Design flood deduction method for coupling GAMLSS and BMA models in changing environment

Abstract

The invention relates to a design flood deduction method for coupling a GAMLSS model and a BMA model in a change environment, and relates to the technical field of hydrological response and influence evaluation thereof, and the method comprises the steps: firstly, carrying out the quantitative recognition of the change condition of meteorological and hydrological elements in a future change environment, and carrying out the non-consistency frequency analysis according to the distribution characteristics and change rules of the change condition; and then design flood integration is carried out through a BMA model based on non-consistent frequency analysis results obtained by different global climate modes, so that the situation that a BMA method is directly applied to a runoff sequence, and a set simulation result is homogenized due to uncertainty of input data, so that a design flood analysis result has relatively large deviation is effectively avoided; and the problems of uncertainty and inconsistency faced by the current conventional method are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological response and impact assessment, and in particular to a design flood derivation method for coupling a GAMLSS and BMA model under a changing environment. Background Art

[0002] The global hydrological cycle and water resource distribution have shifted due to climate change and human activities. According to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, released in 2021, human activities, such as greenhouse gas emissions and land use change, have significantly altered the global water cycle since the mid-20th century, including an overall increase in atmospheric humidity and precipitation intensity. In the future, as greenhouse gas emissions continue to rise, radiative forcing is projected to increase, leading to significant changes in temperature and precipitation, including changes in extreme precipitation, further exacerbating the impact on the water cycle.

[0003] Therefore, the impact of future climate change on extreme hydrological events is inevitable, as is the impact on design flood values. Scientifically assessing the impact of future climate change on hydrological extreme events and design flood calculations can provide important insights for the sustainable development and safe utilization of water resources in a river basin. This assessment involves two steps: the first involves simulating and analyzing hydrological extreme value sequences under a transformed environment; the second involves performing hydrological frequency analysis and design flood calculations based on the resulting hydrological extreme value sequences. This assessment faces two major challenges: inconsistency and uncertainty. Traditional hydrological frequency analysis and calculations are based on historical hydrological sequences and assume consistency and stability. However, due to the impact of global climate change and human activities in recent years, this assumption has become difficult to meet. Furthermore, due to the uncertainty in the outputs of different global climate models, the simulated runoff and the resulting hydrological extreme value sequences also differ accordingly. The resulting design flood calculations also exhibit significant uncertainty.

[0004] To address the above issues, the present invention proposes a method for calculating inconsistent design floods under changing environments by fusing multi-modal output data. GAMLSS stands for Generalized Additive Models for Location, Scale, and Shape, and BMA stands for Bayesian Model Averaging. By coupling the GAMLSS model with the BMA model, the uncertainty and inconsistency problems are simultaneously addressed, while avoiding the averaging of extreme value sequence simulation results. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the present invention aims to provide a method for deducing design floods by coupling GAMLSS and BMA models under a changing environment, comprising the following steps: S100, based on representative sites of the reservoir to be analyzed, collect characteristic data of the watershed, establish a watershed hydrological model, and calibrate the hydrological model based on measured runoff data from historical periods; S200, selecting historical large-scale meteorological data output by a global climate model, calibrating the SDSM downscaling model based on the measured meteorological data of the watershed and the output historical large-scale meteorological data, downscaling the output future large-scale meteorological factor data to the watershed, obtaining the watershed meteorological data, and simultaneously performing bias correction on the precipitation data; S300, using the hydrological model with the determined driving rate to simulate runoff in the historical period, obtaining the annual maximum daily flow series in the historical period, and performing conventional frequency analysis based on the simulated annual maximum daily flow series and the measured series in the historical period to obtain conventional frequency analysis results; S400, inputting the downscaled basin meteorological data into the hydrological model with a predetermined rate, and selecting representative stations to simulate the runoff during the forecast period; S500: Complete flood series sampling during the forecast period based on the annual maximum sampling method, and perform non-uniform design flood frequency analysis based on multi-distribution optimization using the GAMLSS model; S600: Based on the inconsistent design flood frequency analysis results obtained from different global climate models, they are integrated through the BMA model to obtain the design flood values ​​corresponding to different frequencies.

[0006] Furthermore, the watershed characteristic data in S100 includes digital elevation data, land use and soil type data.

[0007] Furthermore, the S100 specifically collects characteristic data of the watershed according to the representative site of the reservoir to be analyzed, loads digital elevation data, automatically generates the watershed river network, and then adds control sites at the same time to complete the sub-watershed division and sub-watershed parameter calculation. After completing the sub-watershed division, the land use and soil type data are input in sequence to divide the hydrological response units, and then the measured meteorological data are input to complete the construction of the hydrological model, and perform parameter sensitivity analysis and model calibration.

[0008] Furthermore, the deviation correction in S200 uses the quantile mapping method to correct the deviation of precipitation data, and the specific steps are as follows: S210, using the empirical frequency method to calculate the cumulative distribution probability CDF of the simulated sequence and the measured sequence respectively; S220. Correct the simulation sequence based on the principle that the simulation value and the observed value corresponding to the same CDF are equal. The calculation formula is: ; Where, is the original simulation value, is the simulated value after correction, is the cumulative probability distribution function of the simulated sequence, is the inverse function of the cumulative probability distribution function of the observation sequence; S230, using the non-parametric conversion method is to establish the transfer function F between the corrected simulation sequence and the observation sequence, and its calculation formula is: .

[0009] Furthermore, S300 specifically performs simulation based on the optimal model parameters after calibration in S100, inputs the downscaled meteorological data into the calibrated hydrological model, and selects representative sites to perform runoff simulation during the forecast period.

[0010] Furthermore, S400 specifically adopts the annual maximum value sampling method to complete the flood series sampling in the forecast period, obtains the annual maximum daily flow series, calculates the annual precipitation based on the Thiessen polygon method, and draws the annual maximum daily flow-annual precipitation process line of the representative station in the forecast period; uses the GAMLSS model for distribution optimization and parameter calibration, and performs the inconsistent design flood frequency analysis under the future changing environment of the representative station based on the calibrated GAMLSS model.

[0011] Furthermore, S400 also includes converting the dynamic design flood value into a fixed value using a bisection iteration method based on an equal reliability method. The calculation formula of the equal reliability method is: ; Where, is the design flood value corresponding to the return period of D years when the design service life of the project is T years, The flood value exceeding the design value does not occur in the tth year probability; that is, the design flood quantile value representing the future change environment of the site is obtained.

[0012] Furthermore, based on the S300 conventional frequency analysis results, the BMA method was used to integrate the conventional frequency analysis results based on the global climate model to obtain the historical period BMA frequency curve integration model.

[0013] Furthermore, S600 specifically performs BMA integration on the design flood frequency analysis results under the future changing environment based on the calibrated BMA integration model of the historical frequency curve and the frequency curve based on different global climate model data under the future changing environment. During the integration process, the design flood values ​​corresponding to different frequencies are obtained, and the corresponding confidence intervals are also obtained.

[0014] Before using the BMA model to integrate the design flood under future changing environment, the BMA model has been trained and calibrated based on the historical simulation results and measured results.

[0015] The specific steps for training and calibrating the BMA model are: S610 , establishing a BMA model based on the historical frequency analysis results obtained in S300 , wherein the frequency analysis results obtained based on the global climate model simulation are the model forecast set, and the frequency analysis results obtained based on the measured series are the expected output results.

[0016] S620, use the expectation maximization algorithm to train and calibrate the BMA model to obtain the weight of each individual model , model prediction error Parameters such as BMA ensemble forecast calculation formula: ; Where: is the BMA model ensemble forecast value, is the K-th model weight, For the prediction value of the Kth model, S630 uses the Monte Carlo sampling method to obtain the confidence interval (uncertainty interval) of the prediction value. Specifically, it randomly generates an integer k between 0 and K, indicating that the kth model is randomly selected. Based on the probability distribution of the kth model at time t, Randomly generate a flow , Indicates the mean , the variance is Repeat the above steps 1000 times to obtain 1000 samples of BMA ensemble forecast at time t, sort them from small to large, and the part between the 5% and 95% quantiles is the 90% confidence interval.

[0017] The beneficial effects of the present invention are: 1. The present invention first quantitatively identifies the changes in meteorological and hydrological elements under a changing environment, and then performs inconsistent frequency analysis based on their distribution characteristics and changing patterns. Then, based on the inconsistent frequency analysis results obtained from different global climate models, the design flood integration is performed through the BMA model, effectively realizing the effective integration of inconsistent frequency analysis under a changing environment and multi-model ensemble simulation.

[0018] 2. By performing multi-model ensemble simulation of design floods, this method effectively avoids the problem of directly applying the BMA method to runoff series, which can lead to homogenization of ensemble simulation results due to uncertainty in input data, and thus to significant deviations in design flood analysis results. This method forms a comprehensive approach for assessing the impact of future environmental changes on hydrological extreme events and design flood calculations, while simultaneously addressing the uncertainty and inconsistency issues faced by current conventional methods. The data used is readily available, making it universally applicable and operational. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a runoff process line diagram of a representative station during the historical period according to a specific embodiment of the present invention; Figure 2 It is a frequency curve diagram based on BMA integration for a representative station historical period according to a specific embodiment of the present invention; Figure 3 It is a process line diagram of annual maximum daily flow-annual precipitation under the future changing environment of a representative station in a specific embodiment of the present invention; Figure 4 It is a frequency curve diagram of a representative station in a future changing environment according to a specific embodiment of the present invention; Figure 5 This is a frequency curve diagram based on BMA integration in a future changing environment of a representative station in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The exemplary embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0021] A design flood derivation method for coupling GAMLSS and BMA models under changing environment includes the following steps: S100. According to the representative sites of the reservoir to be analyzed, collect the characteristic data of the watershed, establish the watershed hydrological model, and calibrate the hydrological model based on the measured runoff data in the historical period; the watershed characteristic data include digital elevation data, land use and soil type data. Load DEM data in ArcGIS, automatically generate the river network of the watershed, and then add control sites at the same time to complete the sub-watershed division and sub-watershed parameter calculation. After completing the sub-watershed division, input the land use and soil type data in sequence to divide the hydrological response units, and then input the measured meteorological data to complete the construction of the hydrological model. This embodiment uses the SWAT-CUP (SWAT Calibration and Uncertainty Programs) program to perform parameter sensitivity analysis and model calibration, and simulates based on the optimal model parameters after the calibration is completed to obtain Figure 1 Runoff process line diagram for this historical period.

[0022] S200. Select a global climate model and calibrate the SDSM downscaling model based on the measured meteorological data of the watershed and the historical large-scale meteorological data output by the global climate model. Downscale the future large-scale meteorological factor data output by the global climate model to the watershed to obtain the watershed meteorological data, and simultaneously perform bias correction on the precipitation data. The SDSM downscaling model is calibrated based on the measured meteorological data and the historical large-scale meteorological data output by the global climate model (this example selects four global climate models: CanESM, MPI-ESM, GFDL, and NorESM). Then, downscale the large-scale meteorological data output by the global climate model to the study area to obtain the watershed meteorological data. The precipitation data is then bias corrected using the quantile mapping method. The specific steps of the quantile mapping method are as follows:

[0023] S210 uses the empirical frequency method to calculate the cumulative distribution probability CDF of the simulated sequence and the measured sequence respectively.

[0024] S220 corrects the simulation sequence according to the principle that the simulation value corresponding to the same CDF is equal to the observed value. The calculation formula is: ; Where, is the original simulation value, is the simulated value after correction, is the cumulative probability distribution function of the simulated sequence, is the inverse function of the cumulative probability distribution function of the observation sequence.

[0025] S230 uses a non-parametric conversion method to establish the transfer function F between the corrected simulation sequence and the observation sequence. The calculation formula is: .

[0026] S300 and the calibrated hydrological model are used to simulate the runoff in the historical period to obtain the annual maximum daily flow series in the historical period. Conventional frequency analysis is performed based on the simulated annual maximum daily flow series and the measured series in the historical period to obtain the conventional frequency analysis results. Simulation is performed based on the optimal model parameters after S100 calibration, and the downscaled meteorological data are input into the calibrated SWAT model to simulate the daily runoff at each station.

[0027] First, based on the specific method described in S200, downscaling is performed on historical large-scale meteorological data output by various selected global climate models. A hydrological model is then driven to simulate runoff, generating a historical daily runoff series. The annual maximum daily flow series for the historical period is then obtained using the annual maximum sampling method. Based on the simulated annual maximum daily flow series and the historical measured series, conventional frequency analysis is performed using the optimized line fit method based on the Pearson-III distribution to obtain conventional frequency analysis results.

[0028] Figure 2 This is a frequency curve diagram based on BMA integration for the historical period. Based on the conventional frequency analysis results, the BMA method is used to integrate the frequency analysis results based on different global climate models to obtain a frequency curve diagram based on BMA integration. For easy comparison, Figure 2 The frequency curves of the simulated series based on different global climate models and the measured series are shown together.

[0029] S400, inputting the basin meteorological data obtained by downscaling in S200 into the hydrological model with a predetermined rate, wherein the precipitation data is the data after bias correction using the quantile mapping method, and selecting representative stations to simulate the runoff during the forecast period; S500. Complete the flood series sampling in the forecast period based on the annual maximum sampling method to obtain the annual maximum daily flow series in the forecast period, and perform inconsistent frequency analysis based on multi-distribution optimization through the GAMLSS model.

[0030] Figure 3 This is a graph showing the flood (maximum daily discharge) versus annual precipitation process under a changing future environment. The maximum daily discharge sequence is obtained using the annual maximum sampling method. Annual precipitation is calculated using the Thiessen polygon method. The maximum daily discharge versus annual precipitation process is then plotted for representative stations during the forecast period.

[0031] Figure 4 To generate frequency curves for future variable environments, the Pearson-III distribution (P-III), gamma distribution (GA), Weibull distribution (WEI), and Gumbel distribution (GU) were selected as candidate distributions. The GAMLSS model was used for distribution optimization and parameter calibration. Based on the calibrated GAMLSS model, a non-uniform design flood frequency analysis was performed for representative sites under future variable environments. Based on the equal reliability method, a bisection iterative method was used to convert dynamic design flood values ​​into fixed values. The calculation formula for the equal reliability method is: ; Where, is the design flood value corresponding to the return period of D years when the design service life of the project is T years, The flood value exceeding the design value does not occur in the tth year After executing the above process, the design flood quantile value representing the future change environment of the site can be obtained, that is, Figure 4 Frequency curves based on different global climate model data under future change environments are shown.

[0032] S600: Based on the inconsistent design flood frequency analysis results obtained from different global climate models, they are integrated through the BMA model to obtain the design flood values ​​corresponding to different frequencies and the corresponding confidence intervals.

[0033] Figure 5 Figure 2 shows the frequency curve based on BMA integration under a future changing environment. Before using the BMA model to integrate the design flood under a future changing environment, the BMA model has been trained and calibrated based on historical simulation results and measured results.

[0034] The specific steps for training and calibrating the BMA model are: S610 , establishing a BMA model based on the historical frequency analysis results obtained in S300 , wherein the frequency analysis results obtained based on the global climate model simulation are the model forecast set, and the frequency analysis results obtained based on the measured series are the expected output results.

[0035] S620, use the expectation maximization algorithm to train and calibrate the BMA model to obtain the weight of each individual model , model prediction error Parameters such as BMA ensemble forecast calculation formula: ; Where: is the BMA model ensemble forecast value, is the K-th model weight, For the prediction value of the Kth model, S630 uses the Monte Carlo sampling method to obtain the confidence interval (uncertainty interval) of the prediction value. Specifically, it randomly generates an integer k between 0 and K, indicating that the kth model is randomly selected. Based on the probability distribution of the kth model at time t, Randomly generate a flow , Indicates the mean , the variance is Repeat the above steps 1000 times to obtain 1000 samples of BMA ensemble forecast at time t, sort them from small to large, and the part between the 5% and 95% quantiles is the 90% confidence interval.

[0036] Based on the calibrated BMA integration model of historical frequency curves and the frequency curves based on different global climate model data under future changing environments, BMA integration is performed on the design flood frequency analysis results under future changing environments. During the integration process, the design flood values ​​corresponding to different frequencies are obtained, and the corresponding confidence intervals are also obtained.

[0037] Although the present invention has been described in detail above using general descriptions and specific embodiments, the scope of protection of the present invention is not limited thereto. It will be apparent to those skilled in the art that modifications or improvements may be made based on the present invention. Therefore, such modifications or improvements that do not depart from the spirit of the present invention are intended to fall within the scope of protection claimed by the present invention.

Claims

1. A design flood derivation method for coupling GAMLSS and BMA models under changing environments, characterized by: The following steps are involved: S100, based on representative sites of the reservoir to be analyzed, collect characteristic data of the watershed, establish a watershed hydrological model, and calibrate the hydrological model based on measured runoff data from historical periods; S200, selecting a global climate model, calibrating the SDSM downscaling model based on the measured meteorological data of the watershed and the historical large-scale meteorological data output by the global climate model, downscaling the outputted future large-scale meteorological factor data to the watershed, obtaining the watershed meteorological data, and simultaneously performing bias correction on the precipitation data; S300, using the hydrological model with the determined driving rate to simulate runoff in the historical period, obtaining the annual maximum daily flow series in the historical period, and performing conventional frequency analysis based on the simulated annual maximum daily flow series and the measured series in the historical period to obtain conventional frequency analysis results; S400, inputting the downscaled basin meteorological data into the hydrological model with a predetermined rate, and selecting representative stations to simulate the runoff during the forecast period; S500: Complete flood series sampling during the forecast period based on the annual maximum sampling method, and perform non-uniform design flood frequency analysis based on multi-distribution optimization using the GAMLSS model; S600: Based on the inconsistent design flood frequency analysis results obtained from different global climate models, they are integrated through the BMA model to obtain the design flood values ​​corresponding to different frequencies.

2. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 1 is characterized in that: The watershed characteristic data in S100 include digital elevation data, land use and soil type data.

3. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 1 is characterized in that: Specifically, the S100 collects characteristic data of the watershed according to the representative site of the reservoir to be analyzed, loads digital elevation data, automatically generates the river network of the watershed, and then adds control sites at the same time to complete the sub-watershed division and sub-watershed parameter calculation. After completing the sub-watershed division, the land use and soil type data are input in sequence to divide the hydrological response units, and then the measured meteorological data is input to complete the construction of the hydrological model and perform parameter sensitivity analysis and model calibration.

4. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 1 is characterized in that: The deviation correction in S200 uses the quantile mapping method to correct the deviation of precipitation data. The specific steps are as follows: S210, using the empirical frequency method to calculate the cumulative distribution probability CDF of the simulated sequence and the measured sequence respectively; S220. Correct the simulation sequence based on the principle that the simulation value and the observed value corresponding to the same CDF are equal. The calculation formula is: ； Where, is the original simulation value, is the simulated value after correction, is the cumulative probability distribution function of the simulated sequence, is the inverse function of the cumulative probability distribution function of the observation sequence; S230, using the non-parametric conversion method is to establish the transfer function F between the corrected simulation sequence and the observation sequence, and its calculation formula is: 。 5. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 1 is characterized in that: Specifically, S300 performs simulation based on the optimal model parameters after calibration in S100, inputs the downscaled meteorological data into the calibrated hydrological model, and selects representative sites to simulate runoff during the forecast period.

6. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 1 is characterized in that: Specifically, S400 uses the annual maximum sampling method to complete the flood series sampling in the forecast period, calculates the annual precipitation based on the Thiessen polygon method, and draws the annual maximum daily flow-annual precipitation process line of the representative station in the forecast period; uses the GAMLSS model for distribution optimization and parameter calibration, and conducts the non-consistent design flood frequency analysis of the forecast period under the future change environment of the representative station based on the calibrated GAMLSS model.

7. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 6 is characterized in that: S400 also includes, based on the equal reliability method, using a bisection method to iteratively convert the dynamic design flood value into a fixed value. The calculation formula of the equal reliability method is: ； Where, is the design flood value corresponding to the return period of D years when the design service life of the project is T years, The flood value exceeding the design value does not occur in the tth year The probability of the design flood under the future change environment of the station is obtained, that is, the frequency curve based on different global climate model data under the future change environment is obtained.

8. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 1 is characterized in that: Based on the S300 conventional frequency analysis results, the BMA method is used to integrate the conventional frequency analysis results based on the global climate model to obtain the historical period BMA frequency curve integration model.

9. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 8, characterized in that: Specifically, S500 performs BMA integration on the design flood frequency analysis results under future changing environments based on the calibrated BMA integration model of historical frequency curves and frequency curves based on different global climate model data under future changing environments. During the integration process, the design flood values ​​corresponding to different frequencies are obtained, as well as the corresponding confidence intervals.

10. The design flood derivation method of coupling GAMLSS and BMA models under changing environment according to claim 8, characterized in that: Before using the BMA model to integrate design floods under future changing environments, the BMA model is first trained and calibrated based on historical simulation results and measured results. The specific steps for training and calibrating the BMA model are as follows: S610, establishing a BMA model based on the historical frequency analysis results obtained in S300, wherein the frequency analysis results obtained based on the global climate model simulation are the model forecast set, and the frequency analysis results obtained based on the measured series are the expected output results; S620, use the expectation maximization algorithm to train and calibrate the BMA model to obtain the weight of each individual model , model prediction error parameter; The BMA ensemble forecast calculation formula is: ； Where: is the BMA model ensemble forecast value, is the K-th model weight, is the predicted value of the K-th model; S630 uses Monte Carlo sampling to obtain the confidence interval of the forecast value. Specifically, it randomly generates an integer k between 0 and K, which represents the random selection of the kth model, and then calculates the confidence interval of the forecast value based on the probability distribution of the kth model at time t. Randomly generate a flow , Indicates the mean , the variance is Repeat the above steps 1000 times to obtain 1000 samples of BMA ensemble forecast at time t, sort them from small to large, and the part between the 5% and 95% quantiles is the 90% confidence interval.

Images