratio of inorganic carbon sources from rock weathering.

[0055] S5. Based on the quantitative analysis results of hydrological processes, calculate the contribution rate of water resources to surface runoff, interflow, and groundwater runoff in the high-altitude cold basin during each freeze-thaw period; based on water resources... 87 Sr / 86 Sr isotope values ​​and representative end-member rock samples 87 Sr / 86Sr isotope values ​​were used to distinguish the contribution of silicate weathering and carbonate weathering to the carbon source of rock weathering in dissolved inorganic carbon. Based on the water source contribution rate, final contribution ratio, and contribution ratio, combined with the dissolved inorganic carbon concentration of the water source, the transport contribution rate of the freeze-thaw process to the transport of dissolved inorganic carbon in the high-altitude cold basin was calculated. The freeze-thaw period included the freeze-thaw season, the pre-monsoon season, and the monsoon flood season.

[0056] Specifically, the freeze-thaw period can refer to the research period that distinguishes the differences in freeze-thaw action and monsoon hydrological regulation in high-altitude cold watersheds. The freeze-thaw period can include the freeze-thaw season, the pre-monsoon period, and the monsoon flood season. The freeze-thaw period can be used to distinguish the differentiated driving effects of freeze-thaw action on hydrology and carbon transport at different times. Surface runoff refers to the rapidly flowing water in the surface channels of the watershed, which is the most direct form of runoff output in high-altitude cold watersheds. Interflow refers to the runoff components that move within the soil layer, which is the key stream for soil water replenishment to the river channels during the freeze-thaw period. Flow patterns; underground runoff can refer to the runoff components that are stably transported in deep strata, and is an important carrier of baseflow and steady-state carbon transport in a watershed; silicate weathering can refer to the weathering process in which silicate rocks in a watershed undergo water-rock reactions, resulting in the dissolution of substances and the consumption of carbon; carbonate weathering can refer to the weathering process in which carbonate rocks in a watershed undergo dissolution reactions, resulting in the dissolution of substances and the release of carbon; dissolved inorganic carbon concentration can refer to the content parameter of dissolved inorganic carbon in various water sources, and dissolved inorganic carbon concentration can be used to quantify the baseline of carbon transport flux in water bodies.

[0057] Optionally, server 101 can retrieve quantitative analysis results of hydrological processes, and extract the δD isotope characteristics and δ¹ values ​​of water sources corresponding to each freeze-thaw period during the freeze-thaw season, the pre-monsoon season, and the monsoon flood season. 8 Based on the O isotope characteristics, the contribution rates of precipitation, permafrost water, and surface water to surface runoff, interflow, and groundwater were calculated using the endmember mixing method. Server 101 can access water resources. 87 Sr / 86 Sr isotope values ​​and representative end-member rock samples 87 Sr / 86 Based on the Sr isotopic values ​​and the isotopic differences between silicate and carbonate endmembers, the contribution ratios of silicate and carbonate weathering to the carbon source of rock weathering are calculated. Server 101 can integrate the water source contribution rate, final contribution ratio, and contribution ratios of silicate and carbonate weathering for each freeze-thaw period, and, combined with the dissolved inorganic carbon concentration of each water source, calculate the inorganic carbon source contribution during the freeze-thaw season and the pre-monsoon period. Server 101 can construct a baseline level using the contribution amount in the pre-monsoon period, calculate the net increase in carbon transport during the freeze-thaw season, and finally obtain the dissolved inorganic carbon transport contribution rate corresponding to the freeze-thaw process by using the ratio of the net increase in carbon transport during the freeze-thaw season to the contribution amount during the freeze-thaw season.

[0058] S6. Input the water source contribution rate, average runoff residence time, fresh water ratio, contribution ratio, and transport contribution rate into the structural equation model for causal coupling integration analysis to obtain the causal coupling analysis results.

[0059] Specifically, structural equation modeling (SEM) refers to a statistical analysis model that can integrate multiple types of observed variables, construct causal paths of latent variables, and achieve quantitative analysis of multi-process coupling mechanisms. SEM can solve the problem of the mutual coupling of multiple processes such as freeze-thaw, hydrology, weathering, and carbon transport in high-altitude cold watersheds, and the difficulty in directly quantifying causal relationships. Observed variables can refer to quantitative parameters obtained through experimental calculations. Observed variables can be water source contribution rate, average runoff residence time, fresh water ratio, contribution proportion, and transport contribution rate. Observed variables can be used to provide basic quantitative indicators for model fitting. Causal coupling integrated analysis can refer to quantifying the interaction strength, influence direction, and correlation degree between various parameters according to a preset causal transmission path, and achieving integrated analysis of the coupling mechanism of the entire process of freeze-thaw hydrology-rock weathering-carbon transport. Causal coupling analysis results can refer to the path coefficients, model fit degree, and causal response laws between processes output after the structural equation model is fitted. Causal coupling analysis results can be used to reveal the intrinsic coupling mechanism of freeze-thaw action driving hydrological evolution, weathering processes, and carbon transport in high-altitude cold watersheds.

[0060] Optionally, server 101 can compile a standardized observation dataset containing water source contribution rate, average runoff residence time, fresh water proportion, contribution ratio, and transport contribution rate. Server 101 can construct a measurement model for the structural equation model using freeze-thaw intensity, hydrological connectivity, weathering intensity, and carbon release risk as latent variables, and water source contribution rate, average runoff residence time, fresh water proportion, contribution ratio, and transport contribution rate as observed variables. Server 101 can build a structural model for the structural equation model according to a fixed causal logic: freeze-thaw intensity points to hydrological connectivity, hydrological connectivity points to weathering intensity, and weathering intensity points to carbon release risk. Server 101 can perform iterative parameter estimation and model fitting verification on the constructed structural equation model, outputting the path coefficients of each causal path and the overall model fit, ultimately obtaining the causal coupling analysis results of freeze-thaw hydrology-rock weathering-carbon transport.

[0061] In the aforementioned quantitative analysis method based on multi-isotope joint tracing in high-altitude watersheds using freeze-thaw hydrology-carbon coupling, δD and δ¹ are used... 8 O, δ¹³C-DIC and 87 Sr / 86Sr multi-isotope joint tracing breaks through the technical barrier that traditional single isotope analysis can only independently resolve water or carbon cycles. By dividing the research period into freeze-thaw season, pre-monsoon season, and monsoon flood season, the mixing ratio of surface water and permafrost water, average runoff retention time, and fresh water ratio are calculated in different time periods to accurately capture the evolution characteristics of hydrological connectivity at different freeze-thaw stages. Through cross-validation of Bayesian isotope mixing models and Monte Carlo river inversion models, the contribution of inorganic carbon sources from rock weathering is quantitatively distinguished, solving the technical challenges of complex carbon sources and low source tracing accuracy in high-altitude permafrost regions. By quantifying the contribution rate of each water source, distinguishing the proportion of silicate and carbonate weathering, and calculating the transport contribution rate of the freeze-thaw process based on the carbon transport differences between the freeze-thaw season and the non-freeze-thaw season, a quantitative coupled analysis of the entire chain of hydrology-weathering-carbon transport driven by freeze-thaw is achieved.

[0062] In one exemplary embodiment, the formula for calculating the mixing ratio can be:

[0063] ;

[0064] in, This refers to the mixing ratio of surface water with water in the permafrost layer. This represents the mixing ratio of water above the permafrost layer with surface water. The δD isotope value of water above the permafrost layer. The δD isotope value of surface water. The δD isotope value is for precipitation.

[0065] In an exemplary embodiment, δ¹ for precipitation, surface water, and permafrost water 8 The time series of O isotope values ​​were fitted with a sine wave to obtain δ¹ 8 The amplitude and phase of the O isotope value; based on the amplitude and phase, the mean residence time of runoff and the proportion of fresh water are calculated using a gamma distribution model. The mixing ratio, mean residence time of runoff, and proportion of fresh water are combined to obtain quantitative analysis results of the hydrological process, including the following steps:

[0066] S11. Using the sine wave fitting method, the δ¹ values ​​of precipitation, surface water, and permafrost water are analyzed. 8 The amplitude and phase were obtained by fitting the time series of O isotope values.

[0067] Specifically, the sine wave fitting method can refer to the method that adapts δ¹ to precipitation, surface water, and permafrost water. 8 A signal fitting algorithm for the periodic variation characteristics of O isotope values ​​over time series was used, employing the δ¹⁸ signal from the high-altitude cold basin. 8 The characteristic of O isotope values ​​fluctuating regularly with the annual freeze-thaw cycle, and its influence on the discrete time-series distribution of δ¹ 8 Reconstructing periodic functions from O isotope value time series.

[0068] Optionally, the server can retrieve δ¹ values ​​for precipitation, surface water, and permafrost water. 8 For O isotope value time series data, a pre-defined sine wave fitting algorithm is used to perform matching and fitting on the time series data of precipitation, surface water, and permafrost water one by one. The server can uniformly use a fixed annual periodic frequency to complete the periodic signal iterative fitting, and solve for the mean, amplitude parameters, and phase parameters of precipitation, surface water, and permafrost water respectively. The server can perform significance testing and accuracy screening on the fitting results, and remove abnormal time series results with fitting failure and excessive deviation, and finally obtain a stable and effective amplitude and phase dataset.

[0069] Preferably, the formula for calculating the sine wave fitting can be:

[0070] ;

[0071] in, δ¹ of surface water 8 O isotope fitting values δ¹ of precipitation 8 O isotope fitting values δ¹ of water above the permafrost layer 8 O isotope fitting values δ¹ of surface water 8 Amplitude of O isotope values δ¹ of precipitation 8 Amplitude of O isotope values δ¹ of water above the permafrost layer 8 Amplitude of O isotope values δ¹ of surface water 8 Phase of O isotope values δ¹ of precipitation 8 Phase of O isotope values δ¹ of water above the permafrost layer 8 Phase of O isotope values The annual cycle signal frequency, δ¹ of surface water 8 The mean term of the O isotope value with respect to the time series. δ¹ of precipitation 8 The mean term of the O isotope value with respect to the time series. δ¹ of water above the permafrost layer 8 The mean term of the O isotope value with respect to the time series. This represents the number of days since the start of sampling.

[0072] S12. Calculate the surface water amplitude ratio based on the amplitudes of surface water and precipitation, and calculate the surface water phase shift based on the phases of surface water and precipitation; calculate the frozen soil surface water amplitude ratio based on the amplitudes of water above the frozen soil layer and precipitation, and calculate the frozen soil surface water phase shift based on the phases of water above the frozen soil layer and precipitation; input the surface water amplitude ratio and surface water phase shift, and the frozen soil surface water amplitude ratio and frozen soil surface water phase shift into the gamma distribution model respectively, and iteratively solve the shape parameters and proportion parameters of surface water and water above the frozen soil layer.

[0073] Specifically, the surface water amplitude ratio can refer to the surface water δ¹ 8 Amplitude of O isotope values ​​and precipitation δ¹ 8 The amplitude ratio parameter of O isotope values, the surface water amplitude ratio can be used to quantify the degree of attenuation of surface water isotope periodic fluctuations relative to precipitation isotope periodic fluctuations; surface water phase shift can refer to surface water δ¹ 8 Phase of O isotope values ​​and precipitation δ¹ 8 The phase difference parameter of O isotope values, the surface water phase shift, can be used to characterize the degree of lag in the runoff response of surface water relative to precipitation; the amplitude ratio of water above the frozen soil layer can be referred to as the δ¹ of water above the frozen soil layer. 8 Amplitude of O isotope values ​​and precipitation δ¹ 8 The amplitude ratio parameter of O isotope values, specifically the amplitude ratio of water in the frozen soil layer, can be used to quantify the degree of attenuation of the periodic fluctuations of isotopes in the frozen soil layer relative to the periodic fluctuations of isotopes in precipitation; the phase shift of water in the frozen soil layer can be referred to as the δ¹⁴ phase shift of water in the frozen soil layer. 8 Phase of O isotope values ​​and precipitation δ¹ 8 The phase difference parameter of the O isotope value and the phase shift of water in the permafrost layer can be used to characterize the degree of lag in the runoff response of water in the permafrost layer relative to precipitation; the shape parameter and the scale parameter are the core characteristic parameters of the gamma distribution model, and the shape parameter and the scale parameter together determine the probability distribution shape of the runoff residence time.

[0074] Optionally, the server can retrieve amplitude and phase data corresponding to precipitation, surface water, and permafrost water, and calculate the surface water amplitude ratio and phase shift relative to precipitation, as well as the permafrost water amplitude ratio and phase shift relative to precipitation. The server can use the surface water amplitude ratio and phase shift as one set of input parameters, and the permafrost water amplitude ratio and phase shift as another set of input parameters, importing them into a preset gamma distribution model. The server can gradually optimize the model parameters through multiple iterations and error correction, ultimately converging to obtain the shape and scale parameters corresponding to surface water and permafrost water.

[0075] Preferably, the shape parameters and proportion parameters of surface water can be solved using the following formulas:

[0076]

[0077] in, The amplitude of surface water. The amplitude of precipitation. For the phase of surface water, For the phase of precipitation, The shape parameters of surface water, For the proportion of surface water, For precipitation δ¹ 8 The annual cycle frequency of O isotope values.

[0078] Preferably, the shape parameters and proportion parameters of water in the frozen soil layer can be solved using the following formulas:

[0079]

[0080] in, This represents the amplitude of water above the permafrost layer. The amplitude of precipitation. This refers to the phase of water above the permafrost layer. For the phase of precipitation, These are the shape parameters of water above the permafrost layer. This refers to the proportion of water above the permafrost layer. For precipitation δ¹ 8 Annual cycle frequency of O isotope values.

[0081] S13. Multiply the shape parameter and proportion parameter of surface water to obtain the average residence time of surface water runoff; multiply the shape parameter and proportion parameter of water above the permafrost layer to obtain the average residence time of water above the permafrost layer runoff; according to the incomplete gamma function under regularization, calculate the proportion of surface water and water above the permafrost layer with a runoff residence time less than the preset age threshold in the total runoff of the high-altitude cold water basin to obtain the new water ratio; wherein, the runoff residence time includes the time it takes for precipitation to become surface water through the watershed and the time it takes for precipitation to pass through the active permafrost layer to become water above the permafrost layer, and the new water ratio includes the new water ratio of surface water and the new water ratio of water above the permafrost layer.

[0082] Specifically, the incomplete gamma function under regularization can refer to the characteristic function used to statistically analyze the distribution ratio of runoff residence time intervals. The incomplete gamma function under regularization can screen out runoff components whose residence time meets the threshold condition. The preset age threshold can refer to the water body age determination standard set in advance according to the characteristics of the freeze-thaw hydrological cycle in high-altitude cold watersheds. The preset age threshold can be used to distinguish between fresh replenished runoff and old stagnant runoff in the watershed.

[0083] Optionally, the server can retrieve the shape parameters and proportion parameters corresponding to surface water and permafrost water, and multiply the shape parameters and proportion parameters respectively to obtain the average residence time of surface water runoff and the average residence time of permafrost water runoff. The server can call a regularized incomplete gamma function, using a preset age threshold as the judgment boundary, to statistically calculate the distribution ratio of residence time of surface runoff and permafrost water respectively, to obtain the proportion of new surface water and the proportion of new permafrost water.

[0084] Preferably, the formula for calculating the proportion of fresh surface water can be:

[0085]

[0086] in, The proportion of fresh surface water. For standard gamma function, The shape parameters of surface water, For the proportion of surface water, This represents the actual retention age of the runoff in the high-altitude, cold-climate basin. This is a preset age threshold.

[0087] Preferably, the formula for calculating the proportion of fresh water above the frozen soil layer can be:

[0088]

[0089] in, The ratio of fresh water to water above the permafrost layer. For standard gamma function, These are the shape parameters of water above the permafrost layer. This refers to the proportion of water above the permafrost layer. This represents the actual retention age of the runoff in the high-altitude, cold-climate basin. This is a preset age threshold.

[0090] S14, combined with the mixing ratio, average residence time of surface water runoff, average residence time of water runoff above the frozen soil layer, proportion of fresh surface water and proportion of fresh water above the frozen soil layer, to obtain the quantitative analysis results of the hydrological process.

[0091] Optionally, the server can retrieve the mixing ratio, average residence time of surface water runoff, average residence time of permafrost runoff, proportion of fresh surface water, and proportion of fresh permafrost runoff. It can then perform time-series matching and data calibration on these parameters to eliminate discrete parameter errors and time-series biases, obtaining multiple types of hydrological parameters. The server then couples and integrates these calibrated hydrological parameters, unifying the parameter representation dimensions, and ultimately obtaining quantitative analytical results of the hydrological process.

[0092] In one exemplary embodiment, such as Figure 3 As shown, based on the δ¹³C-DIC isotope values ​​of the water source and 87 Sr / 86 Sr isotope values, and representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to quantitatively decompose and cross-validate the sources of dissolved inorganic carbon in high-altitude watersheds using a Bayesian isotope mixing model and a Monte Carlo river inversion model, yielding the final contribution ratio of inorganic carbon sources from rock weathering, including:

[0093] S21, the δ¹³C-DIC isotope values ​​corresponding to the water source and 87 Sr / 86 The Sr isotope values ​​are input into a Bayesian isotope mixing model, and the probability distribution of inorganic carbon sources from rock weathering is obtained by simulating the distribution with no information prior using the Markov chain Monte Carlo sampling method.

[0094] Specifically, the Markov chain Monte Carlo sampling method can refer to an iterative sampling algorithm adapted to the Bayesian isotope mixing model. The Markov chain Monte Carlo sampling method can carry out large-scale random sampling simulation based on limited isotope observation data. The informationless prior distribution can refer to a prior distribution form that does not introduce additional subjective experience parameters and relies entirely on measured isotope data to drive the calculation. The informationless prior distribution can effectively avoid the calculation bias caused by human parameter settings and output the contribution probability distribution results of inorganic carbon sources in rock weathering.

[0095] Optionally, the server can retrieve the δ¹³C-DIC isotope values ​​of the water source and 87 Sr / 86 Sr isotope values, δ¹³C-DIC isotope values ​​and 87 Sr / 86 Sr isotope values ​​are imported as observational input parameters into the Bayesian isotope mixture model. The server can perform iterative sampling calculations using the Markov chain Monte Carlo sampling method. The Bayesian isotope mixture model employs an information-free prior distribution constrained iterative process, avoiding interference from external empirical parameters. After continuous iterative convergence, the server can statistically obtain the contribution probability distribution of inorganic carbon sources from rock weathering.

[0096] S22, the δ¹³C-DIC isotope values ​​corresponding to the water source and 87 Sr / 86 Sr isotope values ​​were used as data to be split, and representative end-member rock samples were analyzed. 87 Sr / 86 Using Sr isotope values ​​as endmember constraints, the Monte Carlo river inversion model is used to obtain the preliminary contribution ratio of inorganic carbon sources from rock weathering.

[0097] Specifically, the data to be split can refer to the measured isotope dataset of water sources used to carry out the inversion calculation of the contribution ratio of dissolved inorganic carbon sources, providing basic sample data for model inversion; the endmember constraint conditions can refer to the benchmark parameters that can limit the endmember isotope characteristics of watershed carbon sources. The endmember constraint conditions can be used to constrain the iterative solution range of the Monte Carlo river inversion model, reduce the uncertainty of multi-source mixed calculation, and ensure the accuracy of the inversion results of the contribution ratio of rock weathering inorganic carbon sources.

[0098] Optionally, the server can retrieve the δ¹³C-DIC isotope values ​​of the water source and 87 Sr / 86 Sr isotope values, δ¹³C-DIC isotope values ​​and 87 Sr / 86 Sr isotope values ​​were compiled into data to be split, and representative end-member rock samples were retrieved. 87 Sr / 86 Sr isotope values ​​are used as fixed endmember constraints. The server can synchronously input the data to be split and the endmember constraints into the Monte Carlo river inversion model, and perform inversion calculations based on the random sampling iteration mechanism of the Monte Carlo river inversion model. The server can continuously iterate and optimize the calculation results within the limits of the endmember constraints until convergence, and obtain the preliminary contribution ratio of inorganic carbon sources from rock weathering.

[0099] S23. By comparing and cross-validating the probability distribution and the initial contribution ratio, the final contribution ratio of inorganic carbon sources from rock weathering is calculated.

[0100] Optionally, the server can retrieve the probability distribution results and preliminary contribution ratio results to establish a matching relationship for inorganic carbon sources in rock weathering and conduct item-by-item comparison and verification. The server can statistically analyze the deviation range and fitting accuracy of the probability distribution results and preliminary contribution ratio results, remove abnormal deviation data, and calibrate and correct the preliminary contribution ratio results. The server can use the expected value of the probability distribution as a benchmark, combine it with the simulation accuracy of the Monte Carlo inversion results to allocate fusion weights, perform weighted fusion of the calibrated preliminary contribution ratios, and use the standard deviation of the probability distribution to set confidence intervals to constrain the fusion results, optimize the numerical results, and finally calculate the final contribution ratio of inorganic carbon sources in rock weathering.

[0101] In an exemplary embodiment, based on the quantitative analysis results of hydrological processes, the contribution rate of water sources to surface runoff, interflow, and groundwater runoff in the high-altitude watershed is calculated during each freeze-thaw period; based on the water source... 87 Sr / 86 Sr isotope values ​​and representative end-member rock samples 87 Sr / 86Sr isotope values ​​were used to differentiate the contribution percentages of silicate weathering and carbonate weathering. Based on the water source contribution rate, final contribution ratio, and contribution percentage, combined with the dissolved inorganic carbon concentration in the water source, the transport contribution rate of the freeze-thaw process to the transport of dissolved inorganic carbon in the high-altitude watershed was calculated, including the following steps:

[0102] S31. Based on the quantitative analysis results of hydrological processes, extract the δD isotope value characteristics and δ¹ values ​​of water sources during each freeze-thaw period. 8 O isotope value characteristics; based on δD isotope value characteristics and δ¹ 8 Based on the characteristics of O isotope values, the contribution rate of water sources to surface runoff, interflow, and groundwater runoff was calculated using the end-member mixing method.

[0103] Specifically, the δD isotope value characteristics and δ¹ 8 O isotope value characteristics can refer to the temporal distribution characteristics and numerical differences of stable hydrogen and oxygen isotopes in different water sources during different freeze-thaw periods; end-member mixing method can refer to a water source splitting calculation method based on the principle of isotope mass conservation, which realizes the quantitative splitting of components of multi-source mixed runoff according to the differences in isotope characteristics of different water sources, and accurately quantifies the contribution of different water sources to the replenishment of multi-stage runoff.

[0104] Optionally, the server can retrieve quantitative analysis results of hydrological processes and extract the δD isotope characteristics and δ¹ values ​​of water sources for each freeze-thaw period, according to the time division criteria of the freeze-thaw season, the pre-monsoon period, and the monsoon flood season. 8 O isotope characteristics. The server can use the isotopic characteristics of different water sources as endmember benchmarks, combined with the isotopic observation characteristics of surface runoff, interflow, and groundwater runoff, to perform isotopic mass conservation calculations using an endmember mixing method. The server can calculate the water source contribution rate of different water sources to surface runoff, interflow, and groundwater runoff during each freeze-thaw period through iterative solution operations.

[0105] S32. Representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were statistically analyzed according to silicate and carbonate rocks to obtain silicate rock endmembers. 87 Sr / 86 Sr eigenvalues ​​and carbonate endmembers 87 Sr / 86 Sr eigenvalue; corresponding to the water source 87 Sr / 86 Sr isotope values ​​are associated with silicate and carbonate endmembers, respectively. 87 Sr / 86 By comparing Sr eigenvalues, the contribution ratio of silicate weathering and carbonate weathering to the rock weathering carbon source of dissolved inorganic carbon in water sources was calculated.

[0106] Specifically, silicate rock end-members 87 Sr / 86 Sr eigenvalues ​​can refer to the strontium isotopic baseline characteristic parameters representing the weathered silicate rocks of the watershed, after classification and statistical analysis; and the end-members of carbonate rocks. 87 Sr / 86 Sr characteristic values ​​can refer to the strontium isotopic baseline characteristic parameters of weathered carbonate rocks in a watershed, after classification and statistical analysis.

[0107] Optionally, the server can retrieve all representative end-member rock samples. 87 Sr / 86 Based on the lithological type of representative end-member rock samples, Sr isotope values ​​were used to classify and statistically analyze silicate and carbonate rock sample data and extract characteristic mean values ​​to determine the corresponding silicate and carbonate end-members. 87 Sr / 86 Sr characteristic value. The server can retrieve the corresponding water source. 87 Sr / 86 The measured Sr isotope values ​​are correlated with those of silicate and carbonate endmembers, respectively. 87 Sr / 86 The Sr eigenvalues ​​are compared and analyzed. The server can combine the isotopic mass conservation relationship to quantitatively calculate and obtain the contribution ratio of silicate weathering and carbonate weathering to the carbon source of rock weathering.

[0108] S33. Based on the water source contribution rate, final contribution ratio, and contribution percentage, and combined with the dissolved inorganic carbon concentration of the water source, calculate the contribution of rock weathering inorganic carbon sources to dissolved inorganic carbon transport in the high-altitude cold basin during the freeze-thaw season and the early monsoon season; subtract the contribution during the early monsoon season from the contribution during the freeze-thaw season to obtain the net increase in carbon transport; divide the net increase in carbon transport by the contribution during the freeze-thaw season to obtain the transport contribution rate.

[0109] Specifically, the contribution can refer to the actual volume of dissolved inorganic carbon transported by different carbon sources in the basin during each freeze-thaw period. The contribution can intuitively reflect the carbon transport capacity of different carbon sources in different periods. The net increase in carbon transport can refer to the difference between the contribution of carbon transport in the freeze-thaw season and the contribution in the early monsoon season. The net increase in carbon transport can be used to characterize the incremental effect of carbon transport brought about by freeze-thaw action.

[0110] Optionally, the server can retrieve data on water source contribution rate, final contribution ratio, contribution percentage, and dissolved inorganic carbon concentration in the water source. Combining this with the time periods of the freeze-thaw season and the pre-monsoon season, the server can calculate the contribution of dissolved inorganic carbon transport corresponding to rock weathering inorganic carbon sources for each time period. The server can also statistically analyze the contribution of various carbon sources in the pre-monsoon season, subtracting the contribution of various carbon sources in the pre-monsoon season from the contribution of carbon sources corresponding to the freeze-thaw season to calculate the net increase in carbon transport from rock weathering inorganic carbon sources. Finally, the server can divide the net increase in carbon transport by the contribution of various carbon sources in the freeze-thaw season to calculate the transport contribution rate of rock weathering inorganic carbon sources under freeze-thaw conditions.

[0111] In an exemplary embodiment, the water source contribution rate, average runoff residence time, fresh water ratio, contribution percentage, and transport contribution rate are input into a structural equation model for causal coupling integration analysis to obtain the causal coupling analysis results, including the following steps:

[0112] S41. Using the freeze-thaw intensity, hydrological connectivity, weathering intensity, and carbon release risk of high-altitude cold basins as potential variables, and the water source contribution rate, average runoff residence time, fresh water ratio, contribution ratio, and transport contribution rate as observation variables, a measurement model of structural equation model is constructed.

[0113] Specifically, the measurement model can refer to the core component of the structural equation model. The measurement model can be used to establish the correspondence between observed variables and latent variables, and to achieve quantitative fitting of the characteristics of implicit processes.

[0114] Optionally, the server can use freeze-thaw intensity, hydrological connectivity, weathering intensity, and carbon release risk as latent variables. The server can match and filter corresponding observed variable indicators, including water source contribution rate, mean runoff residence time, fresh water proportion, contribution percentage, and transport contribution rate as observed variables. The server can establish the attribution relationships between each latent variable and observed variable, completing variable matching, dimensional calibration, and parameter normalization. Based on the variable matching relationships, the server can build a standardized measurement model, clarifying the representation path of observed variables to latent variables, and completing the construction of the measurement model.

[0115] Preferably, the general calculation formula for the measurement model can be:

[0116]

[0117] in, For observed variables, Factor loadings between latent and observed variables. As latent variables, This is the error term.

[0118] S42. Define the causal paths from freeze-thaw intensity to hydrological connectivity, from hydrological connectivity to weathering intensity, and from weathering intensity to carbon release risk, and construct a structural equation model.

[0119] Specifically, causal paths can refer to the relationships that characterize the direction of action and transmission logic among various potential variables. Causal paths can be used to define the intrinsic driving and response mechanisms of multiple processes in high-altitude cold watersheds. Structural models can refer to the core components of structural equation models, which serve as the basis for variable fitting in measurement models. Structural models can be used to build a hierarchical transmission framework among various potential variables and quantitatively characterize the causal coupling laws of the entire process of freeze-thaw, hydrology, weathering, and carbon release.

[0120] Optionally, the server can, based on the established measurement model, analyze the inherent transmission logic of multiple processes in the high-altitude cold watershed, and sequentially define the hierarchical causal transmission paths of freeze-thaw intensity on hydrological connectivity, hydrological connectivity on weathering intensity, and weathering intensity on carbon release risk. The server can clearly define the hierarchical effect and corresponding relationships of each causal path, and unify the transmission direction and constraint logic of the paths. The server can complete the construction of the structural model according to the preset causal path framework, forming a complete structural equation model together with the measurement model.

[0121] Preferably, the general calculation formula for the structural model can be:

[0122]

[0123] in, As a potential dependent variable, The path coefficient matrix between the latent dependent variables. This is the path coefficient matrix between the independent and dependent variables. As an exogenous variable, This is the error term for the latent dependent variable.

[0124] S43. Perform parameter estimation and fitting on the structural equation model to obtain the path coefficients and model fit of each causal path, and output the causal coupling analysis results of freeze-thaw hydrology-rock weathering-carbon transport.

[0125] Specifically, parameter estimation can refer to the quantification process of iteratively solving the causal interaction coefficients between latent variables based on observed variable data. Parameter estimation can be used to accurately determine the intensity of each transmission path. Model fit can refer to the quantitative index that evaluates the overall fit effect and modeling reliability of the structural equation model. Model fit can be used to verify the rationality of model construction and the credibility of analytical results. Path coefficient can refer to the core parameters that characterize the magnitude of the interaction and the direction of positive and negative responses between latent variables. Path coefficient can reflect the coupling driving differences between freeze-thaw, hydrology, weathering and carbon transport processes.

[0126] Optionally, the server can retrieve the structural equation model to perform overall parameter estimation and model fitting calculations. The server can solve for the coefficients of each preset causal transmission path one by one, and statistically obtain the path coefficients corresponding to all paths. The server can simultaneously calculate the overall model fit index to obtain the model fit degree and complete the model validity verification. The server can integrate the path coefficients and model fit degree, and finally output the causal coupling analysis results of freeze-thaw hydrology-rock weathering-carbon transport.

[0127] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0128] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. A quantitative analysis method based on freeze-thaw hydrology-carbon coupling in high-altitude watersheds using multi-isotope joint tracing, characterized in that, The method includes: S1. Obtain the δD isotope values ​​and δ¹ values ​​corresponding to various water sources within the high-altitude cold basin. 8 O isotope value, δ¹³C-DIC isotope value and 87 Sr / 86 Sr isotope values, and corresponding values ​​of representative end-member rock samples 87 Sr / 86 Sr isotope values; wherein, the water source includes precipitation, permafrost water, and surface water; S2. Based on the δD isotope value, calculate the mixing ratio of the surface water and the water above the permafrost layer; S3, δ¹ of the precipitation, the surface water, and the water above the frozen soil layer 8 The time series of O isotope values ​​was sinusoidally fitted to obtain the δ¹ 8 The amplitude and phase of the O isotope value; based on the amplitude and phase, the average residence time of runoff and the proportion of new water are calculated using a gamma distribution model; by combining the mixing ratio, the average residence time of runoff and the proportion of new water, quantitative analysis results of the hydrological process are obtained. S4. Based on the δ¹³C-DIC isotope value of the water source and 87 Sr / 86 Sr isotope values, and the representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to quantitatively decompose and cross-validate the sources of dissolved inorganic carbon in the high-altitude basin using a Bayesian isotope mixing model and a Monte Carlo river inversion model, so as to obtain the final contribution ratio of inorganic carbon sources from rock weathering. S5. Based on the quantitative analysis results of the hydrological process, calculate the water source contribution rate of the water source to surface runoff, interflow, and groundwater runoff in the high-altitude cold basin during each freeze-thaw period; based on the water source... 87 Sr / 86 Sr isotope values ​​and the representative end-member rock sample 87 Sr / 86 Sr isotope values ​​are used to distinguish the contribution ratios of silicate weathering and carbonate weathering to the dissolved inorganic carbon from rock weathering carbon sources; based on the water source contribution rate, the final contribution ratio, and the contribution ratio, combined with the dissolved inorganic carbon concentration of the water source, the transport contribution rate of the freeze-thaw process to the transport of dissolved inorganic carbon in the high-altitude watershed is calculated; wherein, the freeze-thaw period includes the freeze-thaw season, the pre-monsoon season, and the monsoon flood season; S6. Input the water source contribution rate, the average residence time of runoff, the proportion of new water, the contribution ratio, and the transport contribution rate into the structural equation model for causal coupling integration analysis to obtain the causal coupling analysis results.

2. The method according to claim 1, characterized in that, The formula for calculating the mixing ratio is: ； in, The mixing ratio of the surface water in the water above the permafrost layer. The mixing ratio of the water above the permafrost layer to the surface water. The δD isotope value of the water above the permafrost layer. The δD isotope value of the surface water is given. The δD isotope value of the precipitation is given.

3. The method according to claim 1, characterized in that, The δ¹ of the precipitation, the surface water, and the water above the permafrost layer 8 The time series of O isotope values ​​was sinusoidally fitted to obtain the δ¹ 8 The amplitude and phase of the O isotope value; based on the amplitude and phase, the mean residence time of runoff and the proportion of new water are calculated using a gamma distribution model; by combining the mixing ratio, the mean residence time of runoff, and the proportion of new water, quantitative analysis results of the hydrological process are obtained, including: S11. Using a sine wave fitting method, the δ¹ values ​​of the precipitation, surface water, and permafrost water are calculated. 8 The amplitude and phase are obtained by fitting the time series of O isotope values; wherein, the calculation formula for the sine wave fitting is: ； in, δ¹ of the surface water 8 O isotope fitting values δ¹ of the precipitation 8 O isotope fitting values δ¹ of the water in the permafrost layer 8 O isotope fitting values δ¹ of the surface water 8 Amplitude of O isotope values δ¹ of the precipitation 8 Amplitude of O isotope values δ¹ of the water in the permafrost layer 8 Amplitude of O isotope values δ¹ of the surface water 8 Phase of O isotope values δ¹ of the precipitation 8 Phase of O isotope values δ¹ of the water in the permafrost layer 8 Phase of O isotope values The annual cycle signal frequency, δ¹ of the surface water 8 The mean term of the O isotope value with respect to the time series. δ¹ of the precipitation 8 The mean term of the O isotope value with respect to the time series. δ¹ of the water in the permafrost layer 8 The mean term of the O isotope value with respect to the time series. This represents the number of days since the start of the sampling process. S12. Calculate the surface water amplitude ratio based on the amplitudes of the surface water and the precipitation, and calculate the surface water phase shift based on the phases of the surface water and the precipitation; calculate the frozen soil surface water amplitude ratio based on the amplitudes of the water above the frozen soil layer and the precipitation, and calculate the frozen soil surface water phase shift based on the phases of the water above the frozen soil layer and the precipitation; input the surface water amplitude ratio and the surface water phase shift, and the frozen soil surface water amplitude ratio and the frozen soil surface water phase shift into the gamma distribution model respectively, and iteratively solve the shape parameters and proportion parameters of the surface water and the water above the frozen soil layer; S13. Multiply the shape parameters and proportion parameters of the surface water to obtain the average residence time of the surface water runoff; multiply the shape parameters and proportion parameters of the water above the permafrost layer to obtain the average residence time of the water above the permafrost layer runoff; according to the regularized incomplete gamma function, calculate the proportions of surface water and water above the permafrost layer with a runoff residence time less than a preset age threshold in the total runoff of the high-altitude basin to obtain the proportion of new water; wherein, the runoff residence time includes the time it takes for precipitation to become surface water through the basin and the time it takes for precipitation to become water above the permafrost layer through the active permafrost layer, and the proportion of new water includes the proportion of new surface water and the proportion of new water above the permafrost layer; S14. By combining the mixing ratio, the average residence time of surface water runoff, the average residence time of water runoff above the frozen soil layer, the proportion of fresh surface water, and the proportion of fresh water above the frozen soil layer, the quantitative analysis results of the hydrological process are obtained.

4. The method according to claim 1, characterized in that, The δ¹³C-DIC isotope values ​​based on the water source and 87 Sr / 86 Sr isotope values, and the representative end-member rock samples 87 Sr / 86 Sr isotope values ​​were used to quantitatively decompose and cross-validate the sources of dissolved inorganic carbon in the high-altitude basin using a Bayesian isotope mixing model and a Monte Carlo river inversion model, yielding the final contribution ratio of inorganic carbon sources from rock weathering, including: S21, the δ¹³C-DIC isotope values ​​corresponding to the water source and 87 Sr / 86 The Sr isotope value is input into the Bayesian isotope mixing model, and the probability distribution of the inorganic carbon source of rock weathering is obtained by simulating the distribution with no information prior using the Markov chain Monte Carlo sampling method. S22, the δ¹³C-DIC isotope values ​​corresponding to the water source and 87 Sr / 86 Sr isotope values ​​were used as data to be split, and the representative end-member rock samples were... 87 Sr / 86 Using Sr isotope values ​​as endmember constraints, the Monte Carlo river inversion model is input to obtain the preliminary contribution ratio of the inorganic carbon source from rock weathering. S23. The probability distribution and the preliminary contribution ratio are compared and cross-validated to calculate the final contribution ratio of the inorganic carbon source of rock weathering.

5. The method according to claim 1, characterized in that, Based on the quantitative analysis results of the hydrological process, the contribution rate of the water source to surface runoff, interflow, and groundwater runoff in the high-altitude watershed is calculated during each freeze-thaw period; based on the water source... 87 Sr / 86 Sr isotope values ​​and the representative end-member rock sample 87 Sr / 86 Sr isotope values ​​are used to distinguish the contribution ratios of silicate weathering and carbonate weathering to the rock weathering carbon source in the dissolved inorganic carbon. Based on the water source contribution rate, the final contribution ratio, and the contribution ratio, combined with the dissolved inorganic carbon concentration of the water source, the transport contribution rate of the freeze-thaw process to the transport of dissolved inorganic carbon in the high-altitude watershed is calculated, including: S31. Based on the quantitative analysis results of the hydrological process, extract the δD isotope value characteristics and δ¹ values ​​of the water source during each freeze-thaw period. 8 O isotope value characteristics; based on the δD isotope value characteristics and the δ¹ 8 Based on the O isotope value characteristics, the contribution rate of the water source to the surface runoff, the interflow, and the groundwater runoff is calculated using the endmember mixing method. S32. Regarding the representative end-member rock sample... 87 Sr / 86 Sr isotope values ​​were statistically analyzed according to silicate and carbonate rocks to obtain silicate rock endmembers. 87 Sr / 86 Sr eigenvalues ​​and carbonate endmembers 87 Sr / 86 Sr characteristic value; the water source corresponding to 87 Sr / 86 Sr isotope values ​​are respectively associated with the silicate rock endmember and the carbonate rock endmember. 87 Sr / 86 By comparing the Sr characteristic values, the contribution ratio of silicate weathering and carbonate weathering to the rock weathering carbon source of dissolved inorganic carbon in the water source is calculated. S33. Based on the water source contribution rate, the final contribution ratio, and the contribution percentage, and in conjunction with the dissolved inorganic carbon concentration of the water source, calculate the contribution of the weathered inorganic carbon source of rocks in the high-altitude cold basin to the transport of dissolved inorganic carbon during the freeze-thaw season and the pre-monsoon period; subtract the contribution during the pre-monsoon period from the contribution during the freeze-thaw season to obtain the net increase in carbon transport; divide the net increase in carbon transport by the contribution during the freeze-thaw season to obtain the transport contribution rate.

6. The method according to claim 1, characterized in that, The process involves inputting the water source contribution rate, the average runoff retention time, the proportion of new water, the contribution ratio, and the transport contribution rate into a structural equation model for causal coupling integration analysis, yielding causal coupling analysis results, including: S41. Using the freeze-thaw intensity, hydrological connectivity, weathering intensity, and carbon release risk of the high-altitude cold basin as potential variables, and the water source contribution rate, the average runoff residence time, the proportion of new water, the contribution ratio, and the transport contribution rate as observation variables, a measurement model of structural equation model is constructed. S42. Define the causal path from the freeze-thaw intensity to the hydrological connectivity, from the hydrological connectivity to the weathering intensity, and from the weathering intensity to the carbon release risk, and construct the structural model of the structural equation model. S43. Perform parameter estimation and fitting on the structural equation model to obtain the path coefficients and model fit of each causal path, and output the causal coupling analysis results of freeze-thaw hydrology-rock weathering-carbon transport.

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