Design flood estimation method using coupled GAMLSS and BMA models under changing conditions

Abstract

This invention relates to a method for estimating design floods using coupled GAMLSS and BMA models under changing environments, and pertains to the field of hydrological response and its impact assessment technology. The invention first quantitatively identifies changes in meteorological and hydrological elements under future changing environments, and then performs inconsistency frequency analysis based on their distribution characteristics and variation patterns. Then, based on the inconsistency frequency analysis results obtained from different global climate models, it integrates design flood data using the BMA model. This effectively avoids the problem of homogenization in the ensemble simulation results caused by the uncertainty of input data when directly applying the BMA method to runoff sequences, which leads to significant deviations in the design flood analysis results. This invention solves the uncertainty and inconsistency problems faced by current conventional methods.

Description

Technical Field

[0001] This invention relates to the field of hydrological response and its impact assessment technology, specifically to a method for estimating design floods by coupling GAMLSS and BMA models under changing environments. Background Technology

[0002] The global hydrological cycle and water resource distribution have changed due to the impacts of climate change and human activities. According to the assessment results of the Sixth Assessment Report released by the Intergovernmental Panel on Climate Change (IPCC) in 2021, since the mid-20th century, human activities such as greenhouse gas emissions and land-use change have significantly altered the global water cycle, including an overall increase in atmospheric humidity and precipitation intensity. In the future, with the continued increase in greenhouse gas emissions, radiative forcing is also expected 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 its impact on design flood values. Scientifically assessing the impact of future climate change on extreme hydrological events and design flood calculations can provide important reference for the sustainable development and safe utilization of watershed water resources. The assessment involves two steps: first, simulating and analyzing hydrological extreme value sequences under changing conditions; and second, performing hydrological frequency analysis and design flood calculations based on the obtained hydrological extreme value sequences. Two major challenges arise during the assessment process: inconsistency and uncertainty. Traditional hydrological frequency analysis is based on historical hydrological sequences and relies on the consistency and stability of these sequences as fundamental premises. However, in recent years, due to the impact of global climate change and human activities, this fundamental premise has become difficult to meet. Simultaneously, due to the uncertainty of the output results from different global climate models, the simulated runoff and the obtained hydrological extreme value sequences also differ accordingly. The design flood calculation results derived from this also exhibit significant uncertainty.

[0004] To address the aforementioned issues, this invention proposes a non-consistent design flood calculation method that integrates multi-model output data under changing environments. GAMLSS stands for Generalized Additive Models for Location, Scale, and Shape, while BMA stands for Bayesian Model Averaging. By coupling the GAMLSS model and the BMA model, this method simultaneously addresses uncertainty and inconsistency issues, while avoiding the equalization of extreme value sequence simulation results. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a method for estimating design floods by coupling GAMLSS and BMA models under changing environments, comprising the following steps:

[0006] S100. Based on the representative stations 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 of historical periods.

[0007] S200: Select historical large-scale meteorological data output by the global climate model, calibrate the SDSM downscaling model based on the measured meteorological data of the basin and the output historical large-scale meteorological data, and downscale the output future large-scale meteorological factor data to the basin to obtain basin meteorological data, and simultaneously correct the bias of precipitation data.

[0008] S300, a hydrological model with a fixed driving rate is used to simulate runoff over historical periods to obtain a series of annual maximum daily discharges for historical periods. Based on the simulated series of annual maximum daily discharges and the measured series over historical periods, conventional frequency analysis is performed to obtain the results of conventional frequency analysis.

[0009] S400. Input the downscaled watershed meteorological data into the calibrated hydrological model, and select representative stations to simulate runoff during the forecast period.

[0010] S500: Based on the annual maximum value sampling method, the flood series sampling for the forecast period is completed, and the non-uniform design flood frequency analysis is performed by the GAMLSS model based on multi-distribution optimization.

[0011] S600, based on the non-consistent design flood frequency analysis results obtained from different global climate models, is integrated through the BMA model to obtain the design flood values ​​corresponding to different frequencies.

[0012] Furthermore, the watershed characteristic data mentioned in S100 includes digital elevation data, land use data, and soil type data.

[0013] Further, S100 specifically involves collecting characteristic data of the watershed based on the representative stations of the reservoir to be analyzed, loading digital elevation data, automatically generating the watershed river network, adding control stations simultaneously, completing the sub-watershed division and sub-watershed parameter calculation, inputting land use and soil type data in sequence after completing the sub-watershed division, dividing the hydrological response units, and then inputting measured meteorological data to complete the hydrological model construction, and performing parameter sensitivity analysis and model calibration.

[0014] Furthermore, the bias correction described in S200 uses the quantile mapping method to correct the bias in the precipitation data. The specific steps are as follows:

[0015] S210. The empirical frequency method is used to calculate the cumulative distribution probability (CDF) of the simulated sequence and the measured sequence, respectively.

[0016] S220. The simulation sequence is corrected according to the principle that the simulated value and the observed value are equal for the same CDF. The calculation formula is as follows:

[0017] ;

[0018] In the formula, These are the original simulated values. These are the corrected simulated values. Let be the cumulative probability distribution function of the simulated sequence. It is the inverse function of the cumulative probability distribution function of the observed sequence;

[0019] S230. The non-parametric transformation method is used to establish the transfer function F between the corrected simulated sequence and the observed sequence. Its calculation formula is as follows:

[0020] .

[0021] Furthermore, S300 specifically involves simulating based on the optimal model parameters after S100 calibration, inputting downscaled meteorological data into the calibrated hydrological model, and selecting representative stations to simulate runoff during the forecast period.

[0022] Furthermore, S400 specifically involves using the annual maximum value sampling method to complete the flood series sampling for the forecast period, obtaining the annual maximum daily flow series, calculating the annual precipitation based on the Thiessen polygon method, and plotting the annual maximum daily flow-annual precipitation process line for representative stations during the forecast period; using the GAMLSS model for distribution optimization and parameter calibration, and conducting non-consistent design flood frequency analysis for representative stations under future changing environments based on the calibrated GAMLSS model.

[0023] Furthermore, S400 also includes, based on the equal reliability method, using a bisection method iteratively to convert the dynamic design flood value into a fixed value. The calculation formula for the equal reliability method is:

[0024] ;

[0025] In the formula, This refers to the design flood value corresponding to a return period of D years when the project's design service life is T years. To ensure that the flood value does not exceed the design flood value in year t. The probability; that is, to obtain the design flood quantile value representing the future changing environment of the site.

[0026] 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 BMA frequency curve integrated model.

[0027] Furthermore, S600 specifically involves performing BMA integration on the design flood frequency analysis results under future changing environments, based on the calibrated historical frequency curve BMA integrated model and frequency curves based on different global climate model data. During the integration process, design flood values ​​corresponding to different frequencies are obtained, as well as the corresponding confidence intervals.

[0028] Before integrating the BMA model with design floods under future changing environments, the BMA model was first trained and calibrated based on historical simulation and measurement results.

[0029] The specific steps for training and calibrating a BMA model are as follows:

[0030] S610 and BMA models are established based on historical frequency analysis results obtained from S300. The frequency analysis results obtained from global climate model simulations are the model forecast set, and the frequency analysis results obtained from the measured series are the expected output results.

[0031] S620. The BMA model is trained and calibrated using the expectation-maximization algorithm to obtain the weights of each individual model. Model prediction error Parameters. BMA ensemble forecast calculation formula:

[0032] ;

[0033] In the formula: These are the predicted values ​​from the BMA model ensemble. For the Kth model weight, For the predicted value of the Kth model, S630 uses Monte Carlo sampling to obtain the confidence interval (uncertainty interval) of the predicted value. Specifically, an integer k between 0 and K is randomly generated, representing the random selection of the kth model. Based on the probability distribution of the kth model at time t... Randomly generate a traffic , The mean is The variance is Following the normal distribution, repeat the above steps 1000 times to obtain 1000 samples of BMA set prediction at time t. Sort them from smallest to largest, and the part between the 5th and 95th quantiles is the 90% confidence interval.

[0034] The beneficial effects of this invention are:

[0035] 1. This invention first quantitatively identifies the changes in meteorological and hydrological elements under future changing environments, and then conducts non-uniform frequency analysis based on their distribution characteristics and changing patterns. Then, based on the non-uniform frequency analysis results obtained from different global climate models, it integrates design floods through the BMA model, effectively realizing the effective fusion of non-uniform frequency analysis and multi-model ensemble simulation under changing environments.

[0036] 2. This invention, through multi-model ensemble simulation of design floods, effectively avoids the problem of homogenization in ensemble simulation results caused by the uncertainty of input data when directly applying the BMA method to runoff sequences, which leads to significant deviations in design flood analysis results. It establishes a complete method for assessing the impact of future environmental changes on hydrological extreme events and design flood calculation results, while simultaneously solving the uncertainty and inconsistency problems faced by current conventional methods. Furthermore, the data used is readily available, making it universally applicable and operable. Attached Figure Description

[0037] Figure 1 This is a historical runoff process line diagram of a representative station in a specific embodiment of the present invention;

[0038] Figure 2 This is a frequency curve diagram based on BMA integration from a representative station during the historical period of a specific embodiment of the present invention;

[0039] Figure 3 This is a line graph of the annual maximum daily flow rate versus annual precipitation under future changing conditions at a representative station according to a specific embodiment of the present invention;

[0040] Figure 4 This is a frequency curve diagram representing a station under future changing conditions, based on a specific embodiment of the present invention.

[0041] Figure 5 This is a frequency curve diagram based on BMA integration, representing a specific embodiment of the present invention, under future changing conditions. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention.

[0043] A method for estimating design floods using coupled GAMLSS and BMA models under changing environments includes the following steps:

[0044] S100. Based on the representative stations of the reservoir to be analyzed, collect the characteristic data of the watershed, establish a watershed hydrological model, and calibrate the hydrological model based on historical measured runoff data. The watershed characteristic data includes digital elevation data, land use data, and soil type data. Load the DEM data into ArcGIS to automatically generate the watershed river network, then add control stations simultaneously 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 hydrological model construction. This embodiment uses the SWAT-CUP (SWAT Calibration and Uncertainty Programs) program for parameter sensitivity analysis and model calibration. Simulation is performed based on the optimal model parameters after calibration to obtain... Figure 1 This is a historical runoff flow timeline.

[0045] S200. Select a global climate model. Calibrate the SDSM downscaling model based on measured meteorological data of the watershed and historical large-scale meteorological data output by the global climate model. Downscale the future large-scale meteorological factor data output by the model to the watershed to obtain watershed meteorological data. Simultaneously, perform bias correction on the precipitation data. Based on measured meteorological data and historical large-scale meteorological data output by global climate models (in this example, four global climate models are selected: CanESM, MPI-ESM, GFDL, and NorESM), calibrate the SDSM downscaling model. Then, downscale the large-scale meteorological data output by the global climate model to the study area to obtain watershed meteorological data. Simultaneously, use the quantile mapping method to correct bias in the precipitation data. The specific steps of the quantile mapping method are as follows:

[0046] S210 uses the empirical frequency method to calculate the cumulative distribution probability (CDF) of the simulated sequence and the measured sequence, respectively.

[0047] S220 corrects the simulation sequence based on the principle that the simulated value and the observed value corresponding to the same CDF are equal. The calculation formula is as follows:

[0048] ;

[0049] In the formula, These are the original simulated values. These are the corrected simulated values. Let be the cumulative probability distribution function of the simulated sequence. It is the inverse function of the cumulative probability distribution function of the observed sequence.

[0050] S230 uses a non-parametric transformation method to establish the transfer function F between the corrected simulated sequence and the observed sequence, and its calculation formula is as follows:

[0051] .

[0052] Historical runoff simulations were performed using the S300 and the hydrological model with calibrated driving force to obtain a series of annual maximum daily flow rates for historical periods. Based on the simulated annual maximum daily flow rate series and the measured series for historical periods, conventional frequency analysis was performed to obtain the conventional frequency analysis results. Simulations were then performed using the optimal model parameters after S100 calibration, and downscaled meteorological data were input into the calibrated SWAT model to simulate daily runoff at each station.

[0053] First, based on the specific method described in S200, historical large-scale meteorological data from different selected global climate models are downscaled. Then, a hydrological model is driven to simulate runoff, obtaining a historical daily runoff series. The annual maximum daily discharge series for historical periods is then obtained using the annual maximum sampling method. Based on the simulated annual maximum daily discharge series and the historical measured series, conventional frequency analysis is performed using the optimized fitting method based on the Pearson-III distribution, yielding the conventional frequency analysis results.

[0054] Figure 2 This is a historical frequency curve based on BMA ensemble. Based on conventional frequency analysis results, the BMA method was used to integrate frequency analysis results from different global climate models, resulting in a BMA-integrated frequency curve. For ease of comparison... Figure 2 The study also presents frequency curves based on simulation series and measured series from different global climate models.

[0055] S400: Input the downscaled watershed meteorological data obtained in S200 into the calibrated hydrological model. The precipitation data is the data after bias correction using the quantile mapping method. Representative stations are selected to simulate runoff during the forecast period.

[0056] S500: Based on the annual maximum value sampling method, the flood series sampling for the forecast period is completed to obtain the annual maximum daily flow series for the forecast period. The non-uniform frequency analysis is then performed using the GAMLSS model based on multi-distribution optimization.

[0057] Figure 3 This paper presents a flood (annual maximum daily flow)-annual precipitation process curve for a future changing environment. The annual maximum daily flow sequence is obtained using the annual maximum sampling method, and the annual precipitation is calculated based on the Thiessen polygon method. The process curve of annual maximum daily flow-annual precipitation for representative stations during the forecast period is then plotted.

[0058] Figure 4To generate frequency curves under future changing environments, Pearson-III (P-III), Gamma (GA), Weibull (WEI), and Gumbel (GU) distributions 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 conducted on representative sites under future changing environments. Using the equal reliability method, a bisection iterative approach was employed to convert dynamic design flood values ​​into fixed values. The formula for calculating the equal reliability method is:

[0059] ;

[0060] In the formula, This refers to the design flood value corresponding to a return period of D years when the project's design service life is T years. To ensure that the flood value does not exceed the design flood value in year t. The probability of this. After performing the above process, the design flood quantile value, representing the future changing environment of the site, can be obtained, i.e., the probability of this. Figure 4 The diagram shows frequency curves based on data from different global climate models under future changing environments.

[0061] S600, based on the non-consistent design flood frequency analysis results obtained from different global climate models, is integrated through the BMA model to obtain the design flood values ​​corresponding to different frequencies, as well as the corresponding confidence intervals.

[0062] Figure 5 This is a frequency curve diagram based on BMA ensemble for future changing environments. Before using the BMA model to integrate design floods under future changing environments, the BMA model has been trained and calibrated based on historical simulation results and measured results.

[0063] The specific steps for training and calibrating a BMA model are as follows:

[0064] S610 and BMA models are established based on historical frequency analysis results obtained from S300. The frequency analysis results obtained from global climate model simulations are the model forecast set, and the frequency analysis results obtained from the measured series are the expected output results.

[0065] S620. The BMA model is trained and calibrated using the expectation-maximization algorithm to obtain the weights of each individual model. Model prediction error Parameters. BMA ensemble forecast calculation formula:

[0066] ;

[0067] In the formula: These are the predicted values ​​from the BMA model ensemble. For the Kth model weight, For the predicted value of the Kth model, S630 uses Monte Carlo sampling to obtain the confidence interval (uncertainty interval) of the predicted value. Specifically, an integer k between 0 and K is randomly generated, representing the random selection of the kth model. Based on the probability distribution of the kth model at time t... Randomly generate a traffic , The mean is The variance is Following the normal distribution, repeat the above steps 1000 times to obtain 1000 samples of BMA set prediction at time t. Sort them from smallest to largest, and the part between the 5th and 95th quantiles is the 90% confidence interval.

[0068] Based on the calibrated historical frequency curve BMA ensemble model and the frequency curves based on different global climate model data under future changing environments, the design flood frequency analysis results under future changing environments are integrated by BMA. During the integration process, the design flood values ​​corresponding to different frequencies are obtained, as well as the corresponding confidence intervals.

[0069] Although the present invention has been described in detail above with general descriptions and specific embodiments, the scope of protection of the present invention is not limited thereto. Modifications or improvements can be made to the present invention, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for design flood estimation by coupling GAMLSS and BMA models under varying environments, characterized in that, The method comprises the following steps: S100, according to the representative station of the reservoir to be analyzed, collecting the basin characteristic data, establishing a basin hydrological model, and calibrating the hydrological model according to the historical period measured runoff data; S200, selecting a global climate model, calibrating the SDSM downscaling model according to the measured meteorological data of the basin and the historical period large-scale meteorological data output by the global climate model, and downsizing the future large-scale meteorological factor data output by the SDSM downscaling model to the basin to obtain the basin meteorological data, and simultaneously correcting the deviation of the precipitation data; S300, driving the calibrated hydrological model to simulate the historical period runoff to obtain the historical period annual maximum daily flow series, performing conventional frequency analysis on the simulated annual maximum daily flow series and the measured series in the historical period to obtain the conventional frequency analysis result; S400, inputting the downsized basin meteorological data into the calibrated hydrological model, and selecting a representative station to simulate the prediction period runoff; S500, completing the prediction period flood series sampling based on the annual maximum value sampling method, and performing non-consistency design flood frequency analysis based on multiple distributions through the GAMLSS model; S500 is specifically based on the calibrated historical period frequency curve BMA integrated model and the frequency curve based on different global climate model data under the future changing environment, BMA integration is performed on the design flood frequency analysis result under the future changing environment, the design flood value corresponding to different frequencies is obtained in the integration process, and the corresponding confidence interval is also obtained; S600, based on the non-consistency design flood frequency analysis result obtained by different global climate models, the BMA model is integrated to obtain the design flood value corresponding to different frequencies; Based on the conventional frequency analysis result of S300, the BMA method is used to integrate the conventional frequency analysis result based on the global climate model to obtain the historical period BMA frequency curve integrated model; Before using the BMA model to integrate the design flood under the future changing environment, the BMA model is trained and calibrated based on the simulation result and the measured result in the historical period, and the specific steps of training and calibrating the BMA model are as follows: S610, the BMA model is established based on the historical period frequency analysis result obtained in S300, wherein the frequency analysis result simulated based on the global climate model is a model prediction set, and the frequency analysis result obtained based on the measured series is an expected output result; S620, training and rating the BMA model by using the expectation maximization algorithm to obtain the weight of each single model , model prediction error parameters; The BMA set prediction calculation formula is: ； wherein: is the forecast value for the BMA model ensemble, is the Kth model weight, is the forecast value for the Kth model; S630 adopts Monte Carlo sampling method to obtain the confidence interval of the forecast value, specifically: randomly generate an integer k between 0~K, which represents randomly selecting the kth model, and according to the probability distribution of the kth model at time t Randomly generate a flow , representing a normal distribution with a mean of and a variance of Repeat the above steps 1000 times to obtain 1000 samples of the BMA set forecast at time t, sort them from small to large, and the part between the 5% and 95% quantiles is the 90% confidence interval.

2. The method for design flood estimation by coupling GAMLSS and BMA model under varying environment according to claim 1, wherein, The basin characteristic data of S100 includes digital elevation data, land use and soil type data.

3. The method of claim 1, wherein the method is characterized in that, S100 is specifically that, according to the representative station of the reservoir to be analyzed, collecting the basin characteristic data, loading the digital elevation data, automatically generating the basin river network, then simultaneously adding the control station, completing the sub-basin division and sub-basin parameter calculation, after completing the sub-basin division, inputting the land use and soil type data in sequence, performing hydrological response unit division, and then inputting the measured meteorological data, that is, completing the hydrological model construction, performing parameter sensitivity analysis and model calibration.

4. The method of claim 1, wherein the method is characterized in that, The deviation correction of S200 adopts the quantile mapping method to correct the deviation of the precipitation data, and the specific steps are as follows: S210, the experience frequency method is respectively calculated the cumulative distribution probability CDF of analog sequence and measured sequence; S220, according to the principle of equal corresponding simulation value and observation value of the same CDF, the analog sequence is corrected, and the calculation formula is: ； wherein is the original analog value, is the corrected analog value, is the cumulative probability distribution function of the analog sequence, is the inverse function of the cumulative probability distribution function of the observation sequence; S230, the nonparametric conversion method is used to establish the transfer function F of the corrected simulation sequence and the observation sequence, and the calculation formula is: 。 5. The method of claim 1, wherein the method is characterized in that, S300 is specifically, based on the optimal model parameter calibrated by S100, the simulated meteorological data is input into the calibrated hydrological model, and the representative station is selected to simulate the runoff in the prediction period.

6. The method of claim 1, wherein the method is characterized in that, S400 is specifically, the annual maximum value sampling method is used to complete the sampling of the prediction period flood series, the annual precipitation is calculated based on the Thiessen polygon method, and the annual maximum daily runoff-annual precipitation process line of the representative station in the prediction period is drawn; the GAMLSS model is used for distribution optimization and parameter calibration, and the non-consistent design flood frequency analysis of the representative station in the future changing environment is carried out based on the calibrated GAMLSS model.

7. The method of claim 6, wherein the method is characterized in that, S400 also includes, based on the equal reliability method, the dynamic design flood value is converted into a fixed value by using the dichotomy iteration, and the calculation formula of the equal reliability method is: ； In the formula, is the design flood value corresponding to the D-year return period when the project design service life is T years, is the probability of not exceeding the design flood value in the tth year; and the design flood quantile value under the future changing environment is obtained, that is, the frequency curve based on different global climate model data under the future changing environment is obtained.

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