Abstract
Reliability and validity of model prediction play a decisive role in water resource simulation and prediction. Among many prediction models, the combined model (CM) is widely used because it can combine the prediction results of multiple single models and make full use of the information provided by various methods. CM is an effective method to improve the predictive veracity but the weight of single model estimation is the key to the CM. Previous studies take errors as the objective function to calculate the weight, and the uncertainty of the weight of the individual model cannot be considered comprehensively. In order to consider the uncertainty of the weight and to improve universal applicability of the CM, in this paper, the authors intend the Markov chain Monte Carlo based on adaptive Metropolis algorithm (AM-MCMC) to solve the weight of a single model in the CM, and obtain the probability distribution of the weight and the joint probability density of all the weight. Finally, the optimal weight combination is obtained. In order to test the validity of the established model, the author put it into the prediction of monthly groundwater level. The two single models in the CM are time series analysis model (TSAM) and grey model (GM (1,1)), respectively. The case study showed that the uncertainty characteristic of the weight in the CM can be obtained by AM-MCMC. According to the study results, CM has obtained a least average root mean square error (RMSE) of 0.85, a mean absolute percentage error (MAPE) of 8.61, and a coefficient of determination (R2) value of 0.97 for the studied forecast period.