The analysis of the law of drought propagation under climate change is of great significance for drought early warning and reducing social and economic losses. In spite of large spatiotemporal variability in drought propagation, the propagation probability and threshold from meteorological to hydrological droughts were not examined at seasonal and regional scales over the Luanhe River basin. To estimate the propagation probability and threshold of the Luanhe River basin, the meteorological and hydrological variables were obtained at a grid resolution of 0.25◦ Lat × 0.25◦ Lon in this study. Based on the GAMLSS framework, the stationary model and the non-stationary model were constructed to capture the characteristics of seasonal droughts without considering climate change and considering climate change. Then the Copula model was constructed, and the drought propagation probability and the threshold under stationary and non-stationary conditions were calculated. The results show that, under the combined influence of AMO, temperature, relative humidity and wind speed, the propagation probabilities became larger and the propagation thresholds became higher, especially in spring and winter in the upstream and midstream regions. The increase in temperature and the decrease in relative humidity may be the key factors contributing to the occurrence of hydrological drought in the basin.

A time series analysis is proposed for an adaptive design framework in nonstationary conditions. In this study, a dynamic Bayesian autoregressive moving average model (t-ARMA) is developed for modelling a standardized runoff index (SRI) time series. The t-ARMA model takes into account the possible change points in the SRI series, and the structure of the model changes with time. Bayesian theory is carried out to estimate the t-ARMA model parameters and locations of change points using a strategy of Markov chain Monte Carlo (MCMC) methods. The results demonstrate that using the Bayesian method to estimate the parameters of the ARMA and t-ARMA models could capture the SRI series characteristics, and the performances of the t-ARMA model are compared with those of the traditional autoregressive moving average (ARMA) model, showing that the t-ARMA model capable of taking the change point of the time series into account is more robust than the traditional ARMA model.