Bayesian dynamic modelling for nonstationary hydroclimatic time series forecasting along with uncertainty quantification

Abstract

Forecasting of hydrologic time series, with the quantification of uncertainty, is an important tool for adaptive water resources management. Nonstationarity, caused by climate forcing and other factors, such as change in physical properties of catchment (urbanization, vegetation change, etc.), makes the forecasting task too difficult to model by traditional Box–Jenkins approaches. In this paper, the potential of the Bayesian dynamic modelling approach is investigated through an application to forecast a nonstationary hydroclimatic time series using relevant climate index information. The target is the time series of the volume of Devil's Lake, located in North Dakota, USA, for which it was proved difficult to forecast and quantify the associated uncertainty by traditional methods. Two different Bayesian dynamic modelling approaches are discussed, namely, a constant model and a dynamic regression model (DRM). The constant model uses the information of past observed values of the same time series, whereas the DRM utilizes the information from a causal time series as an exogenous input. Noting that the North Atlantic Oscillation (NAO) index appears to co-vary with the time series of Devil's Lake annual volume, its use as an exogenous predictor is explored in the case study. The results of both the Bayesian dynamic models are compared with those from the traditional Box–Jenkins time series modelling approach. Although, in this particular case study, it is observed that the DRM performs marginally better than traditional models, the major strength of Bayesian dynamic models lies in the quantification of prediction uncertainty, which is of great value in hydrology, particularly under the recent climate change scenario.