Hydrological Frequency Analysis in Changing Environments Based on Empirical Mode Decomposition and Metropolis-Hastings Sampling Bayesian Models

The consistency of hydrological sequences has been affected by climate change and human activities, resulting in significant uncertainty in the results of hydrological frequency analysis. The Mann-Kendall test and Hurst coefficient method are used to distinguish and test the trend of hydrological series. Based on the Mann-Kendall rank test and sliding $t$-test, the mutation of the hydrological series is identified and tested. The empirical mode decomposition is used to obtain the trend term, and the consistency correction is performed on the nonconsistent hydrological sequences. The Bayesian model is constructed to estimate the parameters and analyze the uncertainty of the results with the Metropolis-Hastings (M-H) sampling. Taking the annual inflow runoff series of Taolinkou Reservoir, China, as an example, the parameter estimation results of the constructed model are compared with the parameter estimation results of the analytical method. The uncertainty of the parameter estimation results before and after the separation of trend components in the hydrological series is compared. The results indicate that the Bayesian estimation method based on the empirical mode decomposition with the M-H sampling can effectively obtain parameter estimates, and the uncertainty of parameter estimation is relatively small. This study proposes a model that can identify and correct the uncertainty of hydrological series. To reduce the uncertainty of parameter estimation, a Bayesian model is introduced, which can be used for inconsistent hydrological frequency analysis. With the modified original sequence, the interval of parameter estimation becomes smaller, and the uncertainty of parameter estimation decreases. The modified series can reflect the characteristics of the decreasing trend of runoff in the basin. The analysis shows that the design value of Bayesian estimation is more stable and can effectively reduce the design values.

Due to the impact of climate change and human activities, the consistency of hydrological series has changed, making it difficult for hydrological series to pass data review. To provide support for the design of hydraulic structures, it is necessary to study hydrological frequency analysis methods for nonconsistent sequences. Using the component analysis method, empirical mode decomposition is used to obtain the trend term, and then consistency correction is performed on the hydrological series. M-H sampling Bayesian parameter estimation are used to estimate the parameters and analyze the uncertainty of the results. The research results show that the Bayesian estimation method based on empirical mode decomposition (EMD) and M-H sampling can better obtain the parameter estimation values, and the uncertainty of the parameter estimation of this method is small.