Runoff change attribution uncertainty quantification method

Abstract

The invention provides a runoff change attribution uncertainty quantification method. The runoff change attribution uncertainty quantification method comprises the following steps: S1, forming a scheme set according to different combinations of a staging method (SEG), potential evapotranspiration calculation (PET), a surface average meteorological parameter calculation method (MET) and a Budyko equation form (EQ); s2, calculating the elastic coefficient of each scheme in the reference period; s3, according to the elastic coefficient and the two-stage statistical magnitude, a climate item caused by rainfall and potential evapotranspiration and a remaining item caused by an underlying surface (human activity) are obtained respectively, and the climate contribution rate is calculated; and S4, constructing a Bayesian hierarchical model of Beta regression by taking the climate contribution rate of each scheme as a response, introducing random effects of SEG, PET, MET and EQ and optimal second-order interaction at a logit scale, completing posterior inference through methods such as Markov chain Monte Carlo and the like, and quantifying the uncertainty contribution of the factors to an attribution result. The method is simple in process, reproducible, high in interpretability and suitable for scientific research and engineering evaluation of drainage basin scale runoff change attribution.

Description

Technical Field

[0001] This invention relates to the field of hydrological and water resources uncertainty analysis, and specifically to a method for quantifying the uncertainty of runoff change attribution. Background Technology

[0002] In watershed-scale runoff change studies, the Budyko framework is widely used to decompose the relative contributions of climate change and human activities to runoff. In practice, researchers need to choose from different staging methods, potential evapotranspiration calculation methods, surface averaging methods of meteorological elements, and the Budyko equation family. Different combinations of methods often lead to significant differences, resulting in uncertainty in the results. Existing work mostly presents these differences through cross-sectional comparisons or empirical discussions, lacking a unified, statistically consistent framework to quantify the uncertainty in attribution results caused by different calculation schemes. Therefore, there is an urgent need to provide a method for quantifying the uncertainty of runoff change attribution that can address the aforementioned technical problems. Summary of the Invention

[0003] The purpose of this invention is to solve the technical problems mentioned above and to propose a method for quantifying the uncertainty of runoff change attribution, comprising the following steps: S1. A set of schemes is formed according to different combinations of the phased method (SEG), potential evapotranspiration calculation (PET), meteorological element surface average interpolation method (MET), and Budyko equation form (EQ); S2, the elasticity coefficients of each scheme in the scheme set formed in step S1 of the baseline period calculation; S3. Based on the elasticity coefficient and the two-period statistics, obtain the climate term caused by climate change such as precipitation and potential evapotranspiration, and the residual term caused by the underlying surface (human activities), and calculate the climate contribution rate. S4. A Bayesian hierarchical model with Beta regression is constructed in response to the climate contribution rate of each scheme. Random effects of staging method (SEG), potential evapotranspiration calculation (PET), meteorological element surface average interpolation method (MET), and Budyko equation form (EQ) are introduced at the logit scale, and the optimal second-order interaction (staging method SEG × Budyko equation form EQ, potential evapotranspiration calculation PET × surface average meteorological parameter calculation method MET) is performed. After-a priori inference is performed using Markov chain Monte Carlo and other methods, and the uncertainty contribution of the above factors to the attribution results is quantified.

[0004] In the preferred embodiment, step S1 further includes the following steps: S11. Determine the set of scheme factors, each factor should contain no less than two different method levels; S12. Perform Cartesian combinations of the levels of each factor to obtain a list of schemes; the preferred approach is a full factorial design. S13. Based on the phased approach for each scheme, determine the base period (T1) and the change period (T2). S14. Using the PET and MET specified in this scheme, calculate the multi-year average precipitation, potential evapotranspiration and runoff for T1 and T2 respectively (denoted as P1, PET1, R1 and P2, PET2, R2).

[0005] In the preferred embodiment, step S2 includes the following steps: S21. Calculate annual runoff based on daily runoff data, perform mutation detection using the Bayesian method, and divide the long runoff series into natural periods based on the mutation detection results. T 1 and the period of influence T 2; S22. The multi-year average precipitation, potential evapotranspiration and runoff (P1, PET1, R1) of T1 are used as the benchmark for evaluating the elasticity coefficient. S23. Based on the Budyko equation specified for each scheme, calculate the elastic coefficients of precipitation and potential evapotranspiration based on the definition of elastic coefficients, and obtain the elastic coefficient parameter set corresponding to each scheme.

[0006] In the preferred embodiment, step S3 includes the following steps: S31. Based on the elasticity coefficient and the two-period statistics, calculate the absolute amounts of climate contribution and human contribution under each scenario.

[0007] S32, in Calculating the climate contribution rate when it is non-zero ;when When the value is close to zero, absolute values ​​should be retained first.

[0008] S33. Form a “Scheme-Indicator Table” which includes at least: scheme identifier (SEG, PET, MET, EQ), absolute amount of climate contribution, absolute amount of human contribution, and climate contribution rate.

[0009] In the preferred embodiment, step S4 includes the following steps: S41. Use the climate contribution rate of each scheme as the response variable; S42. Define a set of four core schemes: the staging scheme (SEG), the potential evapotranspiration calculation scheme (PET), the Budyko equation scheme (EQ), and the meteorological data preprocessing scheme (MET). Construct a cross-stochastic effects structure, introduce the stochastic intercepts and physically meaningful second-order interaction terms (SEG×EQ, PET×MET) of each scheme, and establish the model mean expression at the logit scale. S43. Based on measured watershed data, literature experience, and the physical meaning of the Budyko framework, a relaxed normal prior is set for the model intercept (the value corresponding to the climate contribution rate of the baseline scheme), a half-t distribution weak information prior is set for the variance of the random effects of each scheme, and a gamma prior is set for the precision parameter of the Beta distribution, thus balancing data-driven and prior constraints. S44. Complete the inference. The posterior distribution of parameters is obtained using Markov chain Monte Carlo. MCMC sampling is carried out using the NUTS algorithm. The sampling convergence is verified by Gelman-Rubin diagnostics, effective sample size, and trace plot. Finally, based on the proportion of random effects variance contribution, the uncertainty contribution of each scheme and interaction term to the climate contribution rate is quantified.

[0010] In the preferred embodiment, step S1 specifically includes: The control section of the watershed under study was determined, and the daily runoff of the control section for ≥35 consecutive years was obtained from sources such as hydrological yearbooks. and water level For missing or incomplete data, the water level-flow relationship method or other relevant analysis methods are used for interpolation to ensure the integrity of the data sequence.

[0011] The vector boundary of the study area, the locations of meteorological stations within and near the boundary, and the corresponding diurnal precipitation data were determined. near-surface temperature relative humidity Or dew point / vapor pressure, wind speed at 2m near ground shortwave radiation Or hours of sunshine Station altitude / air pressure; The diurnal runoff series is processed into an adult runoff series, denoted as... In the formula, N is the sequence length. Preferably, three methods are used for mutation detection: Pettitt mutation test: for any cut point definition Significance approximation level When the specified requirements are met, the mutation location for The largest ; Buishand R test: Constructing a cumulative sum for annual series ,when A mean jump is determined when the value exceeds a given significance level; the jump location is located at... Place; SNHT test: for all candidate cut points (recommend Calculate the test statistic (year). ,Pick , Estimated mutation location; Time series are divided into three types based on three mutation detection methods. , Two time periods; Potential evapotranspiration (PET) calculation: PET is first calculated on a daily scale, then aggregated to an annual scale, and finally... , The following calculation method can be used to take the average over many years: FAO56 Penman–Monteith: ; In the formula: Net radiation, For soil heat flux, For temperature, The wind speed is 2 m. These are the saturated and actual water vapor pressures, respectively. The slope of the saturated water vapor pressure curve. The thermometer constant is given by the saturated vapor pressure. Approximate calculation; Priestley-Taylor method: ; Hargreaves method: ; In the formula Radiation from outside the zenith; Hydrometeorological Surface Mean (MET) Processing Method: Thiessen polygon interpolation: Construct Voronoi polygons from the stations and take the area of ​​each polygon falling within the watershed. As a weight:

[0012] Inverse distance weighted interpolation: at point interpolation value In the formula, Unknown point With known points distance, The power exponent is used to perform area averaging on the grid within the watershed mask after interpolation; Kriging interpolation: In the formula It is a point The estimated value at the location, weight From the Kriging equation and the semivariogram get; Budyko Equation Method (EQ): Recording the wet / dry index , evapotranspiration ratio runoff ratio Preferably, the Budyko equations used are: Fu-Budyko equation: ; Choudhury-Yang equation: ; Turc-Pike equations: ; Based on the mutation test results and different calculation schemes for each parameter, the multi-year average statistics for the two periods were statistically analyzed: , It is generated by the Cartesian product of "phased method × PET method × surface average method × Budyko equation", and each term specifies the SEG, PET, MET, EQ used and their corresponding values. Years; Finally, the calculation scheme was obtained.

[0013] In the preferred scheme, the difference between the multi-year average statistics of the two periods is calculated: ; Define the dryness index: Runoff coefficient function ,in These are the parameters of the underlying surface.

[0014] set up , Define the elasticity coefficients of runoff with respect to precipitation, potential evapotranspiration, and underlying surface. , They are respectively: ; The above formula is The value at this location is: ; In the preferred scheme, substituting the partial derivatives of the Fu-Budyko equation, the Choudhury-Yang equation, and the Turc-Pike equation into the above equation yields: Fu-Budyko equation:

[0015] Choudhury-Yang equation:

[0016] The Turc-Pike equations are parameterless equations, therefore... calculate: .

[0017] In the preferred embodiment, step S3 specifically includes: Based on the elasticity coefficient obtained in step S2, the absolute values ​​of runoff changes caused by climate change and human activities are further calculated. The calculation process is as follows: Runoff changes caused by precipitation and runoff changes caused by potential evapotranspiration They are respectively:

[0018] Changes in runoff caused by climate change for:

[0019] According to the residual method, runoff changes caused by changes in the underlying surface are analyzed. for:

[0020] The contribution rates of precipitation / evapotranspiration / underlying surface changes to runoff changes They are respectively: ; This yields the contribution rate results of each factor under the 81 schemes mentioned in step S101; when When the value is close to 0, subsequent analyses should prioritize the absolute values ​​of climate contribution and human contribution.

[0021] In the preferred embodiment, step S4 specifically involves: For detailed calculation, for each combination of schemes Below Record The climate contribution rate obtained in step S103 is taken as the response: ; Keep only " and Same number and The combination of ""; The total number of levels for the four factors; The observation layer uses a Beta-based mean-precision parameterization, with the mean linked to the linear predictor via a logit. ; In the formula This is the conditional mean of the combination. For accuracy parameters, It is a linear predictor on the logit scale; It consists of the overall intercept, the random intercepts of the four main effects, and two second-order interactions: ; in, For the overall intercept, The main effect random intercepts of the four types of factors are shown. , For the two interactive random intercepts; To avoid confusion with the intercept, the main effects are zero-sum / centered within the group, and the interactions are centered in both the row and column directions: ; ; When it is necessary to restore the results to the original scale, use ; The intercept is taken from a loose normal prior; the random effects are taken from a hierarchical normal prior with a half-t prior given to their standard deviation; and the observation level precision is taken from a gamma prior. ; ; ; in For each category of a priori criteria; Complete the inference and uncertainty quantification (variance contribution ratio). Perform MCMC sampling using NUTS and complete the convergence test. Quantify the "source of uncertainty" based on the variance contribution ratio of random effects: Let... Let be the standard deviation of the category, then: ; right By summing the median and 95% confidence interval across all posterior samples, we obtain the proportions of variation in climate contribution rates for the phase (SEG), potential evapotranspiration (PET), meteorological mean (MET), equation form (EQ), and the interaction between the two factors; simultaneously, we can... By extrapolating back to the original scale for each random effect, we provide estimates and intervals of the climate contribution rates at the overall and individual scenario levels, and output the results for each combination. The posterior prediction results.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Uncertainty quantification of all factors. The full factor combination of stage (SEG), potential evapotranspiration (PET), surface average (MET) and Budyko equation (EQ) is uniformly incorporated into the hierarchical Bayesian (Beta-logit) framework to perform posterior estimation of main effects and key second-order interactions and to give the variance contribution share and interval estimate of each source. Compared with existing methods that rely only on a single scheme or empirical comparison, this invention achieves explicit decomposition and traceable quantification of methodological uncertainty, which significantly improves the robustness and comparability of attribution conclusions.

[0023] (2) Objective selection and measurable model selection mechanism. The effects and importance of each candidate method (SEG / PET / MET / EQ) are learned simultaneously within a unified statistical layer to form a ranking of method importance, avoiding manual "method selection" and selective reporting bias; based on this, the scheme library can be automatically reduced and standardized to maintain consistent results under different watershed / time period / data quality conditions, strong reproducibility, and low implementation cost, demonstrating the engineering transferability advantages over existing technologies. Attached Figure Description

[0024] Figure 1 This is a flowchart of the evaluation method provided in the embodiments of this application.

[0025] Figure 2 This is a diagram showing the setup of an uncertainty assessment scheme set. Detailed Implementation

[0026] This application discloses a method and system for quantifying the attribution uncertainty of runoff change based on the Budyko elasticity and Bayesian hierarchical model. First, a set of scenarios is formed according to different combinations of the staging method (SEG), potential evapotranspiration calculation (PET), surface average meteorological parameter calculation method (MET), and Budyko equation form (EQ). The elasticity coefficients under each scenario are calculated to determine the climate change and human activity contributions of each scenario, thus obtaining the climate contribution rate. ; based on each plan In response, a Bayesian hierarchical model of Beta regression was constructed; the uncertainty of attribution outcomes caused by the random effects of SEG, PET, MET, EQ, and key second-order interactions was quantified. For details of the process, please refer to [link to documentation]. Figure 1 .

[0027] The technical solution of this application will be further described in detail below through embodiments: Based on the above embodiments, step S101 includes: The control section of the watershed under study was determined, and the daily runoff of the control section for ≥35 consecutive years was obtained from sources such as hydrological yearbooks. and water level For missing or incomplete data, the water level-flow relationship method or other relevant analysis methods are used for interpolation to ensure the integrity of the data sequence.

[0028] The vector boundary of the study area, the locations of meteorological stations within and near the boundary, and the corresponding diurnal precipitation data were determined. near-surface temperature relative humidity Or dew point / vapor pressure, wind speed at 2m near ground shortwave radiation Or hours of sunshine Station altitude / air pressure.

[0029] (1) Process the diurnal runoff series into an adult runoff series, denoted as In the formula, N is the sequence length. Preferably, three methods are used for mutation detection: Pettitt mutation test: for any cut point definition Significance approximation level When the specified requirements are met, the mutation location for The largest .

[0030] Buishand R test: Constructing a cumulative sum for annual series ,when A mean jump is determined when the value exceeds a given significance level; the jump location is located at... Place.

[0031] SNHT test: for all candidate cut points (recommend Calculate the test statistic (year). ,Pick , Estimated mutation location.

[0032] Based on the three mutation detection methods mentioned above, time series are divided into... , Two time periods.

[0033] (2) Potential evapotranspiration (PET) calculation: PET is first calculated on a daily scale, then aggregated to an annual scale, and finally... , The average over several years is taken. The following calculation method can be used: FAO56 Penman–Monteith:

[0034] In the formula: Net radiation (MJ·m⁻²·d⁻¹) This represents soil heat flux (which can be approximated as 0 daily). Temperature (°C) The wind speed is 2 m (m·s⁻¹). These are the saturated / actual water vapor pressures (kPa), respectively. The slope of the saturated water vapor pressure curve (kPa·℃⁻¹) is given. The thermometer constant is (kPa·℃⁻¹), and the saturated vapor pressure can be obtained from... Approximate calculation.

[0035] Priestley-Taylor method:

[0036] Hargreaves method:

[0037] In the formula It is radiation from outside the zenith.

[0038] (3) Hydrometeorological Surface Mean (MET) processing method: Thiessen polygon interpolation: Construct Voronoi polygons from the stations and take the area of ​​each polygon falling within the watershed. As a weight:

[0039] Inverse distance weighted interpolation: at point interpolation value In the formula, Unknown point With known points distance, The power exponent is used to perform area averaging on the grid within the watershed mask after interpolation.

[0040] Kriging interpolation: In the formula It is a point The estimated value at the location, weight From the Kriging equation and the semivariogram get.

[0041] (4) Budyko Equation Method (EQ): Record the wet-dry index , evapotranspiration ratio runoff ratio Preferably, the Budyko equations used are: Fu-Budyko equation:

[0042] Choudhury-Yang equation:

[0043] Turc-Pike equations:

[0044] (5) Based on the mutation test results and different calculation schemes for each parameter, calculate the multi-year average statistics for the two periods: , Generate 81 groups using the Cartesian product of "phased method × PET method × surface average method × Budyko equation" (e.g., 3 × 3 × 3 × 3 = 81 groups), specifying the SEG, PET, MET, EQ used for each item and their corresponding values. The final calculation scheme is as follows: Figure 2 .

[0045] Based on the above embodiments, step S102 includes: Calculate the difference between the multi-year average statistics for two periods: .

[0046] Define the dryness index: Runoff coefficient function ,in These are the parameters of the underlying surface.

[0047] set up , Define the elasticity coefficients of runoff with respect to precipitation, potential evapotranspiration, and underlying surface. , They are respectively:

[0048] The above formula is The value at this location is:

[0049] Preferably, substituting the partial derivatives of the Fu-Budyko equation, the Choudhury-Yang equation, and the Turc-Pike equation into the above equation yields: Fu-Budyko equation:

[0050] Choudhury-Yang equation: The Turc-Pike equations are parameterless equations, therefore... calculate:

[0051] Based on the above embodiments, step S103 includes: Based on the elasticity coefficient obtained in step S102, the absolute values ​​of runoff changes caused by climate change and human activities are further calculated. The calculation process is as follows: Runoff changes caused by precipitation and runoff changes caused by potential evapotranspiration They are respectively:

[0052] Changes in runoff caused by climate change for:

[0053] According to the residual method, runoff changes caused by changes in the underlying surface are analyzed. for:

[0054] The contribution rates of precipitation / evapotranspiration / underlying surface changes to runoff changes They are respectively:

[0055] This yields the contribution rate results of each factor under the 81 schemes mentioned in step S101. When When the value is close to 0, subsequent analyses should prioritize the absolute values ​​of climate contribution and human contribution.

[0056] Based on the above embodiments, step S104 includes: Determine the climate contribution rate For the response variable. For detailed calculations, for each combination of options... (corresponding to the SEG / PET / MET / EQ respectively) (at each level) Record The climate contribution rate obtained in step S103 is taken as the response:

[0057] Keep only " and Same number and Combinations of ""; such as individual If you get 0 or 1, adjust the interval slightly before using it. This represents the total number of levels for the four types of factors.

[0058] Construct a Bayesian hierarchical model. The observation layer uses Beta's "mean-precision" parameterization, with the mean linked to the linear predictor via logit.

[0059] In the formula This is the conditional mean of the combination. For accuracy parameters, It is a linear predictor on the logit scale.

[0060] It consists of the overall intercept, the random intercepts of the four main effects, and two second-order interactions:

[0061] in For the overall intercept, The main effect random intercepts of the four types of factors are shown. , For the two interactive random intercepts.

[0062] To avoid confusion with the intercept, main effects are zero-sum / centered within groups, and interactions are centered in both row and column directions, for example:

[0063] When it is necessary to restore the results to the original scale, you can use .

[0064] Priors are defined. The intercept is taken from a loosely normal prior; the random effects are taken from a hierarchical normal prior with a half-t prior given to their standard deviation; and the observation level precision is taken from a gamma prior.

[0065] in For each category of prior scale (main effect can be taken) Interactive features are desirable ).

[0066] Complete the inference and uncertainty quantification (variance contribution ratio). Perform MCMC sampling using NUTS and complete the convergence test. Quantify the "source of uncertainty" based on the variance contribution ratio of random effects: Let... For category The standard deviation of the main effect or interaction (obtained from the posterior sample) is then

[0067] right By summing the median and 95% confidence interval across all posterior samples, we obtain the proportions of variation in climate contribution rates for the phase (SEG), potential evapotranspiration (PET), meteorological mean (MET), equation form (EQ), and the interaction between the two factors; simultaneously, we can... By extrapolating back to the original scale for each random effect, we provide estimates and intervals of the climate contribution rates at the overall and individual scenario levels, and output the results for each combination. The posterior prediction results.

[0068] A specific embodiment of the present invention also provides a computer-readable medium.

[0069] The computer-readable medium is a server workstation; the server workstation stores a computer program executed by an electronic device, which, when the computer program is run on the electronic device, causes the electronic device to execute the steps of the runoff change attribution uncertainty quantification method based on the Budyko elasticity and Bayesian hierarchical model of the present invention.

[0070] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0071] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be defined by the appended claims.

Claims

1. A method for quantifying the uncertainty of runoff change attribution, characterized by: Includes the following steps: S1. Form a set of solutions according to different combinations of SEG, PET, MET and EQ; S2, the elasticity coefficients of each scheme in the scheme set formed in step S1 of the baseline period calculation; S3. Based on the elasticity coefficient and the two-period statistics, obtain the climate term caused by climate change and the residual term caused by human activities, and calculate the climate contribution rate. S4. Construct a Bayesian hierarchical model with Beta regression in response to the climate contribution rate of each scheme. Introduce random effects and preferred second-order interactions of SEG, PET, MET and Budyko equation forms of EQ at the logit scale. Perform a post-hoc inference using the Markov chain Monte Carlo method and quantify the contribution of the above factors to the uncertainty of the attribution results.

2. The method for quantifying the uncertainty of runoff change attribution according to claim 1, characterized in that: Step S1 also includes the following steps: S11. Determine the set of scheme factors, each factor should contain no less than two different method levels; S12. Perform Cartesian combinations of the levels of each factor to obtain a list of schemes; the preferred approach is a full factorial design. S13. Determine the base period T1 and the change period T2 according to the phased method of each scheme; S14. Using the PET and MET specified in this scheme, calculate the multi-year average precipitation, potential evapotranspiration and runoff for T1 and T2 respectively.

3. The method for quantifying the uncertainty of runoff change attribution according to claim 1, characterized in that: Step S2 includes the following steps: S21. Calculate annual runoff based on daily runoff data, perform mutation detection using the Bayesian method, and divide the long runoff series into natural periods based on the mutation detection results. T 1 and the period of influence T 2; S22. The multi-year average precipitation, potential evapotranspiration and runoff (P1, PET1, R1) of T1 are used as the benchmark for evaluating the elasticity coefficient. S23. Based on the Budyko equation specified for each scheme, calculate the elastic coefficients of precipitation and potential evapotranspiration based on the definition of elastic coefficients, and obtain the elastic coefficient parameter set corresponding to each scheme.

4. The method for quantifying the uncertainty of runoff change attribution according to claim 1, characterized in that: Step S3 includes the following steps: S31. Based on the elasticity coefficient and the two-period statistics, calculate the absolute amounts of climate contribution and human contribution under each scenario. S32, in Calculating the climate contribution rate when it is non-zero ;when When the value is close to zero, prioritize retaining absolute values. S33. Form a scheme-indicator table, which shall include at least: scheme identifier, absolute amount of climate contribution, absolute amount of human contribution, and climate contribution rate.

5. The method for quantifying the uncertainty of runoff change attribution according to claim 1, characterized in that: Step S4 includes the following steps: S41. Use the climate contribution rate of each scheme as the response variable; S42. Define four core schemes: SEG, PET, EQ, and MET. Construct a cross-random effects structure and introduce the random intercepts and physically meaningful second-order interaction terms of each scheme to establish the model mean expression under the logit scale. S43. Based on measured watershed data, literature experience, and the physical meaning of the Budyko framework, a relaxed normal prior is set for the model intercept, a half-t distribution weak information prior is set for the variance of the random effects of each scheme, and a gamma prior is set for the precision parameter of the Beta distribution, thus balancing data-driven and prior constraints. S44. The posterior distribution of parameters is obtained by Markov chain Monte Carlo method, and MCMC sampling is carried out by NUTS algorithm. The sampling convergence is verified by Gelman-Rubin diagnosis, effective sample size and trace graph. Finally, the uncertainty contribution of each scheme and interaction term to the climate contribution rate is quantified based on the proportion of random effect variance contribution.

6. The method for quantifying the uncertainty of runoff change attribution according to claim 1, characterized in that: Step S1 is as follows: The control section of the watershed under study was determined, and the daily runoff of the control section for ≥35 consecutive years was obtained from sources such as hydrological yearbooks. and water level For missing or incomplete data, the water level-flow relationship method or other relevant analysis methods are used for interpolation to ensure the integrity of the data sequence. The vector boundary of the study area, the locations of meteorological stations within and near the boundary, and the corresponding diurnal precipitation data were determined. near-surface temperature relative humidity Or dew point / vapor pressure, wind speed at 2m near ground shortwave radiation Or hours of sunshine Station altitude / air pressure; The diurnal runoff series is processed into an adult runoff series, denoted as... In the formula, N is the sequence length; Three methods were used to perform mutation detection: Pettitt mutation test: for any cut point definition Significance approximation level When the specified requirements are met, the mutation location for The largest ; Buishand R test: Constructing a cumulative sum for annual series ,when A mean jump is determined when the value exceeds a given significance level; the jump location is located at... Place; SNHT test: for all candidate cut points Calculate the test statistic ,Pick , Estimated mutation location; Time series are divided into three types based on three mutation detection methods. , Two time periods; PET calculation: PET is first calculated on a daily scale, then aggregated to an annual scale, and then... , The following calculation method can be used to take the average over many years: FAO56 Penman–Monteith: ； In the formula: Net radiation, For soil heat flux, For temperature, The wind speed is 2 m. These are the saturated and actual water vapor pressures, respectively. The slope of the saturated water vapor pressure curve. For thermometer constant, the saturated vapor pressure can be obtained from... Approximate calculation; Priestley-Taylor method: ； Hargreaves method: ； In the formula Radiation from outside the zenith; MET processing method: Thiessen polygon interpolation: Construct Voronoi polygons from the stations and take the area of ​​each polygon falling within the watershed. As a weight: Inverse distance weighted interpolation: at point interpolation value In the formula, Unknown point With known points distance, The power exponent is used to perform area averaging on the grid within the watershed mask after interpolation; Kriging interpolation: In the formula It is a point The estimated value at the location, weight From the Kriging equation and the semivariogram get; EQ: Record the dryness index , evapotranspiration ratio runoff ratio The Budyko equations used include: Fu-Budyko equation: ； Choudhury-Yang equation: ； Turc-Pike equations: ； Based on the mutation test results and different calculation schemes for each parameter, the multi-year average statistics for the two periods were statistically analyzed: , It is generated by the Cartesian product of "phased method × PET method × surface average method × Budyko equation", and each term specifies the SEG, PET, MET, EQ used and their corresponding values. Years; Finally, the calculation scheme was obtained.

7. The method for quantifying the uncertainty of runoff change attribution according to claim 6, characterized in that: Step S2 specifically involves calculating the difference between the multi-year average statistics for the two periods: ； Define the dryness index: Runoff coefficient function ,in These are the parameters of the underlying surface; set up , Define the elasticity coefficient of runoff with respect to precipitation, potential evapotranspiration, and underlying surface. , They are respectively: ； The above formula is The value at this location is: 。 8. The method for quantifying the uncertainty of runoff change attribution according to claim 7, characterized in that: Substituting the partial derivatives of the Fu-Budyko equation, the Choudhury-Yang equation, and the Turc-Pike equation into the above equation, we get: Fu-Budyko equation: Choudhury-Yang equation: The Turc-Pike equations are parameterless equations, therefore... calculate: 。 9. The method for quantifying the uncertainty of runoff change attribution according to claim 7, characterized in that: Step S3 is as follows: Based on the elasticity coefficient obtained in step S2, the absolute values ​​of runoff changes caused by climate change and human activities are further calculated. The calculation process is as follows: Runoff changes caused by precipitation and runoff changes caused by potential evapotranspiration They are respectively: Changes in runoff caused by climate change for: According to the residual method, runoff changes caused by changes in the underlying surface are analyzed. for: The contribution rates of precipitation / evapotranspiration / underlying surface changes to runoff changes They are respectively: ； This yields the contribution rates of each factor under different schemes; when When the value is close to 0, subsequent analyses should prioritize the absolute values ​​of climate contribution and human contribution.

10. The method for quantifying the uncertainty of runoff change attribution according to claim 9, characterized in that: Step S4 is as follows: For detailed calculation, for each combination of schemes Below Record The climate contribution rate obtained in step S103 is taken as the response: ； Keep only " and Same number and The combination of ""; The total number of levels for the four factors; The observation layer uses Beta's "mean-precision" parameterization, with the mean linked to the linear predictor via logit. ； In the formula This is the conditional mean of the combination. For accuracy parameters, It is a linear predictor on the logit scale; It consists of the overall intercept, the random intercepts of the four main effects, and two second-order interactions: ； in, For the overall intercept, The main effect random intercepts of the four types of factors are shown. , For the two interactive random intercepts; To avoid confusion with the intercept, the main effects are zero-sum / centered within the group, and the interactions are centered in both the row and column directions: ； ； When it is necessary to restore the results to the original scale, use ; The intercept is taken from a loose normal prior; the random effects are taken from a hierarchical normal prior with a half-t prior given to their standard deviation; and the observation level precision is taken from a gamma prior. ； ； ； in For each category of a priori criteria; Inference and uncertainty quantification were completed, MCMC sampling was performed using NUTS, and convergence testing was completed. The quantification of "sources of uncertainty" is based on the calculation of the variance contribution ratio of random effects: Let... Let be the standard deviation of the category, then: ； right By summing the median and 95% confidence interval across all posterior samples, we obtain the proportions of the variability in the contribution rates of phased SEG, potential evapotranspiration (PET), MET, EQ, and their interactions to climate change; simultaneously, we can... By extrapolating back to the original scale for each random effect, we provide estimates and intervals of the climate contribution rates at the overall and individual scenario levels, and output the results for each combination. The posterior prediction results.

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